2016

• T. Cardoso, M. D. Oliveira, A. Barbosa-Póvoa, and S. Nickel. Moving towards an equitable long-term care network: A multi-objective and multi-period planning approach. Omega, 58, 69 - 85, 2015.

  Abstract: This study proposes a multi-objective and multi-period mathematical programming model to support planning decisions in the Long-Term Care (LTC) sector. The model provides information to help planning the delivery of institutional LTC services in the medium-term, both in terms of location selection and capacity planning, when it is intended a move towards an equitable provision of care. For this purpose, three equity-related objectives are accounted for-equity of access, geographical equity and socioeconomic equity. Cost considerations are also taken into account. The model objective function incorporates multiple objectives which are scaled into a common unit through weights that are built with the Measuring Attractiveness by a Category-Based Evaluation Technique. The applicability of the model is illustrated through the resolution of a case study in the Great Lisbon region in Portugal. Full text.

• A. Zander and U. Mohring. Dynamic appointment scheduling with patient time preferences and different service time lengths. International Conference on Applied Operational Research, Proceedings, 8, 72 - 77, 2016.

  Abstract: Advance admission scheduling in the field of health care is an important and complex problem. Often, exact models of realistic size cannot be solved due to the curse of dimensionality and heuristics have to be used. In this paper we consider the appointment schedule of a physician's day. We assume patient types defined by different time preferences and service time lengths. Patient requests for the day are handled directly during a booking horizon. We present a mixed integer linear programming model to determine a set of appointments to offer a patient requesting an appointment. The objective is to schedule the requesting patient while also taking future demand into account. We want to maximize the overall utilization assuring a certain fairness level. We further perform a simulation in order to test the mixed integer linear program and to compare it to simpler online heuristics. We develop different scenarios and show that using the mixed integer linear program to schedule patients is beneficial.

• I. Correia, S. Nickel, and F. Saldanha-da-Gama. A modeling framework for stochastic multi-period capacitated multiple allocation hub location. ILS 2016 - 6th International Conference on Information Systems, Logistics and Supply Chain, 2016.

  Abstract: We propose a two-stage stochastic programming modeling framework for multi-period multiple allocation hub location under uncertainty. A discretized planning horizon is considered and stochasticity is assumed for the flows to be routed through the network. When uncertainty can be described by a discrete random vector with a finite support it is possible to derive the extensive form of the deterministic equivalent. However, this results in a large-scale mixed-integer linear programming model that nonetheless can be enhanced using several families of valid inequalities. Computational tests performed using benchmark data are reported and show that the new sets of valid inequalities are able to provide a good polyhedral description of the feasibility set, which is of relevance.

• I. Heckmann, S. Nickel, and F. Saldanha-da-Gama. The risk-aware multi-period capacitated plant location problem (CPLP-Risk). ILS 2016 - 6th International Conference on Information Systems, Logistics and Supply Chain, 2016.

  Abstract: Unexpected deviations and disruptions - subsumed under the notion of supply chain risk - increasingly aggravate the planning and optimization of supply chains. Over the last decade there has been a growing interest in including risk aspects for supply chain optimization models. This development has led to the adoption of risk concepts, terminologies and methods defined and applied in a broad variety of related research fields and methodologies. In [3] the core characteristics of supply chain risk have been identified. Based on contemporary research gaps identified in [3] for optimization approaches we introduce a mixed-integer two-stage stochastic programming model that extends the capacitated plant location problem and additionally offers the possibility to formalize and operationalize supply chain risk. The evaluation of the developed optimization model discloses its usefulness in terms of providing risk- Aware solutions and of approaching risk by stochastic programming.

• F. Dunke and S. Nickel. A general modeling approach to online optimization with lookahead. Omega, 63, 134 - 153, 2016.

  Abstract: A vast number of real world problems are coined by an information release over time and the related need for repetitive decision making over time. Optimization problems arising in this context are called online since decisions have to be made although not all data is known. Due to technological advances, algorithms may also resort to a limited preview (lookahead) on future events. We first embed the paradigm of online optimization with lookahead into the theory of optimization and develop a concise understanding of lookahead. We further find that the effect of lookahead can be decomposed into an informational and a processual component. Based on analogies to discrete event systems, we then formulate a generic modeling framework for online optimization with lookahead and derive a classification scheme which facilitates a thorough categorization of different lookahead concepts. After an assessment of performance measurement approaches with relevance to practical needs, we conduct a series of computational experiments which illustrate how the general concept of lookahead applies to specific instantiations and how a knowledge pool on lookahead effects in applications can be built up using the general classification scheme. Full text.

• I. Heckmann and S. Nickel. Supply chain risk analysis - Common flaws, core areas, and main tasks. ILS 2016 - 6th International Conference on Information Systems, Logistics and Supply Chain, 2016.

  Abstract: Supply chain networks are globalized and complex systems. Due to unexpected deviations and disruptions, which are subsumed under the notion of supply chain risk, the planning and optimizing of such systems is harder than ever. Therefore, making well-informed decisions requires risk analysis. In some areas such as finance, insurance, crisis management and health care, the importance of considering risk is largely acknowledged and well-elaborated, yet rather heterogeneous concepts and approaches for risk management have been developed. The increased frequency and the severe consequences of past supply chain disruptions have resulted in an increasing interest in risk. This development has led to the adoption of the risk concepts, terminologies and methods from related fields, which most often do not fit for risk consideration in the supply chain context. This paper consists of a theoretical discussion on common risk biases and main elements tailored for supply chain risk analysis.

• F. Dunke and S. Nickel. Time traps in supply chains: Is optimal still good enough? European Journal of Operational Research, article in press, 2016.

  Abstract: Operations Researchers support Supply Chain Management and Supply Chain Planning by developing adequate mathematical optimization models and providing suitable solution procedures. In this paper we discuss what adequate could mean. Therefore, we may ask several questions concerning "optimality" in Supply Chain Planning under causal and temporal uncertainty: What is an optimal solution? When is it optimal? For how long is it optimal? How should the design of a supply chain be changed when conditions and requirements ask for new structures? In particular, we discuss new approaches to Supply Chain Planning in order to give an optimal transformation from an initial solution over multiple periods to a desired one rather than just specifying an optimal snapshot solution. Time and uncertainty are the factors triggering the whole discussion. In particular, several flaws often found when dealing with these factors result in so-called "time traps". We look at the impact of recent technological developments like the Internet of Things or Industry 4.0 on operational supply chain planning and control, and we show how online optimization can help to cope with real-time challenges. Moreover, we re-coin the concept of risk in the realm of Supply Chain Planning. Here the question is how to measure supply chain specific risks and how to incorporate them "adequately" into mathematical models. Full text.

• S. Nickel, M. Reuter-Oppermann, and F. Saldanha-da-Gama. Ambulance location under stochastic demand: A sampling approach. Operations Research for Health Care, 8, 24 - 32, 2016.

  Abstract: In this paper, we investigate the problem of choosing the location and number of ambulances and their bases in a certain region. The goal is to minimize the total cost for installing (and maintaining) these facilities but assuring a minimum coverage level. Demand is assumed to be stochastic. A scenario-indexed formulation is considered for the problem. By using a small illustrative example we show that even when demand can be captured by a finite number of scenarios, rapidly the number of scenarios becomes too large, thus preventing the effective use of the model. We also show that the possibility of considering just one sample of scenarios can lead to a totally misleading solution. These insights motivate the development of a sampling approach in which we draw several samples of scenarios and solve the restricted model associated with each of them. The sample of optimal values obtained by this procedure can be combined in order to estimate the optimal value of the original problem. The same happens with the sample of optimal solutions obtained, which can be combined heuristically to produce a feasible solution to the whole problem. We test the new approach using a set of random instances. Full text.

• J. Wirnitzer, I. Heckmann, A. Meyer, and S. Nickel. Patient-based nurse rostering in home care. Operations Research for Health Care, 8, 91 - 102, 2016.

  Abstract: The monthly nurse rostering is one of the most time consuming planning tasks of our project partner, a leading German home care provider. The planning is currently done manually by experienced senior nurses. However, the planning setup is very complex due to requirements such as legal working time restrictions, availabilities of full and part time nurses, and patient requests with differing requirements on qualification and frequency. The objective is to assign as few different nurses as possible to each patient. Although this continuity is important for quality of care, it is hardly addressed in literature. In this paper, we elaborate a mid-term home care rostering problem (HCR) that fits the requirements of our partner. It implies the assignment of nurses to weekly recurring patient-visit-tours under consideration of the aforementioned continuity of care. We propose different measures of continuity, which are used in five novel MIP formulations, each incorporating all hard planning constraints. We evaluate the models by means of 45 generated instances with realistic features. Further experiments on a real-world instance show that the approach improves continuity of care considerably compared to the manual solution. Full text.

2015

• T. Cardoso, M. D. Oliveira, A. Barbosa-Póvoa, and S. Nickel. An integrated approach for planning a long-term care network with uncertainty, strategic policy and equity considerations. European Journal of Operational Research, 247(1), 321 - 334, 2015.

  Abstract: Considering key uncertainties and health policy options in the reorganization of a long-term care (LTC) network is crucial. This study proposes a stochastic mixed integer linear programming model for planning the delivery of LTC services within a network of care where such aspects are modeled in an integrated manner. The model assists health care planners on how to plan the delivery of the entire range of LTC services - institutional, home-based and ambulatory services - when the main policy objective is the minimization of expected costs and while respecting satisficing levels of equity. These equity levels are modeled as constraints, ensuring the attainment of equity of access, equity of utilization, socioeconomic equity and geographical equity. The proposed model provides planners with key information on: when and where to locate services and with which capacity, how to distribute this capacity across services and patient groups, and which changes to the network of care are needed over time. Model outputs take into account the uncertainty surrounding LTC demand, and consider strategic health policy options adopted by governments. The applicability of the model is demonstrated through the resolution of a case study in the Great Lisbon region in Portugal with estimates on the equity-cost trade-off for several equity dimensions being provided. Full text.

• T. Cardoso, M. D. Oliveira, A. Barbosa-Póvoa, and S. Nickel. Introducing health gains in location-allocation models: A stochastic model for planning the delivery of long-term care. Journal of Physics: Conference Series, 616(1), 012007, 2015.

  Abstract: Although the maximization of health is a key objective in health care systems, location-allocation literature has not yet considered this dimension. This study proposes a multi-objective stochastic mathematical programming approach to support the planning of a multi-service network of long-term care (LTC), both in terms of services location and capacity planning. This approach is based on a mixed integer linear programming model with two objectives - the maximization of expected health gains and the minimization of expected costs - with satisficing levels in several dimensions of equity - namely, equity of access, equity of utilization, socioeconomic equity and geographical equity - being imposed as constraints. The augmented ε-constraint method is used to explore the trade-off between these conflicting objectives, with uncertainty in the demand and delivery of care being accounted for. The model is applied to analyze the (re)organization of the LTC network currently operating in the Great Lisbon region in Portugal for the 2014-2016 period. Results show that extending the network of LTC is a cost-effective investment. Full text.

• J. Kalcsics, S. Nickel, J. Puerto, and A.M. Rodríguez-Chía. Several 2-facility location problems on networks with equity objectives. Networks, 65(1), 1 - 9, 2015.

  Abstract: We consider 2-facility location problems with equity measures, defined on networks. The models discussed are, the variance, the mean of absolute weighted deviations, the maximum weighted absolute deviation, the sum of absolute weighted differences, and the range. We give new algorithmic results for these models in the 2-facility case. Full text.

• J. Grzybowski, J. Kalcsics, S. Nickel, D. Pallaschke, and R. Urbański. On max–min representations of ordered median functions. Optimization, 64(2), 339 - 348, 2015.

  Abstract: An ordered median function is a continuous piecewise linear function. It is well known, that in finite dimensional spaces every continuous piecewise linear function admits a max–min representation in terms of its linear functions. We give an explicit representation of an ordered median function in max–min form using a purely combinatorial approach. Full text.

• H. Sahebi, S. Nickel, J. Ashayeri. Joint venture formation and partner selection in upstream crude oil section: Goal programming application. International Journal of Production Research, 53(10), 3047 - 3061, 2015.

  Abstract: In the past three decades, the magnitude of business dynamics has increased rapidly due to increased complexity, uncertainty and risk of international projects. This fact made it increasingly tough to go alone into the international projects. As a consequence, companies with diverse strengths and weaknesses cooperatively bid for joint ventures (JV) formation. Joint venture is also a well-established aspect of the crude oil industry, specifically in the upstream segment. Making decision on the optimal form of JVs is still a challenging problem. In addition, the success of a JV is intertwined with the accuracy of the partner selection phase. Therefore, this paper formulates a multi-criteria mathematical model to select the best partners and form an optimal JV for undertaking oilfield projects. The lexicographic goal programming technique is employed to minimise undesirable deviations from diverse goals such as resources needs (technological and expertise), budgetary requirements, time, etc. The model is validated with a real-life-based example and provides insightful views on alternative formats of cooperation. Full text.

• J. Grzybowski, J. Kalcsics, S. Nickel, D. Pallaschke, and R. Urbański. On topological types of ordered median functions. Optimization, 64(1), 149 - 160, 2015.

  Abstract: An ordered median functions is a continuous piecewise-linear function. It is well known that in finite dimensional spaces every continuous piecewise-linear function admits a max-min representation in terms of its linear functions. An explicit representation of an ordered median function in max-min form is given by the authors and will appear in a forthcoming issue of this journal. Based on this representation, we give a topological classification of ordered median functions through their simplicial complex of ascent (resp. descent) cones. Full text.

• S.A. Alumur, S. Nickel, F. Saldanha-da-Gama, Y. Seçerdin. Multi-period hub network design problems with modular capacities. Annals of Operations Research, 2015.

  Abstract: In this paper, a modeling framework is proposed for multi-period hub location. The problems to be studied are extensions of classical hub location problems to the situation in which the hub network can be progressively built and its capacity gradually expanded over time. Both the single allocation and the multiple allocation cases are considered. For each case, a mixed-integer linear programming formulation is proposed and a set of valid inequalities is derived for enhancing the corresponding model. The results of a set of computational tests performed using the formulations proposed and their enhancements are reported. The value of the multi-period solution is discussed as a measure for evaluating the relevance of considering a multi-period model instead of a static counterpart. Full text.

• S. Gelareh, R. Neamatian Monemi, and S.Nickel. Multi-period hub location problems in transportation. Transportation Research Part E: Logistics and Transportation Review, 75, 67 - 94, 2015.

  Abstract: Many transport service providers operate on hub-and-spoke network structures. Major operators may have several dedicated hub facilities that are leased for a time horizon rather than being owned or constructed. For a given discrete planning horizon, service providers must decide on the location of the hub ports (i.e. terminals), the period when the lease contract starts, the period when the existing contracts must be terminated and the flow routing over the entire planning horizon so as to minimize the total operational cost. Thus, we propose a mathematical model for a Multi-period Uncapacitated Multiple Allocation Hub Location Problem with Budget Constraint. The proposed model incorporates several features of practice, particularly from maritime and land transport practices. We also propose a meta-heuristic solution algorithm that produces high-quality solutions in a reasonable amount of time. By exploiting the decomposable structure of the model, we extended a Benders decomposition approach by proposing several improvements. Extensive computational experiments confirm the efficiency of the proposed methods and also show its limitations. Full text.

• I. Heckmann, T. Comes, and S. Nickel. A critical review on supply chain risk - Definition, measure and modeling. Omega, 52, 119 - 132, 2015.

  Abstract: Economic systems are increasingly prone to complexity and uncertainty. Therefore, making well-informed decisions requires risk analysis, control and mitigation. In some areas such as finance, insurance, crisis management and health care, the importance of considering risk is largely acknowledged and well-elaborated, yet rather heterogeneous concepts and approaches for risk management have been developed. The increased frequency and the severe consequences of past supply chain disruptions have resulted in an increasing interest in risk. This development has led to the adoption of the risk concepts, terminologies and methods from related fields. In this paper, existing approaches for quantitative supply chain risk management are reviewed by setting the focus on the definition of supply chain risk and related concepts. Full text.

• C. Messer, A. Zander, I. Arnolds, S. Nickel, and M. Schuster. How many patient transfer rooms are necessary for my OR suite?: Effect of the number of OR transfer rooms on waiting times and patient throughput in the OR – analysis by simulation [Wie viele Patientenschleusen braucht mein OP-Bereich?: Einfluss der Zahl von OP-Schleusen auf Wartezeiten und Patientendurchsatz im OP – Analyse mithilfe einer Simulation]. Anaesthesist, 64(12), 958 - 967, 2015.

  Abstract: Introduction. In most hospitals the operating rooms (OR) are separated from the rest of the hospital by transfer rooms where patients have to pass through for reasons of hygiene. In the OR transfer room patients are placed on the OR table before surgery and returned to the hospital bed after surgery. It could happen that the number of patients who need to pass through a transfer room at a certain point in time exceed the number of available transfer rooms. As a result the transfer rooms become a bottleneck where patients have to wait and which, in turn, may lead to delays in the OR suite. In this study the ability of a discrete event simulation to analyze the effect of the duration of surgery and the number of ORs on the number of OR transfer rooms needed was investigated. Methods. This study was based on a discrete event simulation model developed with the simulation software AnyLogic®. The model studied the effects of the number of OR transfer rooms on the processes in an OR suite of a community hospital by varying the number of ORs from one to eight and using different surgical portfolios. Probability distributions for the process duration of induction, surgery and recovery and transfer room processes were calculated on the basis of real data from the community hospital studied. Furthermore, using a generic simulation model the effect of the average duration of surgery on the number of OR transfer rooms needed was examined. Results. The discrete event simulation model enabled the analysis of both quantitative as well as qualitative changes in the OR process and setting. Key performance indicators of the simulation model were patient throughput per day, the probability of waiting and duration of waiting time in front of OR transfer rooms. In the case of a community hospital with 1 transfer room the average proportion of patients waiting before entering the OR was 17.9 % ± 9.7 % with 3 ORs, 37.6 % ± 9.7 % with 5 ORs and 62.9 % ± 9.1 % with 8 ORs. The average waiting time of patients in the setting with 3 ORs was 3.1 ± 2.7 min, with 5 ORs 5.0 ± 5.8 min and with 8 ORs 11.5 ± 12.5 min. Based on this study the community hospital needs a second transfer room starting from 4 ORs so that there is no bottleneck for the subsequent OR processes. The average patient throughput in a setting with 4 ORs increased significantly by 0.3 patients per day when a second transfer room is available. The generic model showed a strong effect of the average duration of surgery on the number of transfer rooms needed. Conclusion. There was no linear correlation between the number of transfer rooms and the number of ORs. The shorter the average duration of surgery, the earlier an additional transfer room is required. Thus, hospitals with shorter duration of surgery and fewer ORs may need the same or more transfer rooms than a hospital with longer duration of surgery and more ORs. However, with respect to an economic analysis, the costs and benefits of installing additional OR transfer rooms need to be calculated using the profit margins of the specific hospital. Full text.

• M. Reuter-Oppermann and A. Zander. Service Optimization. Fundamentals of Service Systems, In: Cardoso, J.; Fromm, H.; Studer, R.; Nickel, S.; Weinhardt, C.; Satzger, G. (eds.), 217 - 260, 2015.

  Abstract: This textbook addresses the conceptual and practical aspects of the various phases of the lifecycle of service systems, ranging from service ideation, design, implementation, analysis, improvement and trading associated with service systems engineering. Written by leading experts in the field, this indispensable textbook will enable a new wave of future professionals to think in a service-focused way with the right balance of competencies in computer science, engineering, and management. Fundamentals of Service Systems is a centerpiece for a course syllabus on service systems. Each chapter includes a summary, a list of learning objectives, an opening case, and a review section with questions, a project description, a list of key terms, and a list of further reading bibliography. All these elements enable students to learn at a faster and more comfortable peace. For researchers, teachers, and students who want to learn about this new emerging science, Fundamentals of Service Systems provides an overview of the core disciplines underlying the study of service systems. It is aimed at students of information systems, information technology, and business and economics. It also targets business and IT practitioners, especially those who are looking for better ways of innovating, designing, modeling, analyzing, and optimizing service systems. Full text.

2014

• A. Butsch, J. Kalcsics, and G. Laporte. Districting for arc routing. Informs Journal on Computing, 26(4), 809 - 824, 2014.

  Abstract: This paper proposes a heuristic for districting problems arising in an arc routing context. The aim is to design districts by amalgamating edges of a graph as opposed to cells. Solutions must satisfy two hard criteria (complete and exclusive assignment as well as connectedness) and several soft criteria (balance, small deadheading, local compactness, and global compactness). The latter criteria are amalgamated into a weighted objective. The proposed heuristic applies a construction procedure followed by a tabu search improvement phase in which several subroutines are defined and selected according to a roulette wheel mechanism, as in adaptive large neighborhood search. Extensive tests conducted on instances derived from real-world street data confirm the efficiency of the proposed methodology. Full text.

• H. Sahebi and S. Nickel. Offshore oil network design with transportation alternatives. European Journal of Industrial Engineering, 8(6), 739 - 761, 2014.

  Abstract: Petroleum industry plays a vital role in the modern global economy, owing to the fact that it is the largest source of energy in the world. Design and planning of the oilfield developments have become crucial concerns of the oil industry managers. In addition, crude oil transportation plays a critical role in the global supply chain of oil industry. In this work, we develop a model to design the oilfield development and plan crude oil transportation problems. A mixed integer model is proposed to extend the classical facility location-allocation problems by several features. Additionally, the model supports the selection of the transportation system and the planning of pipeline networks installations. This work ends with two sensitivity analyses. Two one-factor-at-a-time sensitivity analyses have been done with respect to the length of the planning horizon and the number of potential wells. Full text.

• I. Averbakh, O. Berman, D. Krass, J. Kalcsics, and S. Nickel. Cooperative covering problems on networks. Networks, 63(4), 334 - 349, 2014.

  Abstract: In this article, we consider the cooperative maximum covering location problem on a network. In this model, it is assumed that each facility emits a certain "signal" whose strength decays over distance according to some "signal strength function." A demand point is covered if the total signal transmitted from all the facilities exceeds a predefined threshold. The problem is to locate facilities so as to maximize the total demand covered. For the 2-facility problem, we present efficient polynomial algorithms for the cases of linear and piecewise linear signal strength functions. For the p-facility problem, we develop a finite dominant set, a mixed-integer programming formulation that can be used for small instances, and two heuristics that can be used for large instances. The heuristics use the exact algorithm for the 2-facility case. We report results of computational experiments Full text.

• I. Correia, S. Nickel, and F. Saldanha-da-Gama. Multi-product Capacitated Single-Allocation Hub Location Problems: Formulations and Inequalities. Networks and Spatial Economics, 14(1), 1 - 25, 2014.

  Abstract: In this paper we extend the classical capacitated single-allocation hub location problem by considering that multiple products are to be shipped through the network. We propose a unified modeling framework for the situation in which no more than one hub can be located in each node. In particular, we consider the case in which all hubs are dedicated to handling a single-product as well as the case in which all hubs can handle all products. The objective is to minimize the total cost, which includes setup costs for the hubs, setup costs for each product in each hub and flow routing costs. Hubs are assumed to be capacitated. For this problem several models are proposed which are based on existing formulations for the (single-product) capacitated single-allocation hub location problem. Additionally, several classes of inequalities are proposed in order to strengthen the models in terms of the lower bound provided by the linear relaxation. We report results of a set of computational experiments conducted to test the proposed models and their enhancements Full text.

• M.T. Melo, S. Nickel, and F. Saldanha-da-Gama. An efficient heuristic approach for a multi-period logistics network redesign problem. TOP, 22(1), 80 - 108, 2014.

  Abstract: In this paper, a multi-period logistics network redesign problem arising in the context of strategic supply chain planning is studied. Several aspects of practical relevance are captured, namely, multiple echelons with different types of facilities, product flows between facilities in the same echelon, direct shipments to customers, and facility relocation. A two-phase heuristic approach is proposed to obtain high-quality feasible solutions to the problem, which is initially modeled as a large-scale mixed-integer linear program. In the first phase of the heuristic, a linear programming rounding strategy is applied to find initial values for the binary location variables. The second phase of the heuristic uses local search to correct the initial variable choices when a feasible solution is not identified, or to improve the initial feasible solution when its quality does not meet given criteria. The results of a computational study are reported for randomly generated instances comprising a variety of logistics networks. Full text.

• J. Kalcsics, S. Nickel, M.A. Pozo, J. Puerto, and A.M. Rodríguez-Chía. The multicriteria p-facility median location problem on networks. European Journal of Operational Research, 235(3), 484 - 493, 2014.

  Abstract: In this paper we discuss the multicriteria p-facility median location problem on networks with positive and negative weights. We assume that the demand is located at the nodes and can be different for each criterion under consideration. The goal is to obtain the set of Pareto-optimal locations in the graph and the corresponding set of non-dominated objective values. To that end, we first characterize the linearity domains of the distance functions on the graph and compute the image of each linearity domain in the objective space. The lower envelope of a transformation of all these images then gives us the set of all non-dominated points in the objective space and its preimage corresponds to the set of all Pareto-optimal solutions on the graph. For the bicriteria 2-facility case we present a low order polynomial time algorithm. Also for the general case we propose an efficient algorithm, which is polynomial if the number of facilities and criteria is fixed. Full text.

• H. Sahebi, S. Nickel, and J. Ashayeri. Environmentally conscious design of upstream crude oil supply chain. Industrial and Engineering Chemistry Research, 53(28), 11501 - 11511, 2014.

  Abstract: In the past few decades, very rapid growth in environmental legislation has resulted in an increasing will of companies to address environmental thinking through their supply chain. In this context, great strides have been made to incorporate the environmental concerns, such as "green" and "sustainable" supply chains, along with the traditional economic indicators. To assess the environmental impacts, there is no agreement on a universal environmental metric. Hence, a plethora of indicators has been developed to measure environmental impacts. The environmental indicators (e.g., Eco-indicator 99) that are founded on the Life Cycle Assessment (LCA) framework and nowadays are becoming among the popular environmental assessment methodologies. The crude oil tankers and utilities consumptions are the main origins of emissions through the crude oil supply chain. The energy required for operating upstream facilities in the crude oil supply chain represents enormous energy consumption. Whereas, ships and oil tankers are of the highest polluting combustion origins, per unit of fuel used. As a result, environmentally conscious design of upstream crude oil supply chain has created intriguing new challenges for practitioners and the managers. In this work, we introduce an environmentally conscious mathematical model to design the Upstream Oil Supply Chain (i.e., oil field development, and crude oil transportation). The model configure the supply network, select the technologies, establish the pipeline network, and plan the oil tankers with optimizing the economic objective value (i.e., the net present value) and the environmental metric value (i.e., the standard Eco-indicator 99 value). Full text.

• H. Sahebi, S. Nickel, and J. Ashayeri. Strategic and tactical mathematical programming models within the crude oil supply chain context: A review. Computers and Chemical Engineering, 68, 56 - 77, 2014.

  Abstract: In today's business world, oil companies cannot be productive and competitive, and thus, will not survive without taking the supply chain management concepts into account. Consequently, the management of a crude oil supply chain (COSC) is increasingly receiving substantial importance. The growing number of papers and books on this topic is a further witness of this fact. To foster insight into issues intertwined with COSC problems, this paper is devoted to an extensive review of mathematical programming models in this context. The classification approach for this review is based on a taxonomy framework. In this framework, ongoing and emerging challenges surrounding the strategic and tactical decisions of COSC problems are investigated. As a main goal, the gaps of literature are analyzed to recommend possible research directions. Full text.

2013

• I. V. Arnolds and S. Nickel. Multi-period layout planning for hospital wards. Socio-Economic Planning Sciences, 47(3), 220 - 237, 2013.

  Abstract: Layout planning for hospitals is a long-term decision. Nevertheless, medical and organizational factors change over time. For example, demand for different- sized bed rooms varies based on medical requirements and patient preferences. In this paper, we consider the planning of ward layouts over multiple periods using different approaches. The fixed ward layout models aim at minimizing either the number of demand violations or costs for installing fixed patient rooms. In contrast, the variable ward layout model allows for layout adaptations to satisfy demand. Thus, additional costs for the movement of walls have to be considered. The application of the different approaches as a decision support tool for hospital planners is explained. Hence, it can be derived in which settings the costs for adapting a layout do not exceed the benefits of such a change. Computational experiments demonstrate the applicability of the models for realistic instances. Full text.

• I. Correia, S. Nickel, and F. Saldanha-da Gama. Multi-product capacitated single-allocation hub location problems: Formulations and inequalities. Networks and Spatial Economics, 1-25, 2013.

  Abstract: In this paper we extend the classical capacitated single-allocation hub location problem by considering that multiple products are to be shipped through the network. We propose a unified modeling framework for the situation in which no more than one hub can be located in each node. In particular, we consider the case in which all hubs are dedicated to handling a single-product as well as the case in which all hubs can handle all products. The objective is to minimize the total cost, which includes setup costs for the hubs, setup costs for each product in each hub and flow routing costs. Hubs are assumed to be capacitated. For this problem several models are proposed which are based on existing formulations for the (single-product) capacitated single-allocation hub location problem. Additionally, several classes of inequalities are proposed in order to strengthen the models in terms of the lower bound provided by the linear relaxation. We report results of a set of computational experiments conducted to test the proposed models and their enhancements. Full text.

• E. Fernández, J. Kalcsics, and S. Nickel. The maximum dispersion problem. Omega, 41(4), 721 - 730, 2013.

  Abstract: In the maximum dispersion problem, a given set of objects has to be partitioned into a number of groups. Each object has a non-negative weight and each group has a target weight, which may be different for each group. In addition to meeting the target weight of each group, all objects assigned to the same group should be as dispersed as possible with respect to some distance measure between pairs of objects. Potential applications for this problem come from such diverse fields as the problem of creating study groups or the design of waste collection systems. We develop and compare two different (mixed-) integer linear programming formulations for the problem. We also study a specific relaxation that enables us to derive tight bounds that improve the effectiveness of the formulations. Thereby, we obtain an upper bound by finding in an auxiliary graph subsets of given size with minimal diameter. A lower bound is derived based on the relation of the optimal solution of the relaxation to the chromatic number of a series of auxiliary graphs. Finally, we propose an exact solution scheme for the maximum dispersion problem and present extensive computational experiments to assess its efficiency. Full text.

• M. Reuter, A. Rashid, and S. Nickel. Modellierung und Planung von Dienstleistungen im Rettungswesen mit Verfahren des Operations Research. In: O. Thomas and M. Nüttgens (editors), Dienstleistungsmodellierung 2012, 291-304. Springer Fachmedien Wiesbaden, 2013.

  Zusammenfassung: Dieser Beitrag stellt sich der Frage, wie Verfahren des Operations Research (OR) in der Dienstleistungsforschung bzw. Dienstleistungsmodellierung im Rettungswesen eingesetzt werden können. Hierfür wird exemplarisch anhand der Rettungsleitstelle demonstriert, dass bisherige Verfahren nicht zufriedenstellend sind und wie OR-Verfahren in die Modellierung und Planung der Dienstleistungen integriert werden können. Als Beispiele werden Verfahren zur Standortplanung und Tourenplanung in Rettungsleitstellen aufgeführt. Dabei zeigt sich auch, dass als Werkzeugunterstützung Geografische Informationssysteme (GIS) geeignet sind. Full text.

• J. Grzybowski, J. Kalcsics, S. Nickel, D. Pallaschke, and R. Urbanski. On max-min representations of ordered median functions. Optimization, 2013. Article in Press.

  Abstract: An ordered median function is a continuous piecewise linear function. It is well known, that in finite dimensional spaces every continuous piecewise linear function admits a max-min representation in terms of its linear functions. We give an explicit representation of an ordered median function in max-min form using a purely combinatorial approach. Full text.

2012

• M. Albareda-Sambola, E. Fernández, and S. Nickel. Multiperiod location-routing with decoupled time scales. European Journal of Operational Research, 217(2), 248 - 258, 2012.

  Abstract: This paper focuses on a multiperiod discrete facility location problem where transportation costs are considered together with location costs to design the operating facility pattern along a time horizon. The problem captures the difference in the scope of the location and routing decisions by considering different scales within the time horizon. Thus, solutions to this problem reflect the stability of locational decisions along time. The high complexity of this problem makes it impossible to be solved in practice with commercial software. For this reason, an approximation based on replacing vehicle routes by spanning trees is proposed, and its capability for providing good quality solutions is assessed in a series of computational experiments. Full text.

• S. A. Alumur, S. Nickel, and F. S. da Gama. Hub location under uncertainty. Transportation Research Part B: Methodological, 46(4), 529 - 543, 2012.

  Abstract: Hub location problems are network design problems which are solved as part of a strategic decision making process. In strategic planning, decisions may have a long lasting effect and the implementation may take considerable time. Moreover, input data is not precisely known in advance. Hence, decisions have to be made anticipating uncertainty. In this paper, we address several aspects concerning hub location problems under uncertainty. Two sources of uncertainty are considered: the set-up costs for the hubs and the demands to be transported between the nodes. Generic models are presented for single and multiple allocation versions of the problems. Firstly, the two sources of uncertainty are analyzed separately and afterwards a more comprehensive model is proposed considering all sources of uncertainty. Using a set of computational tests performed, we analyze the changes in the solutions driven by the different sources of uncertainty considered isolated and combined. Full text.

• S. A. Alumur, S. Nickel, F. S. da Gama, and V. Verter. Multi-period reverse logistics network design. European Journal of Operational Research, 220(1), 67 - 78, 2012.

  Abstract: The configuration of the reverse logistics network is a complex problem comprising the determination of the optimal sites and capacities of collection centers, inspection centers, remanufacturing facilities, and/or recycling plants. In this paper, we propose a profit maximization modeling framework for reverse logistics network design problems. We present a mixed-integer linear programming formulation that is flexible to incorporate most of the reverse network structures plausible in practice. In order to consider the possibility of making future adjustments in the network configuration to allow gradual changes in the network structure and in the capacities of the facilities, we consider a multi-period setting. We propose a multi-commodity formulation and use a reverse bill of materials in order to capture component commonality among different products and to have the flexibility to incorporate all plausible means in tackling product returns. The proposed general framework is justified by a case study in the context of reverse logistics network design for washing machines and tumble dryers in Germany. We conduct extensive parametric and scenario analysis to illustrate the potential benefits of using a dynamic model as opposed to its static counterpart, and also to derive a number of managerial insights. Full text.

• T. Cardoso, M. Oliveira, A. Barbosa-Póvoa, and S. Nickel. Modeling the demand for long-term care services under uncertain information. Health Care Management Science, 15(4), 385-412, 2012.

  Abstract: Developing a network of long-term care (LTC) services is currently a health policy priority in many countries, in particular in countries with a health system based on a National Health Service (NHS) structure. Developing such a network requires proper planning and basic information on future demand and utilization of LTC services. Unfortunately, this information is often not available and the development of methods to properly predict demand is therefore essential. The current study proposes a simulation model based on a Markov cycle tree structure to predict annual demand for LTC services so as to inform the planning of these services at the small-area level in the coming years. The simulation model is multiservice, as it allows for predicting the annual number of individuals in need of each type of LTC service (formal and informal home-based, ambulatory and institutional services), the resources/services that are required to satisfy those needs (informal caregivers, domiciliary visits, consultations and beds) and the associated costs. The model developed was validated using past data and key international figures and applied to Portugal at the Lisbon borough level for the 2010–2015 period. Given data imperfections and uncertainties related to predicting future LTC demand, uncertainty was modeled through an integrated approach that combines scenario analysis with probabilistic sensitivity analysis using Monte Carlo simulation. Results show that the model provides information critical for informing the planning and financing of LTC networks. Full text.

• Z. Drezner, S. Nickel, and H.-P. Ziegler. Stochastic analysis of ordered median problems. Journal of the Operational Research Society, 63(11), 1578-1588, 2012.

  Abstract: Many location problems can be expressed as ordered median objective. In this paper, we investigate the ordered median objective when the demand points are generated in a circle. We find the mean and variance of the kth distance from the centre of the circle and the correlation matrix between all pairs of ordered distances. By applying these values, we calculate the mean and variance of any ordered median objective and the correlation coefficient between two ordered median objectives. The usefulness of the results is demonstrated by calculating various probabilities such as: What is the probability that the mean distance is greater than the truncated mean distance? What is the probability that the maximum distance is greater than 0.9? What is the probability that the range of distances is greater than 0.8? An analysis of an illustrative example also demonstrates the usefulness of the analysis. Full text.

• M. Melo, S. Nickel, and F. S. da Gama. A tabu search heuristic for redesigning a multi-echelon supply chain network over a planning horizon. International Journal of Production Economics, 136(1), 218 - 230, 2012.

  Abstract: This paper addresses the problem of redesigning a supply chain network with multiple echelons and commodities. The problem belongs to a comprehensive class of network redesign problems previously introduced in the literature. Redesign decisions comprise the relocation of existing facilities to new sites under an available budget over a finite time horizon, the supply of commodities by upstream facilities, the inventory levels at storage facilities, and the flow of commodities through the network. The problem is modeled as a large-scale mixed-integer linear program. Feasible solutions are obtained by using a tabu search procedure that explores the space of the facility location variables. The latter prescribe the time periods in which changes in the network configuration occur. They are triggered by the setup of new facilities, which operate with capacity transferred from the existing facilities, and by closing the latter upon their entire relocation. As the problem is highly constrained, infeasible solutions with excess budget are allowed during the course of the search process. However, such solutions are penalized for their infeasibility. Computational experiments on realistically sized randomly generated instances indicate that this strategic oscillation scheme used in conjunction with tabu search performs very well. Full text.

• E. Ebermann and S. Nickel. Scheduling steel plates on a roller furnace. In: D. Klatte, H.-J. Lüthi, and K. Schmedders (editors), Operations Research Proceedings 2011, Operations Research Proceedings, 389-394. Springer Berlin, 2012.

  Abstract: We introduce a single machine scheduling problem arising in the heat treatment of steel plates. To the best of our knowledge, there is no study on this problem in the literature up to now. We refer to this problem as the Heat Treatment Furnace Scheduling Problem with Distance Constraints (HTFSPD) and propose a mixed integer linear program (MILP) formulation. Since the problem itself is NPhard and computational times for real world instances are too high, a genetic algorithm is developed in order to provide heuristic solutions. Computational results for some real data sets1 demonstrate the performance of the algorithm compared to the current solution method used in practice. Full text.

• S. Nickel, F. S. da Gama, and H.-P. Ziegler. A multi-stage stochastic supply network design problem with financial decisions and risk management. Omega, 40(5), 511 - 524, 2012.

  Abstract: In this paper, a multi-period supply chain network design problem is addressed. Several aspects of practical relevance are considered such as those related with the financial decisions that must be accounted for by a company managing a supply chain. The decisions to be made comprise the location of the facilities, the flow of commodities and the investments to make in alternative activities to those directly related with the supply chain design. Uncertainty is assumed for demand and interest rates, which is described by a set of scenarios. Therefore, for the entire planning horizon, a tree of scenarios is built. A target is set for the return on investment and the risk of falling below it is measured and accounted for. The service level is also measured and included in the objective function. The problem is formulated as a multi-stage stochastic mixed-integer linear programming problem. The goal is to maximize the total financial benefit. An alternative formulation which is based upon the paths in the scenario tree is also proposed. A methodology for measuring the value of the stochastic solution in this problem is discussed. Computational tests using randomly generated data are presented showing that the stochastic approach is worth considering in these types of problems. Full text.

• S. Nickel, M. Schröder, and J. Steeg. Mid-term and short-term planning support for home health care services. European Journal of Operational Research, 219(3), 574 - 587, 2012.

  Abstract: In this paper we are looking at routing and scheduling problems arising in the context of home health care services. Many small companies are working in this sector in Germany and planning is still done manually, resulting in long planning times and relatively inflexible solutions. First, we consider the home health care problem (HHCP) which seeks for a weekly optimal plan. However, in practice a master schedule is generated which is modified to incorporate operational changes. We take this approach into account by looking at the master schedule problem (MSP) and at the operational planning problem (OPP). The problems are solved using different metaheuristics combined with methods from constraint programming. This allows a very flexible treatment of realistic constraints. Computational results are presented using real world data. Full text.

2011

• I. Correia, S. Nickel, and F. S. da Gama. Hub and spoke network design with single-assignment, capacity decisions and balancing requirements. Applied Mathematical Modelling, 35(10), 4841 - 4851, 2011.

  Abstract: In this paper, an extension of the capacitated single-allocation hub location problem is considered in which the capacity of the hubs is part of the decision making process and balancing requirements are imposed on the network. The decisions to be made comprise (i) the selection of the hubs, (ii) the allocation of the spoke nodes to the hubs, (iii) the flow distribution through the sub network defined by the hubs and (iv) the capacity level at which each hub should operate. In the latter case, for each potential hub, a set of available capacities is considered among which one can be chosen. The objective is to minimize the total cost, which includes the setup cost for the hubs as well as the flow routing cost. Economies of scale are assumed for the costs. Balancing requirements are imposed to the network. In particular, a value is considered for the maximum difference between the maximum and minimum number of spoke nodes that are allocated to the hubs. Two mixed-integer linear programming formulations are proposed and analyzed for this problem. The results of a set of computational experiments using an off-the-shelf commercial solver are presented. These tests aim at evaluate the possibility of solving the problem to optimality using such a solver with a particular emphasis to the impact of the balancing requirements. The tests also allow an analysis of the gap of the bounds provided by linear relaxation. Full text.

• S. Gelareh and S. Nickel. Hub location problems in transportation networks. Transportation Research Part E: Logistics and Transportation Review, 47(6), 1092 - 1111, 2011.

  Abstract: In this paper we propose a 4-index formulation for the uncapacitated multiple allocation hub location problem tailored for urban transport and liner shipping network design. This formulation is very tight and most of the tractable instances for MIP solvers are optimally solvable at the root node. While the existing state-of-the-art MIP solvers fail to solve even small size instances of problem, our accelerated and efficient primal (Benders) decomposition solves larger ones. In addition, a very efficient greedy heuristic, proven to be capable of obtaining high quality solutions, is proposed. We also introduce fixed cost values for Australian Post (AP) dataset. Full text.

• J. Grzybowski, S. Nickel, D. Pallaschke, and R. Urbanski. Ordered median functions and symmetries. Optimization, 60(7), 801-811, 2011.

  Abstract: In this article, we study symmetry properties of ordered median functions (S. Nickel and J. Puerto, Location Theory – A Unified Approach, Springer-Verlag, Berlin, Heidelberg, 2005). In particular, we prove that every ordered median function is a DCH-function (V.F. Demyanov and A.M. Rubinov, Quasidifferential Calculus, Optimization Software Inc., Publications Division, New York, 1986; D. Pallaschke and R. Urbanski, Pairs of Compact Convex Sets – Fractional Arithmetic with Convex Sets, Mathematics and its Applications, Vol. 548, Kluwer Academic Publishers, Dordrecht, 2002), i.e. can be represented as a difference of two sublinear functions. Moreover, we give a necessary and sufficient condition for an ordered median function to be convex. Full text.

• C. Heib and S. Nickel. Performancevergleich zwischen simulationsbasierter Online- und Offline-Optimierung anhand von Scheduling-Problemen. In: L. März, W. Krug, O. Rose, and G. Weigert (editors), Simulation und Optimierung in Produktion und Logistik, VDI-Buch, 205-214. Springer Berlin, 2011.

  Zusammenfassung: Die Bosch-Gruppe ist ein international führendes Technologie- und Dienstleistungsunternehmen. Mit Kraftfahrzeug- und Industrietechnik sowie Gebrauchsgütern und Gebäudetechnik erwirtschafteten rund 275.000 Mitarbeiter im Geschäftsjahr 2009 einen Umsatz von 38,2 Mrd. €. Das Homburger Bosch-Werk gehört zum Geschäftsbereich Diesel Systems der Robert Bosch GmbH und produziert modernste Dieselkomponenten mittels komplexer Produktionsabläufe. Full text.

• M. Melo, S. Nickel, and F. Saldanha-da Gama. An efficient heuristic approach for a multi-period logistics network redesign problem. TOP, 1-29, 2011.

  Abstract: In this paper, a multi-period logistics network redesign problem arising in the context of strategic supply chain planning is studied. Several aspects of practical relevance are captured, namely, multiple echelons with different types of facilities, product flows between facilities in the same echelon, direct shipments to customers, and facility relocation. A two-phase heuristic approach is proposed to obtain high-quality feasible solutions to the problem, which is initially modeled as a large-scale mixed-integer linear program. In the first phase of the heuristic, a linear programming rounding strategy is applied to find initial values for the binary location variables. The second phase of the heuristic uses local search to correct the initial variable choices when a feasible solution is not identified, or to improve the initial feasible solution when its quality does not meet given criteria. The results of a computational study are reported for randomly generated instances comprising a variety of logistics networks. Full text.

• J. Schuld, T. Schäfer, S. Nickel, P. Jacob, M. K. Schilling, and S. Richter. Impact of it-supported clinical pathways on medical staff satisfaction. a prospective longitudinal cohort study. International Journal of Medical Informatics, 80(3), 151 - 156, 2011.

  Abstract: Clinical pathways (CPs) have been evaluated with regard to process optimization, economic effects, quality of care, patient satisfaction and staff satisfaction. IT- (information technology) supported CPs, integrated within the HIS (hospital information system), have been implemented in our department in 2004 for the first time world-wide. Herein, we describe the effect of this new concept on medical staff satisfaction. A prospective anonymous and voluntary survey with standardized questionnaires was performed annually from 2006 until 2009 evaluating staff satisfaction concerning CPs. Questions comprised satisfaction with the software, staff's attitude towards CPs and the impact of CPs on work-related processes. Within the observation period the term “clinical pathways” became more common among doctors and nurses. Knowledge of the aims of CPs increased significantly in nursing staff (43.4–74.5%), whereas doctor's knowledge was on a constant high level. Standardization, process facilitation and cost effectiveness were the most claimed goals of CPs. Comprehensibility of the single steps within CPs was on a constant high level over the observation period. Generally, graphical layout and usability of CPs ranged on a very high satisfaction level. Acceptability of IT-supported CPs is independent from staffs computer knowledge. Staff satisfaction with IT- supported CPs needs to take into account the job characteristics of the different professional groups. IT-supported CPs are leading to a high staff satisfaction, the aims of CPs are widely understood by medical employees. IT-supported CPs may ameliorate staff satisfaction and thereby enhance workflow efficiencies. Full text.

2010

• A. Beaudry, G. Laporte, T. Melo, and S. Nickel. Dynamic transportation of patients in hospitals. OR Spectrum, 32(1), 77-107, 2010.

  Abstract: This study analyzes and solves a patient transportation problem arising in large hospitals. The aim is to provide an efficient and timely transport service to patients between several locations in a hospital campus. Transportation requests arrive in a dynamic fashion and the solution methodology must therefore be capable of quickly inserting new requests in the current vehicle routes. Contrary to standard dial-a-ride problems, the problem under study includes several complicating constraints which are specific to a hospital context. The study provides a detailed description of the problem and proposes a two-phase heuristic procedure capable of handling its many features. In the first phase a simple insertion scheme is used to generate a feasible solution, which is improved in the second phase with a tabu search algorithm. The heuristic procedure was extensively tested on real data provided by a German hospital. Results show that the algorithm is capable of handling the dynamic aspect of the problem and of providing high-quality solutions. In particular, it succeeded in reducing waiting times for patients while using fewer vehicles. Full text.

• I. Correia, S. Nickel, and F. S. da Gama. The capacitated single-allocation hub location problem revisited: A note on a classical formulation. European Journal of Operational Research, 207(1), 92 - 96, 2010.

  Abstract: In this paper a well-known formulation for the capacitated single-allocation hub location problem is revisited. An example is presented showing that for some instances this formulation is incomplete. The reasons for the incompleteness are identified leading to the inclusion of an additional set of constraints. Computational experiments are performed showing that the new constraints also help to decrease the computational time required to solve the problem optimally. Full text.

• I. Correia, S. Nickel, and F. S. da Gama. Single-assignment hub location problems with multiple capacity levels. Transportation Research Part B: Methodological, 44(8-9), 1047 - 1066, 2010.

  Abstract: In this paper, an extension of the classical capacitated single-allocation hub location problem is studied in which the size of the hubs is part of the decision making process. For each potential hub a set of capacities is assumed to be available among which one can be chosen. Several formulations are proposed for the problem, which are compared in terms of the bound provided by the linear programming relaxation. Different sets of inequalities are proposed to enhance the models. Several preprocessing tests are also presented with the goal of reducing the size of the models for each particular instance. The results of the computational experiments performed using the proposed models are reported. Full text.

• I. Correia, S. Nickel, and F. Saldanha-Da-Gama. Single-allocation hub location problems with capacity decisions and balancing requirements. In: Proceedings of the 12th WSEAS international conference on Mathematical and computational methods in science and engineering, MACMESE'10, 51-56, Stevens Point, Wisconsin, USA, 2010. World Scientific and Engineering Academy and Society (WSEAS).

  Abstract: In this paper an extension of the capacitated single-allocation hub location problem is considered in which the capacity of the hubs is part of the decision making process and also balancing requirements are imposed to the network. The decisions to be made comprise i) the selection of the hubs, ii) the allocation of the nonhub nodes to the hubs, iii) the flow shipment through the sub network defined by the hubs and iv) the capacity level at which each hub should operate. In the latter case, for each potential hub, a set of available capacities is considered among which one can be chosen. The objective is to minimize the total cost which includes the setup cost for the hubs as well as the flow shipment cost. Economies of scale are assumed for the costs. Balancing requirements are imposed to the network. In particular, a value is considered for the maximum difference between the maximum and minimum number of spoke nodes that are allocated to the hubs. Two mixed-integer linear programming formulations are proposed for this problem. In order to evaluate the possibility of solving the problem to optimality using a commercial solver, a set of computational experiments were performed which results are reported. The experiments also include an analysis of the gap of the bounds provided by linear relaxation. Full text.

• E. Fernández, J. Kalcsics, S. Nickel, and R. Z. Ríos-Mercado. A novel maximum dispersion territory design model arising in the implementation of the WEEE-directive. Journal of the Operational Research Society, 61(3), 503-514, 2010.

  Abstract: The problem discussed in this paper is motivated by the new recycling directive Waste Electrical and Electronic Equipment of the European Commission. The core of this law is, that each company which sells electrical or electronic equipment in a European country has the obligation to recollect and recycle an amount of returned items which is proportional to its market share. To assign collection stations to companies, in Germany for one product type a territory design approach is planned. However, in contrast to classical territory design, the territories should be geographically as dispersed as possible to avoid that a company, respectively its logistics provider responsible for the recollection, gains a monopoly in some region. First, we identify an appropriate measure for the dispersion of a territory. Afterwards, we present a first mathematical programming model for this new problem as well as a solution method based on the Greedy Randomized Adaptive Search Procedure methodology. Extensive computational results illustrate the suitability of the model and assess the effectiveness of the heuristic. Full text.

• S. Gelareh, S. Nickel, and D. Pisinger. Liner shipping hub network design in a competitive environment. Transportation Research Part E: Logistics and Transportation Review, 46(6), 991 - 1004, 2010.

  Abstract: A mixed integer programming formulation is proposed for hub-and-spoke network design in a competitive environment. It addresses the competition between a newcomer liner service provider and an existing dominating operator, both operating on hub-and-spoke networks. The newcomer company maximizes its market share—which depends on the service time and transportation cost—by locating a predefined number of hubs at candidate ports and designing its network. While general-purpose solvers do not solve instances of even small size, an accelerated Lagrangian method combined with a primal heuristic obtains promising bounds. Our computational experiments on real instances of practical size indicate superiority of our approach. Full text.

• J. Kalcsics, S. Nickel, J. Puerto, and A. Rodríguez-Chía. The ordered capacitated facility location problem. TOP, 18(1), 203-222, 2010.

  Abstract: In this paper, we analyze flexible models for capacitated discrete location problems with setup costs. We introduce a major extension with regards to standard models which consists of distinguishing three different points of view of a location problem in a logistics system. We develop mathematical programming formulations for these models using discrete ordered objective functions with some new features. We report on the computational behavior of these formulations tested on a randomly generated battery of instances. Full text.

• J. Kalcsics, S. Nickel, J. Puerto, and A. M. Rodríguez-Chía. Distribution systems design with role dependent objectives. European Journal of Operational Research, 202(2), 491 - 501, 2010.

  Abstract: In this paper we introduce flexible models for capacitated discrete location problems. We describe three different points of view of a location problem in a logistics system. Different mathematical programming formulations are presented, illustrated by examples and compared using a battery of test problems. Extensive computational tests are done showing the potentials and limits of this kind of resolution approach. Full text.

• K. Kraus, S. Nickel, R. Richter, M. K. Schilling, U. A. Schmidt, and J. Schuld. Klinische Behandlungspfade - Integration logistischer Planungsaufgaben. Professional Process: Zeitschrift für modernes Prozessmanagement im Gesundheitswesen, 2(1), 12 - 15, 2010.

  Zusammenfassung: Ziel der vorliegenden Untersuchung ist, am Beispiel des am Universitätsklinikum des Saarlandes im OP-Bereich eingesetzten Pfades „Laparoskopische Cholezystektomie“ eine Prozessanalyse mit Hilfe der Netzplantechnik durchzuführen. Hierbei sollen jene Abläufe identifiziert werden, die den Operationsbeginn zeitlich so beeinflussen, dass sie zu einer Verschiebung des Operationsbeginns und zu einer Verlängerung der Verweildauer des Patienten im Krankenhaus führen. Dabei hat eine Operation genau dann Einfluss auf Pfad und Verweildauer, wenn sie nicht am geplanten Tag stattfinden kann, sondern auf einen anderen Tag verschoben werden muss. Full text.

• J. Krebs and S. Nickel. Extensions to the continuous ordered median problem. Mathematical Methods of Operations Research, 71(2), 283-306, 2010.

  Abstract: Classical location models fix an objective function and then attempt to find optimal points to this objective. In the last years a flexible approach, the ordered median problem, has been introduced. It handles a wide class of objectives, such as the median, the center and the centdian function. In this paper we present new properties of the ordered median problem such as solvability for the situation of attractive and repulsive locations. We also develop a new solution method that even yields local optimal points for non-convex objective functions. Furthermore, we discuss separability of ordered median problems without repulsion and derive a sufficient criterion. Finally, we introduce a useful model extension, the facility class model, which allows to deal with a wider range of real world problems in the ordered median setting. Full text.

• A. Marín, S. Nickel, and S. Velten. An extended covering model for flexible discrete and equity location problems. Mathematical Methods of Operations Research, 71(1), 125-163, 2010.

  Abstract: To model flexible objectives for discrete location problems, ordered median functions can be applied. These functions multiply a weight to the cost of fulfilling the demand of a customer which depends on the position of that cost relative to the costs of fulfilling the demand of the other customers. In this paper a reformulated and more compact version of a covering model for the discrete ordered median problem (DOMP) is considered. It is shown that by using this reformulation better solution times can be obtained. This is especially true for some objectives that are often employed in location theory. In addition, the covering model is extended so that ordered median functions with negative weights are feasible as well. This type of modeling weights has not been treated in the literature on the DOMP before. We show that several discrete location problems with equity objectives are particular cases of this model. As a result, a mixed-integer linear model for this type of problems is obtained for the first time. Full text.

2009

• O. Berman, J. Kalcsics, D. Krass, and S. Nickel. The ordered gradual covering location problem on a network. Discrete Applied Mathematics, 157(18), 3689 - 3707, 2009.

  Abstract: In this paper we develop a network location model that combines the characteristics of ordered median and gradual cover models resulting in the Ordered Gradual Covering Location Problem (OGCLP). The Gradual Cover Location Problem (GCLP) was specifically designed to extend the basic cover objective to capture sensitivity with respect to absolute travel distance. The Ordered Median Location problem is a generalization of most of the classical locations problems like p-median or p-center problems. The OGCLP model provides a unifying structure for the standard location models and allows us to develop objectives sensitive to both relative and absolute customer-to-facility distances. We derive Finite Dominating Sets (FDS) for the one facility case of the OGCLP. Moreover, we present efficient algorithms for determining the FDS and also discuss the conditional case where a certain number of facilities is already assumed to exist and one new facility is to be added. For the multi-facility case we are able to identify a finite set of potential facility locations a priori, which essentially converts the network location model into its discrete counterpart. For the multi-facility discrete OGCLP we discuss several Integer Programming formulations and give computational results. Full text.

• Z. Drezner and S. Nickel. Constructing a DC decomposition for ordered median problems. Journal of Global Optimization, 45(2), 187-201, 2009.

  Abstract: In this paper we show how to express ordered median problems as a difference between two convex functions (DC). Such an expression can be exploited in solving ordered median problems by using the special methodology available for DC optimization. The approach is demonstrated for solving ordered one median problems in the plane. Computational experiments demonstrated the effectiveness of the approach. Full text.

• Z. Drezner and S. Nickel. Solving the ordered one-median problem in the plane. European Journal of Operational Research, 195(1), 46 - 61, 2009.

  Abstract: In this paper, we propose a general approach solution method for the single facility ordered median problem in the plane. All types of weights (non-negative, non-positive, and mixed) are considered. The big triangle small triangle approach is used for the solution. Rigorous and heuristic algorithms are proposed and extensively tested on eight different problems with excellent results. Full text.

• H. Hamacher and S. Nickel. Multifacility and restricted location problems multifacility and restricted location problems. In: C. A. Floudas and P. M. Pardalos (editors), Encyclopedia of Optimization, 2409-2413. Springer US, 2009.

  Full text.

• T. Hanne, T. Melo, and S. Nickel. Bringing robustness to patient flow management through optimized patient transports in hospitals. Interfaces, 39(3), 241 - 255, 2009.

  Abstract: Intrahospital transports are often required for diagnostic or therapeutic reasons. Depending on the hospital layout, transportation between nursing wards and service units is either provided by ambulances or by trained personnel who accompany patients on foot. In many large German hospitals, the patient transport service is poorly managed and lacks work-flow coordination. This contributes to higher hospital costs (e.g., because a patient is not delivered to the operating room on time) and to patient inconvenience (e.g., because of long waiting times). We designed a computer-based planning system, Opti-TRANS©, that supports all phases of the transportation flow, including travel booking, dispatching transport requests, and monitoring and reporting trips in real time. The methodology, which we developed to solve the underlying optimization problem—a dynamic dial-a-ride problem with hospital-specific constraints, draws on fast heuristic methods to ensure the efficient and timely provision of transports. We illustrate the strong impact of Opti-TRANS on the daily performance of the patient transportation service of a large German hospital. The major benefits of Opti-TRANS include streamlined transportation processes and work flow, significant savings, and improved patient satisfaction. Moreover, it has contributed to increased awareness among hospital staff of the importance of implementing efficient logistics practices. Full text.

• A. Marín, S. Nickel, J. Puerto, and S. Velten. A flexible model and efficient solution strategies for discrete location problems. Discrete Applied Mathematics, 157(5), 1128 - 1145, 2009.

  Abstract: Flexible discrete location problems are a generalization of most classical discrete locations problems like p-median or p-center problems. They can be modeled by using so-called ordered median functions. These functions multiply a weight to the cost of fulfilling the demand of a customer, which depends on the position of that cost relative to the costs of fulfilling the demand of other customers. In this paper a covering type of model for the discrete ordered median problem is presented. For the solution of this model two sets of valid inequalities, which reduces the number of binary variables tremendously, and several variable fixing strategies are identified. Based on these concepts a specialized branch & cut procedure is proposed and extensive computational results are reported. Full text.

• M. Melo, S. Nickel, and F. S. da Gama. Facility location and supply chain management - a review. European Journal of Operational Research, 196(2), 401 - 412, 2009.

  Abstract: Facility location decisions play a critical role in the strategic design of supply chain networks. In this paper, a literature review of facility location models in the context of supply chain management is given. We identify basic features that such models must capture to support decision-making involved in strategic supply chain planning. In particular, the integration of location decisions with other decisions relevant to the design of a supply chain network is discussed. Furthermore, aspects related to the structure of the supply chain network, including those specific to reverse logistics, are also addressed. Significant contributions to the current state-of-the-art are surveyed taking into account numerous factors. Supply chain performance measures and optimization techniques are also reviewed. Applications of facility location models to supply chain network design ranging across various industries are presented. Finally, a list of issues requiring further research are highlighted. Full text.

• S. Nickel and F. Saldanha-da Gama. Logistics network design. OR Spectrum, 31(3), 461-463, 2009.

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• S. Nickel and U.-A. Schmidt. Process improvement in hospitals: A case study in a radiology department. Quality Management in Health Care, 18(4), 326 - 338, 2009.

  Abstract: To improve processes in hospitals, a case study was conducted at a German university hospital, which consists of more than 30 clinics and institutes on a large campus. The case study focused on the analysis of the patient flow and of machine utilization in the radiology department. Radiological devices are spread over the campus and located in different buildings. Patients with restricted mobility have to be transported by a vehicle transportation service across the campus. However, a vehicle transport can considerably influence the patients' punctual arrival to their appointments. The observations of the case study showed that the current organization of the radiology department results in high patient waiting times and machine idle times. The university hospital is planning to conduct significant organizational changes, especially with regard to the organization of the radiology department. This case study was conducted to support the planning processes of the clinic and to reveal and estimate optimization potential. To analyze the patient flow, a discrete event multicriteria simulation model was designed and implemented. By modeling different scenarios, it was possible to easily compare and assess distinct alternatives. This led to improved machine utilization and reduced waiting times. Full text.