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We describe the formulation and development of a supply-chain optimisation model for Fletcher Challenge Paper Australasia (FCPA). This model, known as Paper Industry Value Optimisation Tool (PIVOT), is a large mixed integer program that finds an optimal allocation of supplier to mill, product to paper machine, and paper machine to customer, while at the same time modelling many of the supply chain details and nuances which are peculiar to FCPA. PIVOT has assisted FCPA in solving a number of strategic and tactical decision problems, and provided significant economic benefits for the company. [ABSTRACT FROM AUTHOR]

Power distribution networks should strive for reliable delivery of energy. In this paper, we support this endeavor by addressing the Maintenance Resources Allocation Problem (MRAP). This problem consists of scheduling preventive maintenance plans on the equipment of distribution networks for a planning horizon, seeking the best trade-offs between system reliability and maintenance budgets. We propose a novel integer linear programming (ILP) formulation to effectively model and solve the MRAP for a single distribution network. The formulation also enables flexibility to suit new developments, such as different reliability metrics and smart-grid innovations. Then we develop a straightforward ILP formulation to address the MRAP for several distribution networks which takes the advantages of exchanging maintenance information between local agents and upper management. Using a general-purpose ILP solver, we performed computational experiments to assess the performance of the proposed approaches. Optimal maintenance trade-offs were achieved with the new formulations for real-scale distribution networks within short running times. To the best of our knowledge, this is the first time that the MRAP is optimally solved using ILP, for single or multiple distribution networks. [ABSTRACT FROM AUTHOR]

In most project portfolio selection (PPS) situations, the presence of multiple attributes and decision-maker preference is inevitable. As Multi-criteria Decision Analysis (MCDA) methods provide a framework well-suited to deal with these challenges in PPS problems, the use of MCDA methods in real-life PPS problems has increased in recent years. This paper provides a comprehensive literature review of the use of different MCDA methods and their individual or combined utilization with other modeling techniques to support PPS problems. First, we summarize how MCDA methods are used in different modeling approaches. Second, we examine the mathematical models that are generally used to combine MCDA with mathematical programming techniques to solve PPS problems with resource constraints. Third, we present the drawbacks of combined utilization and discuss recent advances. Finally, we visualize the summary of the reviewed papers as a decision tree to assist researchers and practitioners in the use of MCDA methods in a specific PPS context and propose some future research directions. [ABSTRACT FROM AUTHOR]

Waste management is an important issue in the field of green logistics. It has consequently drawn the attention of the scientific community and has been extensively investigated over the past few years. Through an analysis of the existing waste management literature, we attempt in this paper to better understand past developments in this area as well as emerging trends and recent developments. Emphasis will be put mainly on Operations Research and Management Science techniques when dealing with waste management problems. To reach this target, we follow bibliometric-based methods, specifically Co-citation Analysis, Betweenness Centrality and Burst Detection combined with network visualization. After identifying the research papers published between 1990 and 2018 within the Thomson Reuters Web of Science database, a Co-citation network has been constructed. We propose an algorithm for modularity-based clustering in small networks that iteratively solves a sequence of Mixed Integer Non-linear Programming problems to maximize the modularity therefore providing a non-overlapping partition of the network. A display of the principal research areas and landmark articles that shape the intellectual structure of the waste management problems during the last 30 years is reported. [ABSTRACT FROM AUTHOR]

This paper studies a framework of Reliable Capacitated Facility Location Problem with Single source constraint, which allows us to capture the mental account management problem for a bank under uncertain environment. In the problem, each facility, corresponding to a financial product, has limited capacity and may fail randomly, which represents that the product fails to reach the threshold level of return. Each customer, corresponding to a mental account, is served by a single primary facility or product, and its demands, or the setting goals, can be split on several backup facilities or alternative investments with redundant capacity. With the operation, a portion of the satisfaction can still be met by the backup facilities when the primary service of a customer fails. We formulate a mixed integer programming model for the problem and design a Lagrangian relaxation based solution algorithm, which sophisticatedly exploits the structure of the model and transfers the complicated relaxation problems into 0–1 knapsack problems to reduce the complexity. A local search procedure is also incorporated into the algorithm to enhance the accuracy of small- and large-scale computation. Finally, a real-life case of mental accounting is investigated to illustrate the application of the decision model. [ABSTRACT FROM AUTHOR]

The uncertain flow is a common factor that leads to risks in hub-and-spoke systems. Confronted with risks, it cannot be ignored that the decision maker has different risk-bearing capacities, which influence decision-making. This paper presents an α -risk appetite to characterize the risk-bearing capacity and employs the concept of belief degree to construct it. A multi-commodity capacitated p-hub median model is built with time windows, uncertain flows and the α -risk appetite objective function. In this model, the uncertain flows are depicted as uncertain variables, which possess an empirical uncertainty distribution even with little data. Uncertainty theory has the advantage in converting the proposed uncertain model into a deterministic equivalent form. While the deterministic model is still a mixed 0–1 integer programming problem and has challenges in theory and practice for addressing large-scale problems. Based on the difficulty, we design a hybrid genetic algorithm, where a new principle of cis-position assignment is proposed and inserted into this algorithm to accelerate the solving process. By comparing the proposed model with a deterministic benchmark model, the computational results demonstrate that taking the α -risk appetite and uncertainty into account could avoid the losses of neglecting risks. The observations of cost and hub location reflect the model's sensitivity about risk appetite levels. Finally, the effectiveness of the proposed algorithm is verified by two data sets, the Civil Aeronautics Board data and the Australian Post data. [ABSTRACT FROM AUTHOR]

The multi-objective integer programming problem often occurs in multi-criteria decision-making situations, where the decision variables are integers. In the present paper, we have discussed an algorithm for finding all efficient solutions of a multi-objective integer quadratic programming problem. The proposed algorithm is based on the aspect that efficient solutions of a multi-objective integer quadratic programming problem can be obtained by enumerating ranked solutions of an integer quadratic programming problem. For determining ranked solutions of an integer quadratic programming problem, we have constructed a related integer linear programming problem and from ranked solutions of this integer linear programming problem, ranked solutions of the original integer quadratic programming problem are generated. Theoretically, we have shown that the developed method generates the set of all efficient solutions in a finite number of steps, and numerically we have elaborated the working of our algorithm and compared our results with existing algorithms. Further, we have analyzed that the developed method is efficient for solving a multi-objective integer quadratic programming problem with a large number of constraints, variables and objectives. [ABSTRACT FROM AUTHOR]

In this paper, we present an integer programming formulation for the windy profitable location rural postman problem (WPLRPP). We state and prove a theorem concerning the dimension of the associated polyhedron. Then, we use this theorem to study some trivial facets of the presented polyhedron. Furthermore, we adapt and validate several large families of valid inequalities for the WPLRPP. We also develop an efficient branch-and-cut algorithm for solving large WPLRPP instances, which leverages those inequalities. We compare our presented branch-and-cut algorithm with other efficient algorithms in the literature. The numerical results show that our algorithm solves larger problem instances and requires considerably less computing time than other algorithms in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider a project-based organization that deals with an assignment problem in which a set of projects must be assigned to a group of project managers. This assignment is done based on the relative contributions of projects to the organizational mission and a matching score between each pair of a project and a project manager. We assume that some projects are deterministic, and the organization has signed their corresponding contracts while others are stochastic, i.e. the organization has submitted bids for these projects and may or may not win them in the future. Furthermore, we consider a finite planning horizon and presume a predetermined start time for each deterministic and stochastic project. We develop two models including a multi-stage stochastic integer programming model and a stochastic dynamic programming model to solve the problem. The latter shows better performance for small-size and less complex instances whereas the former gives better performance for more complex instances. We also developed a heuristic algorithm to solve large-size and more complex instances. Computational results indicate that the developed heuristic algorithm can reach near-optimal solutions in reasonable CPU run times and dominates the two other solution approaches particularly for large-size instances. [ABSTRACT FROM AUTHOR]

Pre-runtime scheduling of avionic systems is used to ensure that the systems provide the desired functionality at the correct time. This paper considers scheduling of an integrated modular avionic system which from a more general perspective can be seen as a multiprocessor scheduling problem that includes a communication network. The addressed system is practically relevant and the computational evaluations are made on large-scale instances developed together with the industrial partner Saab. A subset of the instances is made publicly available. Our contribution is a matheuristic for solving these large-scale instances and it is obtained by improving the model formulations used in a previously suggested constraint generation procedure and by including an adaptive large neighbourhood search to extend it into a matheuristic. Characteristics of our adaptive large neighbourhood search are that it is made over both discrete and continuous variables and that it needs to balance the search for feasibility and profitable objective value. The repair operation is to apply a mixed-integer programming solver on a model where most of the constraints are treated as soft and a violation of them is instead penalised in the objective function. The largest solved instance, with respect to the number of tasks, has 54,731 tasks and 2530 communication messages. [ABSTRACT FROM AUTHOR]

Optimization models typically seek to maximize overall benefit or minimize total cost. Yet fairness is an important element of many practical decisions, and it is much less obvious how to express it mathematically. We provide a critical survey of various schemes that have been proposed for formulating ethics-related criteria, including those that integrate efficiency and fairness concerns. The survey covers inequality measures, Rawlsian maximin and leximax criteria, convex combinations of fairness and efficiency, alpha fairness and proportional fairness (also known as the Nash bargaining solution), Kalai–Smorodinsky bargaining, and recently proposed utility-threshold and fairness-threshold schemes for combining utilitarian with maximin or leximax criteria. The paper also examines group parity metrics that are popular in machine learning. We present what appears to be the best practical approach to formulating each criterion in a linear, nonlinear, or mixed integer programming model. We also survey axiomatic and bargaining derivations of fairness criteria from the social choice literature while taking into account interpersonal comparability of utilities. Finally, we cite relevant philosophical and ethical literature where appropriate. [ABSTRACT FROM AUTHOR]

This paper investigates the selection of third-party logistics providers (3PLs) based on the best prices offered by them. The focus is on outbound logistics where 3PLs must have their own distribution centres for storage and picking activities. They must also have suitable trucks for distribution to different small-scale customers. The motivation for this paper is a case study from Germany in which a furniture company with hundreds of small customers in ten zones is seeking one or more 3PLs to do the distribution. A mathematical programming model was built based on integer programming where demand per order can be expressed using exponential distribution in each customer zone. The main contribution of this paper is that it finds the best 3PLs based on the different pricing methods of the various providers; this means including the location problem indirectly using the new integer programming model. The model takes into consideration three different methods of pricing based on the offers of five 3PLs. These different methods make it difficult for the decision makers to choose the best solution, especially if specific trends in demand are expected in the future for some customer zones. The results show that future increases in demand in terms of the number of orders or order size could affect the optimal solution. The best pricing method with the lowest variability in cost over time is selected. [ABSTRACT FROM AUTHOR]

Disasters may cause significant damages and long-lasting failures in lifeline infrastructure networks (such as gas, power and water), which must be recovered quickly to resume providing essential services to the affected communities. While making repair plans, it is important to consider the interdependencies among network components to minimize recovery times. In this paper, we focus on post-disaster repair operations of multiple interdependent lifeline networks, which involve functional dependencies. We assume that each network component, whether damaged or not, becomes nonfunctional if it depends on another nonfunctional component, and it is recovered when all components that it depends on become functional. We introduce a post-disaster coordinated infrastructure repair routing problem, in which dedicated repair teams of each lifeline infrastructure travel through a road network to visit the sites with damaged network components. We present a mixed integer programming model that assigns repair teams to the sites and constructs routes for each team in order to minimize the sum of the recovery times for all network components. We develop a constructive heuristic and a simulated annealing algorithm to solve the proposed coordinated routing problem. We test the performance of the proposed solution algorithms on a set of instances that are developed based on two interdependent lifeline networks (e.g., power and gas). The computational results show that our heuristics can quickly find high-quality solutions. Our results also indicate that coordinating repair operations can significantly improve the overall recovery time of interdependent infrastructure networks. [ABSTRACT FROM AUTHOR]

The usage of the Internet has grown substantially in recent times. This has resulted in high volumes of data traffic. There is a concomitant rise in bandwidth demands that could result in excessive download delays (or latency). Thus, a single-server system is no more a prudent choice for data storage. Replication of content and placing them on multiple servers is a method that is used to reduce latency. However, this solution comes at a huge cost. Moreover, replicating objects randomly does not necessarily improve system performance. It is possible to arrive at a solution to the problem of placing content so as to achieve better cost performance. Other performance measures include latency, load balancing and data availability. We refer to the problem of locating content as data location problem in information networks, or DLPIN. The choice of server locations, query routing strategy and user assignment are some of the important problems that require attention along with the location of the data/content. Resource constraints and the nature of traffic (static/dynamic) are two important parameters in the problem environment, and therefore are key distinguishing features in the models. The main contribution of this paper is a novel classification and study of DLPIN on the basis of problem features. The research in this area started with files, the smallest units of allocation. Gradually, files and programs, database segments and entire databases (or mirrors) have been studied. We design examples from these use cases to elaborate a variety of problems in a comprehensive review. Facility location models from physical logistics are extensively used to model these problems. Our paper presents a literature survey of such mathematical models for data location problems. We present a gap analysis that provides pointers to possible future research in this area. This paper also serves to document the success in the use of mathematical programming approaches for data location in information networks. [ABSTRACT FROM AUTHOR]

For daily airport operations, the insufficient number and the improper scheduling of ground support vehicles are the main causes of flight delays. In this paper, a novel network model is proposed to complement the optimal scheduling of ferry vehicles for the flight ground support service. In the process of model construction, we first innovatively construct a ferry vehicle capacity network by having the introduced virtual flights and the ferry vehicle depot as nodes, in which the directed edges indicate that the two nodes associated may be consecutively served by the same ferry vehicle. Based on the capacity network, a mixed integer programming model is constructed to minimize the number of ferry vehicles needed. In addition, this paper shows that the mixed integer programming is equivalent to a linear programming when the service start time of each flight is fixed, which makes the solving process more efficient, and the linear programming model can be applied to solve the minimum node-disjoint path cover of directed acyclic graphs. The efficiency and accuracy of the method are validated by the actual flight data obtained from Beijing Capital International Airport. This study will provide a methodological reference for the optimal scheduling of airport ferry vehicles. [ABSTRACT FROM AUTHOR]

The paper tackles a class of bilevel programming where the upper level problem and the lower level problem are integer indefinite quadratic programs. This article presents a new algorithm for solving the integer indefinite quadratic bilevel problem, say IIQBP. Indeed, the upper level indefinite quadratic problem is solved, the optimal solution of which belongs to the efficient solutions set of the corresponding bicriteria problem. The set of efficient solutions is determined by branch and bound method with cuts. The found integer optimal solution is tested for optimality of the main problem by solving the lower level problem. If this solution is non optimal of IIQBP problem, a cut is added to the upper level problem and a new efficient solutions set is determined then a new integer solution of the upper level problem is found. After the presentation and validation of the algorithm, two examples are provided to better visualize the proposed algorithm. [ABSTRACT FROM AUTHOR]

In the last decades, a wide body of literature has been devoted to study different saliency detection methods. These methods are typically devised on the basis of different image analysis paradigms, which leads to different performances that are not always rankable, but rather complementary. In this paper, a network design-based framework for multicriteria robust saliency detection is proposed. The key idea is that a suitable blending of the salient regions obtained by different methods leads to a salient region that outperforms the results obtained, individually, by these methods. Moreover, besides of considering state-of-the-art saliency detection approaches, a new method, which incorporates a novel tool for image contour detection, is designed. Results obtained on different sets of benchmark instances show that the proposed multicriteria robust framework exhibits high accuracy in the detection of salience objects; i.e., the pixels comprising the blended salient object are likely to be part of the actual salient object. This work aims at building further bridges between the areas of image processing and the areas of operations research. [ABSTRACT FROM AUTHOR]

This paper introduces the d-distanceb-matching problem, in which we are given a bipartite graph G = (S , T ; E) with S = { s 1 , ⋯ , s n } , a weight function on the edges, an integer d ∈ Z + and a degree bound function b : S ∪ T → Z + . The goal is to find a maximum-weight subset M ⊆ E of the edges satisfying the following two conditions: (1) the degree of each node v ∈ S ∪ T is at most b(v) in M, (2) if s i t , s j t ∈ M , then | i - j | ≥ d . In the cyclic version of the problem, the nodes in S are considered to be in cyclic order. We get back the (cyclic)d-distance matching problem when b (s) = 1 for s ∈ S and b (t) = ∞ for t ∈ T . We prove that the d-distance matching problem is APX-hard, even in the unweighted case. We show that 2 - 1 d is a tight upper bound on the integrality gap of the natural integer programming model for the cyclic d-distance b-matching problem provided that (2 d - 1) divides the size of S. For the non-cyclic case, the integrality gap is shown to be at most (2 - 2 d) . The proofs give approximation algorithms with guarantees matching these bounds, and also improve the best known algorithms for the (cyclic) d-distance matching problem. In a related problem, our goal is to find a permutation of S maximizing the weight of the optimal d-distance b-matching. This problem can be solved in polynomial time for the (cyclic) d-distance matching problem — even though the (cyclic) d-distance matching problem itself is NP-hard and also hard to approximate arbitrarily. For (cyclic) d-distance b-matchings, however, we prove that finding the best permutation is NP-hard, even if b ≡ 2 or d = 2 , and we give e-approximation algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a real-world liquid fuel distribution problem involving a heterogeneous fleet of multi-compartment vehicles servicing a set of orders of different fuels. Two new features are introduced that affect significantly the performance of the fuel distribution process in terms of safety and efficiency: (i) loading trucks so that the payload remains balanced throughout each phase of a delivery route, and (ii) sequencing the requests for loading trucks at the depot loading facilities. A Mixed Integer Programming formulation is presented and an Adaptive Large Neighbourhood Search algorithm with various novel features is developed and benchmarked. A new loading model is formed and solved for allocating the ordered items (fuel) to vehicle compartments, as part of constructing/repairing delivery routes. The computational performance of the proposed solution approach has been tested on a series of benchmark problems. Moreover, a series of experiments were performed in order to assess the effect of the balanced loading constraints on the traveled distance. The results indicate that the effect of this type of constraint on the total traveled distance is kept at a reasonable level, reaching a maximum increase of 4.37%. The computational tools presented in this work may accommodate the dispatchers' work in producing efficient and safe delivery routes while managing efficiently any potential bottleneck in the truck loading facilities. [ABSTRACT FROM AUTHOR]

The problem of selecting sugarcane varieties has been widely discussed due to its computational complexity and its great impact for the sugar and ethanol industry. This paper proposes a new integrated mathematical programming model to deal with the selection of sugarcane varieties to be planted and the determination of the optimal period for planting and harvesting in order to increase production in the sugarcane industry. The proposed model optimizes the production of sugarcane and improves the quality of biomass whilst satisfying the main constraints imposed by sugarcane companies. The problem is modelled as an integer linear program and solved using an exact method to generate optimal solutions for small and medium problems. For large problems, metaheuristic approaches based on Genetic Algorithm and Variable Neighbourhood Search are proposed. According to the results, the proposed methodology provides sugarcane company managers with decision support in selecting the most suitable varieties and in determining the best period to plant and harvest their sugarcane. [ABSTRACT FROM AUTHOR]

In contrast to methods of parametric linear programming which were developed soon after the invention of the simplex algorithm and are easily included as an extension of that method, techniques for parametric analysis on integer programs are not well known and require considerable effort to append them to an integer programming solution algorithm. The paper reviews some of the theory employed in parametric integer programming, then discusses algorithmic work in this area over the last 15 years when integer programs are solved by different methods. A summary of applications is included and the article concludes that parametric integer programming is a valuable tool of analysis awaiting further popularization. [ABSTRACT FROM AUTHOR]

The Weapon-Target Assignment (WTA) problem aims to assign a set of weapons to a number of assets (targets), such that the expected value of survived targets is minimized. The WTA problem is a nonlinear combinatorial optimization problem known to be NP-hard. This paper applies several existing techniques to linearize the WTA problem. One linearization technique (Camm et al. in Oper Res 50(6):946–955, 2002) approximates the nonlinear terms of the WTA problem via convex piecewise linear functions and provides heuristic solutions to the WTA problem. Such approximation problems are, though, relatively easy to solve from the computational point of view even for large-scale problem instances. Another approach proposed by O'Hanley et al. (Eur J Oper Res 230(1):63–75, 2013) linearizes the WTA problem exactly at the expense of incorporating a significant number of additional variables and constraints, which makes many large-scale problem instances intractable. Motivated by the results of computational experiments with these existing solution approaches, a specialized new exact solution approach is developed, which is called branch-and-adjust. The proposed solution approach involves the compact piecewise linear convex under-approximation of the WTA objective function and solves the WTA problem exactly. The algorithm builds on top of any existing branch-and-cut or branch-and-bound algorithm and can be implemented using the tools provided by state-of-the-art mixed integer linear programming solvers. Numerical experiments demonstrate that the proposed specialized algorithm is capable of handling very large scale problem instances with up to 1500 weapons and 1000 targets, obtaining solutions with optimality gaps of up to 2.0 % within 2 h of computational runtime. [ABSTRACT FROM AUTHOR]

Seru is a relatively new type of Japanese production mode originated from the electronic assembly industry. In practice, seru production has been proven to be efficient, flexible, response quickly, and can cope with the fluctuating production demands in a current volatile market. This paper focuses on scheduling problems in seru production system. Motivated by the realty of labor-intensive assembly industry, we consider learning effect of workers and job splitting with the objective of minimizing the total completion time. A nonlinear integer programming model for the seru scheduling problem is provided, and it is proved to be polynomial solvable. Therefore, a branch and bound algorithm is designed for small sized seru scheduling problems, while a local search-based hybrid genetic algorithm employing shortest processing time rule is provided for large sized problems. Finally, computational experiments are conducted, and the results demonstrate the practicability of the proposed seru scheduling model and the efficiency of our solution methods. [ABSTRACT FROM AUTHOR]

Multi-position refining furnaces are a critical strategy for energy-intensive industries to meet its demands of fast-paced production. In most literature, however, they serve only as a buffer, holding up to at most two ladles to maintain the proper temperature of ladles. These studies do not take full advantage of them, nor do they study the production scheduling of energy-intensive enterprises with multi-position refining furnaces under time-of-use (TOU) tariffs. Therefore, this paper presents a steelmaking-continuous casting (SCC) scheduling problem with multi-position refining furnaces under TOU tariffs. We firstly develop a mixed integer nonlinear programming (MINLP) model with the goals of minimizing jobs completion time, machines idle time, and total electricity costs, which subjects to the double-position characteristics and other process constraints. Owing to the complexity between the time-slots of TOU tariffs and the processing cycles of jobs, we design an intermediate function to calculate objectives efficiently. Furthermore, a Lagrangian relaxation (LR) algorithm based on a subgradient algorithm is utilized to solve the proposed model, and an interior point algorithm is adopted to solve sub-problems obtained by job-level and batch-level decomposition, whose solution approximates optimality comparing to GUROBI solver. The computational results demonstrate that the solution of job-level decomposition algorithm approximates the optimal scheduling scheme in an acceptable time and is superior to that of GUROBI solver. In addition, double-position instance can find a better scheduling scheme than nondouble-position one. [ABSTRACT FROM AUTHOR]

In this paper we combine two modeling tools to predict and evaluate evacuation plans: (dynamic) network flows and locational analysis. We present three exact algorithms to solve the single facility version 1-FlowLoc of this problem and compare their running times. After proving the $\mathcal{NP}$-completeness of the multi facility q-FlowLoc problem, a mixed integer programming formulation and a heuristic for q-FlowLoc are proposed. The paper is concluded by discussing some generalizations of the FlowLoc problem, such as the multi-terminal problem, interdiction problem, the parametric problem and the generalization of the FlowLoc problem to matroids. [ABSTRACT FROM AUTHOR]

The convex hull relaxation (CHR) method (Albornoz in Doctoral Dissertation, , Ahlatçıoğlu in Summer paper, , Ahlatçıoğlu and Guignard in OPIM Dept. Report, ) provides lower bounds and feasible solutions on convex 0-1 nonlinear programming problems with linear constraints. In the quadratic case, these bounds may often be improved by a preprocessing step that adds to the quadratic objective function terms that are equal to 0 for all 0-1 feasible solutions yet increase its continuous minimum. Prior to computing CHR bounds, one may use Plateau's quadratic convex reformulation (QCR) method (2006), or one of its weaker predecessors designed for unconstrained problems, the eigenvalue method of Hammer and Rubin (RAIRO 3:67-79, ) or the method of Billionnet and Elloumi (Math. Program, Ser. A 109:55-68, ). In this paper, we first describe the CHR method, and then present the QCR reformulation methods. We present computational results for convex GQAP problems. [ABSTRACT FROM AUTHOR]

Employee scheduling is a well known problem that appears in a wide range of different areas including health care, air lines, transportation services, and basically any organization that has to deal with workforces. In this paper we model a collection of challenging staff scheduling instances as a weighted partial Boolean maximum satisfiability (maxSAT) problem. Using our formulation we conduct a comparison of four different cardinality constraint encodings and analyze their applicability on this problem. Additionally, we measure the performance of two leading solvers from the maxSAT evaluation 2015 in a series of benchmark experiments and compare their results to state of the art solutions. In the process we also generate a number of challenging maxSAT instances that are publicly available and can be used as benchmarks for the development and verification of modern SAT solvers. [ABSTRACT FROM AUTHOR]

In this paper, we propose a branch-and-price approach for solving the problem of maximizing the expected number of transplants in Kidney Exchange Programs (KEPs). In these programs, the decision on which transplants will be conducted is usually made with the support of optimization models with the assumption that all operations will take place. However, after a plan of transplants is defined, a pair may leave the KEP or a more accurate compatibility evaluation exam may invalidate a transplant. To model these possible events we consider probabilities of failure of vertices and of arcs and the objective of maximizing the expected number of transplants. The proposed approach is based on the so-called cycle formulation, where decision variables are associated with cycles. Built on the concept of type of cycle a branch-and-price algorithm is conceived. One subproblem is defined for each type of cycle. We present computational results of the proposed branch-and-price algorithm and compare them with solving directly the cycle formulation (with a general purpose mixed integer programming solver—CPLEX) showing that the proposed approach is the only one suitable for larger instances. [ABSTRACT FROM AUTHOR]

The Quadratic Assignment Problem (QAP) is known as one of the most difficult problems within combinatorial optimization. It is used to model many practical problems including different layout problems. The main topic of this paper is to provide methods to check whether a particular instance of the QAP is a layout problem. An instance is a layout problem if the distances of the objects can be reconstructed on the plane and/or in the 3-dimensional space. A new mixed integer programming model is suggested for the case if the distances of the objects are supposed to be rectilinear distances. If the distances are Euclidean distances then the use of the well-known Multi-Dimensional Scaling (MDS) method of statistics is suggested for reconstruction purposes. The well-known difficulty of QAP makes it a popular and suitable experimental field for many algorithmic ideas including artificial intelligence methods. These types of results are published sometimes as layout problems. The methods of reconstruction can be used to decide whether the topic of a paper is layout or only general QAP. The issue what the OR community should expect from AI based algorithms, is also addressed. [ABSTRACT FROM AUTHOR]

This paper considers a variant of the bandwidth packing problem that determines paths for selected demands on a telecommunication network with given arc capacities to maximize the total revenue. Facilities on the arcs can be seen as M/M/1 queuing systems, which incur queuing delays that should be minimized by adding them to the objective function as a penalty. We also consider the case in which the demands are uncertain, so both the capacity and queuing delay of an arc should take the uncertainty of demand into account. The mathematical formulation for the problem is stated as a nonlinear integer programming problem due to the queuing delays added in the objective function. We first show that the formulation can be linearized to a mixed integer linear programming problem that can be solved by off-the-shelf MIP solvers like Cplex. We then propose a branch-and-price approach by showing that the column generation problem can be solved efficiently by a dynamic programming algorithm. Computational experiments with benchmark instances show that the proposed approach significantly outperforms the state-of-the-art MIP solver in terms of computational times. We also report a Monte-Carlo simulation study with randomly generated demand scenarios to assert the benefits of the robust approach. [ABSTRACT FROM AUTHOR]

This paper addresses a process-to-machine reassignment problem arising in cloud computing environments. The problem formulation has been posed as the ROADEF/EURO challenge 2012. Our presented approach is basically a large neighborhood search that iteratively improves a given solution. In each iteration only a subset of processes is considered for reassignment and the new assignments are evaluated by a constraint program. In this paper we present our general solution approach. Furthermore, we evaluate different process selection strategies and other optimization means to improve the performance on larger instances. In addition, we present a simple way to compute tight lower bounds of the necessary costs. [ABSTRACT FROM AUTHOR]

We study a problem of integrating the supply chain of roundwood with the supply chain of forest biomass. The developed optimization model is a multiperiod, multicommodity network planning problem with multiple sources of supply, i.e., harvest areas, and multiple types of destinations, i.e., sawmills, pulp mills, and heating plants. This paper presents an extension of previous work where the set of harvest areas was given and market prices for raw materials had linear relationship with corresponding volumes. In this paper, the assumption of predefined areas is removed, and we must make the selection of harvest areas. Instead of using a traditional sequential approach to first select areas and then determine the prices, we present a new synchronous approach that can jointly choose areas and define price levels for different assortments at those chosen supply points. We test the possible settings of discretized price and use sensitivity analysis to evaluate how the variation of fixed cost concerning log forwarding at each supply point affects the wood procurement decisions. A case study from Sweden is used to analyze the market prices in an integrated market. The computational results also highlight the advantage of the proposed synchronous approach over the sequential one in both solution quality and solution time. [ABSTRACT FROM AUTHOR]

In this paper we develop an interactive decision analysis approach to treat a large scale bicriterion integer programming problem, addressing a real world assembly line scheduling problem of a manufacturing company. This company receives periodically a set of orders for the production of specific items (jobs) through a number of specialised production (assembly) lines. The paper presents a non compensatory approach based on an interactive implementation of the ε-constraint method that enables the decision maker to achieve a satisfactory goal for each objective separately. In fact, the method generates and evaluates a large number of non dominated solutions that constitute a representative sample of the criteria ranges. The experience with a specific numerical example shows the efficiency and usefulness of the proposed model in solving large scale bicriterion industrial integer programming problems, highlighting at the same time the modelling limitations. [ABSTRACT FROM AUTHOR]

One-Class Classification (OCC) is a supervised learning technique for classification whereby the classifier is obtained only by training the objects from the target class and identifying whether new observations belong to the class or not. In this paper, we propose a novel approach to OCC, which is based on optimal covering of the target objects by 'good' norm balls. The proposed classifier consists of the selected norm balls from an integer programming model where the finite norm ball candidates from the target objects are used. Computational experiments were carried out to examine the performance and characteristics of the proposed classifier using artificial and real data from the UCI Repository. The results showed that the proposed model was comparable to existing OCC methods in the comparison group. In addition, the proposed model demonstrated high sparsity leading to low testing burden and robustness to noises. [ABSTRACT FROM AUTHOR]

This paper presents an integer programming model and a matheuristic for the physician rostering problem. Constraints related to physician's preferences, legal restrictions, hospital requirements and workload balance are investigated. Moreover, a comparison of physician and nurse rostering is analyzed to identify common constraints present in both problems. The lack of a mathematical model that could be applied in the studied problem motivated the development of a new formulation. Data and constraints of the proposed physician rostering problem were provided by Hospital de Clínicas de Porto Alegre (HCPA), Brazil. Due to the difficulty of solving large instances, a matheuristic which combines integer programming and heuristic techniques was proposed to approach the problem. Computational experiments were conducted employing commercial and open-source solvers. Results revealed that open-source solvers are a good alternative to solve small problems, while the proposed matheuristic generated near-optimal results within acceptable computation time employing larger instances. [ABSTRACT FROM AUTHOR]

In this paper we propose a two-phase approach to solve the shift and break design problem using integer linear programming. In the first phase we create the shifts, while heuristically taking the breaks into account. In the second phase we assign breaks to each occurrence of any shift, one by one, repeating this until no improvement is found. On a set of benchmark instances, composed by both randomly-generated and real-life ones, this approach obtains better results than the current best known method for shift and break design problem. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to use mathematical programming, including linear programming, dynamic programming, integer programming and goal programming to verify rule-based knowledge. We investigate both domain independent verification, exploiting the general structure of rules, and domain dependent verification, exploiting structure in the domain. Mathematical programming software is readily available and is very efficient. As a result, verification using mathematical programming can be very efficient at finding errors. Mathematical programming can be used to more than just find errors in knowledge representation. Once an error has been found, mathematical programming can be used to ‘recommend’ an alternative. The recommendation can take into account the previous verified knowledge to mitigate the potential introduction of redundant knowledge and to help guide the choice process. Normally the development of recommendations to fix errors has been ignored in the verification literature, and treated as a separate knowledge acquisition task. Accordingly, this paper also extends the verification effort by providing a recommendation on how to fix errors. [ABSTRACT FROM AUTHOR]

The FAA has decided to install, operate, and maintain its own national microwave network called the Radio Communications Link (RCL) network. With this network and its capability to provide concentration points at any one of its microwave repeater locations, the FAA can substantially reduce Its leased line budget. This paper addresses the problem of determining the most cost-effective mix of point-to-point leased lines and ‘tail circuits’ to RCL concentrators for connecting communicating pairs of FAA facilities. The problem, formulated as an integer programming (IP) problem, is shown to be similar to the facility location problem. Also, like the facility problem, integral optimal solutions are frequently obtained. (The reason integral optimal solutions are frequently obtained for the facility location problem is not known.) Thus it is an example, more complex than the facility location problem, where such a phenomenon occurs. Also, the dimensionality of the problem precludes its being solved all in one piece. In this paper we formulate the problem, relate it to the facility location problem, and provide the partitioning and reduction techniques used to solve it in a reasonable amount of time. The partitioning and reduction techniques are independent of any particular formulation for this type of problem, and the solution methodology that would be applied to any subproblem. [ABSTRACT FROM AUTHOR]

Increasing number of cancer survivors besides effective medications increase the demand for cancer care services. Therefore, managers have to investigate new ways to enhance the operational performance of the outpatient chemotherapy clinics (OCCs). However, the management process is complex due to significant variability in treatment times as a result of the different cancer types and accordingly different chemotherapy protocols and scarce resources such as nurses, chemotherapy chairs/beds, and pharmacists. In this paper, we address two problems in OCCs. First, in the planning problem, the objective is assigning the optimum first day to start the treatment for a set of new patients, and computing the required number of nurses and pharmacists given the limited resources. Second, the operational problem of scheduling the patients' appointments. In this problem, the objective is to set the best appointment schedules for all patients, new and existing to improve the operational performance of the clinic. As the two problems are highly interrelated, we propose a two-phase solution approach starting by a mixed integer programming model that assigns the starting day of treatment for new patients and finds the optimum number of needed nurses and pharmacists to fulfill two objectives. Then, in the second phase, a discrete event simulation model is used to generate patient appointment schedules that minimise the treatment delay for patients and the total completion times of treatments in each day under resources availability constraints, including two new constraints covering the drug availability and pharmacists working-hours. Finally, the proposed simulation model is applied for evaluating the operations performance of a current case study and finding the best scheduling rule for patient appointment times to achieve a minimum wait time in the OCC. [ABSTRACT FROM AUTHOR]

The problem of optimizing a linear plus linear fractional function is an important field of search, it is a difficult problem since the linear plus linear fractional function doesn't possess any convexity propriety. In this paper, we propose a method that generates the set of the efficient solutions of multiobjective integer linear plus linear fractional programming problem. Our method consists in Branch-and-Bound exploration combined with cutting plane technique that allows to remove from search inefficient solutions. The cutting plane technique takes into account the inefficiency of a solution in another problem that implies the inefficiency of that solution in our problem and uses this link to reduce the exploration's domain. [ABSTRACT FROM AUTHOR]

In this paper we address unbalanced spatial distribution of hub-level flows in an optimal hub-and-spoke network structure of median-type models. Our study is based on a rather general variant of the multiple allocation hub location problems with fixed setup costs for hub nodes and hub edges in both capacitated and uncapacitated variants wherein the number of hub nodes traversed along origin-destination pairs is not constrained to one or two as in the classical models.. From the perspective of an infrastructure owner, we want to make sure that there exists a choice of design for the hub-level sub-network (hubs and hub edges) that considers both objectives of minimizing cost of transportation and balancing spatial distribution of flow across the hub-level network. We propose a bi-objective (transportation cost and hub-level flow variance) mixed integer non-linear programming formulation and handle the bi-objective model via a compromise programming framework. We exploit the structure of the problem and propose a second-order conic reformulation of the model along with a very efficient matheuristics algorithm for larger size instances. [ABSTRACT FROM AUTHOR]

This paper addresses an assembly line balancing problem in which each station is allowed to have more than one worker, with minimization of two objectives: (i) the number of workers used in the line and (ii) the number of stations opened in the line. Each station has an own workpiece, and workers at the same station simultaneously perform different assembly tasks on its workpiece. For solving the balancing problem of these lines, a new mixed integer programming formulation is presented, and then a simulated annealing based heuristic method is proposed. The new formulation requires less number of variables and constraints. The basic property of the proposed heuristic is that it is directly applied to Gantt representations of problem's solutions. Moreover, the paper includes some important neighborhood generation properties for Gantt representations of solutions. Both methods are compared with existing methods available in the literature. Experimental study indicates that the proposed methods can yield promising results. [ABSTRACT FROM AUTHOR]

Dual-feasible functions are valuable tools that can be used to compute both lower bounds for different combinatorial problems and valid inequalities for integer programs. Several families of functions have been used in the literature. Some of them were defined explicitly, and others not. One of the main objectives of this paper is to survey these functions, and to state results concerning their quality. We clearly identify dominant subsets of functions, i.e. those which may lead to better bounds or stronger cuts. We also describe different frameworks that can be used to create dual-feasible functions. With these frameworks, one can get a dominant function based on other ones. Two new families of dual-feasible functions obtained by applying these methods are proposed in this paper. We also performed a computational comparison on the relative strength of the functions presented in this paper for deriving lower bounds for the bin-packing problem and valid cutting planes for the pattern minimization problem. Extensive experiments on instances generated using methods described in the literature are reported. In many cases, the lower bounds are improved, and the linear relaxations are strengthened. [ABSTRACT FROM AUTHOR]