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Assignment problems (AP) are well-known topics in engineering and management science and are used frequently to analyze problems. A linear programming problem form was used in transforming assignment problem for crisp problem and in solving as per Hungarian methodology. Assigning n objects over m objects is an exciting problem that arises in different situations. Here we explore the optimal ways for assigning in n objects over m other objects. Numerous numerical applications are needed in production planning, Sales proportions, airline operators, etc. The existing Hungarian methods and maximized (or minimized) assignment methods have been solved using these methods. Entry details in the cost matrix are not always clear. This parameter is uncertain in many applications, and these uncertain parameters are represented by intervals. To solve interval linear assignment problems, we present interval Hungarian method and interval analysis concept. [ABSTRACT FROM AUTHOR]

This article describes a web-based application that can be used to help teach linear programming (LP) using an active learning approach in business courses such as management science and decision analysis. The software asks 42 integrated questions that guide students in creating product mix models and performing related analysis in Excel with Solver. Automated grading and extensive commentary provide fast feedback and help students more holistically understand topical relationships. Humor helps make learning the material more engaging and fun. The application uses randomized data and cell layout locations to encourage academic integrity and make repeated practice more value-adding. Assessment results suggest that the application offers challenges and supports learning. [ABSTRACT FROM AUTHOR]

While many classes of cutting-planes are at the disposal of integer programming solvers, our scientific understanding is far from complete with regards to cutting-plane selection, i.e., the task of selecting a portfolio of cutting-planes to be added to the LP relaxation at a given node of the branch-and-bound tree. In this paper we review the different classes of cutting-planes available, known theoretical results about their relative strength, important issues pertaining to cut selection, and discuss some possible new directions to be pursued in order to accomplish cutting-plane selection in a more principled manner. Finally, we review some lines of work that we undertook to provide a preliminary theoretical underpinning for some of the issues related to cut selection. [ABSTRACT FROM AUTHOR]

We construct a family of globally defined dynamical systems for a nonlinear programming problem, such that (a) the equilibrium points are the unknown (and sought) critical points of the problem, (b) for every initial condition, the solution of the corresponding initial value problem converges to the set of critical points, (c) every strict local minimum is locally asymptotically stable, (d) the feasible set is a positively invariant set, and (e) the dynamical system is given explicitly and does not involve the unknown critical points of the problem. No convexity assumption is employed. The construction of the family of dynamical systems is based on an extension of the control Lyapunov function methodology, which employs extensions of LaSalle's theorem and are of independent interest. Examples illustrate the obtained results. [ABSTRACT FROM AUTHOR]

Frequently in Management Science courses, instructors focus primarily on teaching students the mathematics of linear programming models. However, the ability to discuss mathematical expressions in business terms is an important professional skill. The authors present an analysis of student abilities to discuss management science concepts through memo homework assignments. The findings indicate that average student grades on homework problems for linear programming formulations were always higher than average student grades on homework memos in which they write about their formulations. These results suggest that teaching managerial writing about analytical work is an important area for future business education research. [ABSTRACT FROM PUBLISHER]

Since Charnes et al. ['Measuring the efficiency of decision making units,' European Journal of Operational Research, 2, 429-444 (1978)] proposed the concept of data envelopment analysis (DEA), many papers have been published using DEA. However, not many of these papers discuss the fundamental characteristics of input and output variables. For instance, the differing relationships among variables are rarely discussed, nor is there any discussion about the effects on evaluating efficiency when data variables are transformed. If the data used for analysis are misused, the relative efficiency among different departments or organizations can be affected. Thus, a clarification of the relative relationships among different variables is essential in order to achieve accuracy in using DEA. This article, therefore, aims to discuss these issues through a focus on the characteristics of input and output variables used in DEA. By means of mathematical analysis, this research proposes four theorems, together with two examples, to discuss the characteristics of the input and output variable in DEA. We put forward seven findings which demonstrate how DEA can be misunderstood and misused. Through these findings, this study seeks to prevent future research from making mistakes through misuse of data. [ABSTRACT FROM AUTHOR]

Presenting an integrated lotsizing, loading, and scheduling model for the capacitated flexible flow shops with sequence-dependent setups is the main contribution of this paper. An exact formulation of the problem is provided as a mixed integer program. To solve this problem, mixed integer programming-based heuristics based on iterative procedures are provided. To test the accuracy of heuristics, two lower bounds are developed and compared against the optimal solution. The trade-offs between solution quality and computational time of heuristics are also provided. [ABSTRACT FROM AUTHOR]

In this paper we propose a preference aggregation procedure for those cases in which the decision-makers express their preferences by means of a ranking of alternatives. Among the most applied methods for this purpose are those inspired by the Borda–Kendall rule, which attach to each alternative an aggregated value of the votes received in the different rank positions, and those based on distance measures between individual and collective preferences, which look for the solution that maximizes the consensus. The main idea here is to integrate these two approaches. Taking into account that the information about the values of weights or utilities assigned to each rank position is imprecise, we propose an evaluation of the alternatives using that vector of weights that minimizes the disagreement between DMs. In order to solve the problem, mixed-integer linear programming models are constructed. Two numerical examples are examined to illustrate the applicability of the proposed procedure. [ABSTRACT FROM AUTHOR]

We propose a method for the control of multi-class queueing networks over a finite time horizon. We approximate the multi-class queueing network by a fluid network and formulate a fluid optimization problem which we solve as a separated continuous linear program. The optimal fluid solution partitions the time horizon to intervals in which constant fluid flow rates are maintained. We then use a policy by which the queueing network tracks the fluid solution. To that end we model the deviations between the queuing and the fluid network in each of the intervals by a multi-class queueing network with some infinite virtual queues. We then keep these deviations stable by an adaptation of a maximum pressure policy. We show that this method is asymptotically optimal when the number of items that is processed and the processing speed increase. We illustrate these results through a simple example of a three stage re-entrant line. [ABSTRACT FROM AUTHOR]

Standard data envelopment analysis (DEA) models assume that all inputs and outputs can be varied at the discretion of management or other users. In any realistic situation, however, there may exist “exogenously fixed” or non-discretionary factors that are beyond the control of a DMU’s management, which also need to be considered. This paper proposes a slacks-based measure (SBM) of efficiency in the presence of non-discretionary factors in data envelopment analysis. This scalar measure deals directly with the discretionary input excess and the discretionary output shortfall of the decision making units (DMUs) concerned. The new measure has a close connection with the measure proposed by . We then apply this measure to a real world data set. [Copyright &y& Elsevier]

This paper gives a modified PRP method which possesses the global convergence of nonconvex function and the R-linear convergence rate of uniformly convex function. Furthermore, the presented method has sufficiently descent property and characteristic of automatically being in a trust region without carrying out any line search technique. Numerical results indicate that the new method is interesting for the given test problems. [ABSTRACT FROM AUTHOR]

Abstract: An engineered evolutionary algorithm for a realistic chemical batch scheduling problem with uncertain data is developed systematically. The problem is formulated as a two stage stochastic integer program with discrete scenarios. The model is solved by a stage decomposition-based hybrid algorithm using an evolutionary algorithm combined with mixed-integer programming. Earlier experiments with a standard evolutionary algorithm led to the hypothesis that the constrained search space is not covered well such that in some cases the population converges to a subset of the solution space which does not include the best known solution. An efficient engineered evolutionary algorithm is developed which is shown to cover the feasible set significantly better such that a high quality feasible schedule can be generated comparatively fast. As the hierarchical structure of the case study is typical for many batch scheduling problems, some general principles may be postulated from the experience gained here. [Copyright &y& Elsevier]

Abstract: In this work we present an outer-approximation algorithm to obtain the global optimum of a nonconvex mixed-integer nonlinear programming (MINLP) model that is used to represent the scheduling of crude oil movement at the front-end of a petroleum refinery. The model relies on a continuous time representation making use of transfer events. The proposed algorithm focuses on effectively solving a mixed-integer linear programming (MILP) relaxation of the nonconvex MINLP to obtain a rigorous lower bound (LB) on the global optimum. Cutting planes derived by spatially decomposing the network are added to the MILP relaxation of the original nonconvex MINLP in order to reduce the solution time for the MILP relaxation. The solution of this relaxation is used as a heuristic to obtain a feasible solution to the MINLP which serves as an upper bound (UB). The lower and upper bounds are made to converge to within a specified tolerance in the proposed outer-approximation algorithm. On applying the proposed technique to test examples, significant savings are realized in the computational effort required to obtain provably global optimal solutions. [Copyright &y& Elsevier]

In designing an MBA core curriculum, student cohorts are assigned to a number of sections in each term. In a given term, different sections have exclusive schedules, while the cohorts in the same section have an identical schedule. By altering the cohorts in the sections through the terms, any cohort can meet as many other cohorts as possible via the core courses. We model this problem as a quadratic integer programming problem and construct the performance measure to characterize the properties of the problem. We design a reactive tabu search metaheuristic that solves the model effectively. Two other solution methods, constraint logic programming and an improved hill-climbing search heuristic, are also discussed. We analyze the computational results for the cases in practice. [ABSTRACT FROM AUTHOR]

In this article, we present a mixed-integer programming formulation for the simultaneous batching and scheduling in multiproduct multistage processes. The proposed sequence-based formulation addresses limitations of existing approaches where batching and scheduling decisions are carried out sequentially. To account for batching decisions, we use additional batch-selection and batch-size variables and introduce demand-satisfaction and unit-capacity constraints. Assignment constraints are active only for the subset of batches that are selected, and sequencing is carried out between batches that are assigned on the same processing unit. We also propose an alternate formulation to handle sequence-dependent changeover costs. Finally, to enhance the computational performance of the model, we present methods that allow us to fix a subset of sequencing variables and we develop a class of tightening inequalities based on time windows. [ABSTRACT FROM AUTHOR]

Abstract: New algorithms based on mixed integer programming formulations are proposed for reactive scheduling in a dynamic, make-to-order manufacturing environment. The problem objective is to update a long-term production schedule subject to service level and inventory constraints, whenever the customer orders are modified or new orders arrive. Different rescheduling policies are proposed, from a total reschedule of all remaining and unmodified customer orders to a non-reschedule of all such orders. In addition, a medium restrictive policy is considered for rescheduling only a subset of remaining customer orders awaiting material supplies. Numerical examples modeled after a real-world scheduling/rescheduling of customer orders in the electronics industry are presented and some results of computational experiments are reported. [Copyright &y& Elsevier]

The author offers his views on integer programming. Being an engineer, he tended to learn about optimization techniques and the underlying mathematics as only as he needed to solve problems. He got his first grant from the U.S. National Science Foundation, which was to study theory and algorithms for set packing, partitioning and covering. OSL had a much better mixed integer programming solver than earlier commercial codes using some of the new technology like lifted cover cuts.

We consider a network interdiction problem on a multicommodity flow network, in which an attacker disables a set of network arcs in order to minimize the maximum profit that can be obtained from shipping commodities across the network. The attacker is assumed to have some budget for destroying (or “interdicting”) arcs, and each arc is associated with a positive interdiction expense. In this paper, we examine problems in which interdiction must be discrete (i.e., each arc must either be left alone or completely destroyed), and in which interdiction can be continuous (the capacities of arcs may be partially reduced). For the discrete problem, we describe a linearized model for optimizing network interdiction that is similar to previous studies in the field, and compare it to a penalty model that does not require linearization constraints. For the continuous case, we prescribe an optimal partitioning algorithm along with a heuristic procedure for estimating the optimal objective function value. We demonstrate on a set of randomly generated test data that our penalty model for the discrete interdiction problem significantly reduces computational time when compared to that consumed by the linearization model. [ABSTRACT FROM AUTHOR]

We propose two line search primal-dual interior-point methods for nonlinear programming that approximately solve a sequence of equality constrained barrier subproblems. To solve each subproblem, our methods apply a modified Newton method and use an ℓ 2-exact penalty function to attain feasibility. Our methods have strong global convergence properties under standard assumptions. Specifically, if the penalty parameter remains bounded, any limit point of the iterate sequence is either a Karush-Kuhn-Tucker (KKT) point of the barrier subproblem, or a Fritz-John (FJ) point of the original problem that fails to satisfy the Mangasarian-Fromovitz constraint qualification (MFCQ); if the penalty parameter tends to infinity, there is a limit point that is either an infeasible FJ point of the inequality constrained feasibility problem (an infeasible stationary point of the infeasibility measure if slack variables are added) or a FJ point of the original problem at which the MFCQ fails to hold. Numerical results are given that illustrate these outcomes. [ABSTRACT FROM AUTHOR]

Because the internal pressure of a reservoir can recover only a fraction of its oil reserve, system operators apply artificial lifting techniques to force the flow of oil to the surface. A favored technique is gas-lifting which consists of injecting compressed gas into the production tubing to reduce the weight of the oil column and, thereby, sustain a continuous flow of oil. The optimal allocation of a limited amount of compressed gas to wells gives rise to the gas-lift optimization problem, a mixed-integer nonlinear programming problem, whose decision variables determine which wells should produce and the rate of gas injected into the active ones. This paper investigates a piecewise linear formulation of the problem, presenting some properties of the polyhedron associated with the space of feasible solutions, and delivering families of valid inequalities that are shown to improve the performance of optimization software. [ABSTRACT FROM AUTHOR]

To study the knowledge creation process, we introduce a conceptual framework that captures the major goals and features of research organizations. The knowledge efficiency of research groups is then empirically studied. The budget of the projects and size of the research groups are inputs of the projects. To make the assessment more reasonable, two-dimensional indicators, including a domestic impact factor and an international impact factor, are jointly used to evaluate the research outputs for Chinese research groups through a Data Envelopment Analysis approach with preferences. Through comparisons of groups with the highest and lowest efficiency, we discover the critical factors influencing productivity and efficiency of these research groups based on the proposed framework. Finally, we provide some management suggestions for research groups to improve their knowledge creation efficiency. [ABSTRACT FROM AUTHOR]

Abstract: The paper presents two situations where unit-cost complexity results are closely related with results from the classical computability. In Section 2 we study an important theorem by Koiran and Fournier from an axiomatic point of view. It is proved that the algebraic Knapsack problem belongs to P over some ordered abelian semi-group iff classically. In this case there would exist a unit-cost machine solving the algebraic Knapsack problem over all ordered abelian semi-groups in some uniform polynomial time. In Section 3 we apply the theorem of Matiyasevich in order to construct a ring with and such that its polynomial hierarchy does not collapse at any level. [Copyright &y& Elsevier]

Abstract: The paper deals with the synthesis problem of mass exchange networks (MEN''s) for waste minimization by adopting a mathematical programming approach based on the stage-wise superstructure representation of the MEN''s, analogous to the one introduced by [Yee, T. F., & Grossmann, I. E. (1990a). Simultaneous optimization models for heat integration. I. Area and energy targeting and modeling of multi-stream exchangers. Computers and Chemical Engineering 14, 1151; Yee, T. F., & Grossmann, I. E. (1990b). Simultaneous optimization models for heat integration. II. Heat exchanger network synthesis. Computers and Chemical Engineering 14, 1165] for synthesis of heat exchange networks (HEN''s). This stage-wise superstructure-based representation cannot only handle multiple transferable components and reactive separating agents directly, but also be extended to include regeneration networks straightforwardly. Not using any heuristics that are based on the concept of pinch points, the proposed superstructure-based representation for MEN''s is formulated as a mixed-integer nonlinear programming (MINLP) optimization model, and therefore the operating cost for the external lean mass separating agents as well as the regenerating agents and the annualized equipment cost for exchange units can be minimized simultaneously. Four benchmark examples from literatures—including those with single recovery component, multiple waste components, reactive mass separating agent, and regenerating streams—are examined to illustrate the applicability of proposed approach for synthesis of various MEN''s. [Copyright &y& Elsevier]

Virtual integration (VI) offers a way to make manufacturing systems more agile and competitive. VI integrates the production resources of many manufacturing systems (partners) efficiently, and that leads to a rapid response to market changes. Based on the VI concept these partners throughout the world will form a virtual enterprise (VE). Thus to select partners is the essential and the most important issue. The main objective of this paper is to develop a partner selection and production-distribution planning with the novel partner selection model, based on the analytic hierarchy process (AHP) methodology, multi-attribute utility theory (MAUT) and integer programming (IP), for the VI with multiple criteria. The AHP and MAUT methods are use to assess and set weights for each partner candidate and the IP model applies these weights to find the optimal partners from the potential ones and provide the suitable production-distribution plan to the elective partners. Finally, a case study has been provided to substantiate a feasible quality solution of the proposed model. [ABSTRACT FROM AUTHOR]

in this paper we present an efficient integer programming (IP) based data association approach to simultaneous localization and mapping (SLAM). in this approach, the feature-based SLAM data association problem is formulated as a 0-I IP problem. The IP problem is approached by first solving a relaxed linear programming (LP) problem. Based on the optimal LP solution, a suboptimal solution to the IP problem is then obtained by applying an iterative heuristic greedy rounding (IHGR) procedure. Unlike the traditional nearest-neighbor (NN) algorithm, the proposed algorithm deals with the global matching between existing features and measurements of each scan and is more robust for an environment of high-density features (the feature number is high and the distances between features are often very close) which is usually the case in outdoor applications. Detailed simulation and experimental studies show that the proposed IHGR- based algorithm has moderate computational requirement and offers a better performance with higher successful rate of SLAM for complex environments of high density of features than the NN algorithm. [ABSTRACT FROM AUTHOR]

Abstract: This work proposed a set-covering model using the concept of fuzzy set theory todefine “fuzzy covers.” The proposed fuzzy set-covering model can be reduced to a nonlinear integer programming problem which is easily solvable with modern software. This model is a nature extension of the classical set-covering model, and is able to handle uncertainty. [Copyright &y& Elsevier]

The Traveling Salesman Problem (TSP), well known to operations research enthusiasts, is one of the most challenging combinatorial optimization problems. In this article, the authors present one approach to solving a classic TSP through a special purpose linear programming model, zero-one programming, and Microsoft Excel©Solver. [ABSTRACT FROM AUTHOR]

In this paper, we tackle scheduling the bottleneck operation of a Printed Wiring Board (PWB) manufacturing line. The problem may be characterized as unrelated parallel machines and we are interested in several performance measures including: makespan, the average finish time, mean flow time, utilization, the number of lots and the total amount of overtime beyond the release interval. Due to setup reduction techniques employed by the company, setups are negligible, and we construct an Integer Programming (IP) model with a special structure- unimodularity. Thus, the corresponding linear programming optimal solution always satisfies the integrality constraints. In order to account for multiple objectives of the scheduling system, we introduce preference constraints and bring them into the objective function by Lagrangian Relaxation (LR). We give a heuristic procedure to select constraints to he relaxed, and formulations to determine the Lagrange multipliers. To verify the validity of the proposed method, we compare it with a network model and with a modified FIFO method. The proposed method presents very promising results in terms of our measures of interest. [ABSTRACT FROM AUTHOR]

A solution methodology is described and demonstrated to determine optimal design configurations for nonrepairable series-parallel systems with cold-standby redundancy. This problem formulation considers non-constant component hazard functions and imperfect switching. The objective of the redundancy allocation problem is to select from available components and to determine an optimal design configuration to maximize system reliability. For cold-standby redundancy, other formulations have generally required exponential component time-to-failure and perfect switching assumptions. For this paper, there are multiple component choices available for each subsystem and component time-to-failure is distributed according to an Erlang distribution. Optimal solutions are determined based on an equivalent problem formulation and integer programming. Compared to other available algorithms, the methodology presented here more accurately models many engineering design problems with cold-standby redundancy. Previously, it has been difficult to determine optimal solutions for this class of problems or even to efficiently calculate system reliability. The methodology is successfully demonstrated on a large problem with 14 subsystems. [ABSTRACT FROM AUTHOR]

This paper provides the modeling of dynamic ramping in unit commitment. Ramping up/down limits could be a constant, stepwise, or piecewise linear function of generation dispatch. The dynamic ramping limit is modeled as mixed integer linear constraints, and unit commitment is solved by a mixed integer programming (MIP) solver. Test results show the impact of dynamic ramping on unit commitment and the importance of modeling dynamic ramping in the minimization of system costs while taking into consideration physical and financial constraints of power systems. [ABSTRACT FROM AUTHOR]

The problem of 3-D shape recovery from image focus can be described as the problem of determining the shape of the focused image surface (FIS)—the surface formed by the best focused points. The shape from focus (SFF) methods in the literature are fast but inaccurate because of the piecewise constant approximation of FIS. The SFF method based on FIS has shown better results by exhaustive search of FIS shape using a planar surface approximation at the cost of a considerably higher number of computations. We present a method to search FIS shape as an optimization problem, i.e., maximization of focus measure in the 3-D image volume. Each image frame in the image volume (sequence) is divided into subimage frames, and the whole image volume is divided into a number of subimage volumes. A rough depth map at only the central pixel of each subimage frame is determined using one of the traditional SFF methods. A few image frames around the image frame, whose image number in the image volume is obtained from the rough depth at the central pixel of subimage frame, are selected for the subimage volumes. The search of FIS shape is now performed in the subimage volumes using a dynamic programming optimization technique. The final depth map is obtained by collecting the depth map of the subimage volumes. The new algorithm considerably decreases the computational complexity by searching FIS shape in subimage volumes and shows better results. [ABSTRACT FROM AUTHOR]