The capacitated multi-level lot sizing problem with backorders has received a great deal of attention in extant literature on operations and optimization. The facility location model and the classical inventory and lo...
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The capacitated multi-level lot sizing problem with backorders has received a great deal of attention in extant literature on operations and optimization. The facility location model and the classical inventory and lot sizing model with (l, S) cuts have been proposed to formulate this problem. However, their comparative effectiveness has not yet been explored and is not known. In this paper, we demonstrate that on linear programming relaxation, the facility location formulation yields tighter lower bounds than classical inventory and lot sizing model. It further shows that the facility location formulation is computationally advantageous for deriving both lower and upper bounds. The results are expected to provide guidelines for Choosing an effective formulation during the development of solution procedures. We also propose a Lagrangian relaxation-based heuristic along with computational results that indicate its competitiveness with other heuristics and a prominent commercial solver, Cplex 11.2. (C) 2013 Elsevier Ltd. All rights reserved.
The facility layout problem (FLP) is generally defined as locating a set of departments in a facility with a given dimension. In this paper, a hybrid genetic algorithm (GA)/linear programming (LP) approach is proposed...
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The facility layout problem (FLP) is generally defined as locating a set of departments in a facility with a given dimension. In this paper, a hybrid genetic algorithm (GA)/linear programming (LP) approach is proposed to solve the FLP on the continuous plane with unequal area departments. This version of the FLP is very difficult to solve optimally due to the large number of binary decision variables in mixed integer programming (MIP) models as well as the lack of tight lower bounds. In this paper, a new encoding scheme, called the location/shape representation, is developed to represent layouts in a GA. This encoding scheme represents relative department positions in the facility based on the centroids and orientations of departments. Once relative department positions are set by the GA, actual department locations and shapes are determined by solving an LP problem. Finally, the output of the LP solution is incorporated into the encoding scheme of the GA. Numerical results are provided for test problems with varying sizes and department shape constraints. The proposed approach is able to either improve on or find the previously best known solutions of several test problems.
Since their inception in the early 1980s industrial model predictive controllers (MPC) rely on continuous quadratic programming (QP) formulations to derive their optimal solutions. More recent advances in mixed-intege...
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Since their inception in the early 1980s industrial model predictive controllers (MPC) rely on continuous quadratic programming (QP) formulations to derive their optimal solutions. More recent advances in mixed-integerprogramming (MIP) algorithms show that MIP formulations have the potential of being advantageously applied to the MPC problem. In this paper, we present an MIP formulation that can overcome difficulties faced in the practical implementation of MPCs. In particular, it is possible to set explicit priorities for inputs and outputs, define minimum moves to overcome hysteresis, and deal with digital or integer inputs. The proposed formulation is applied to simulated process systems and the results compared with those achieved by a traditional continuous MPC. The solutions of the resulting mixed-integer quadratic programming (MIQP) problems are derived by a computer implementation of the Outer Approximation method (OA) also developed as part of this work. (C) 2013 Elsevier Ltd. All rights reserved.
Owing to today's increasingly competitive market and ever-changing manufacturing environment, the inventory problem is becoming more complicated to solve. The incorporation of heuristics methods has become a new t...
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Owing to today's increasingly competitive market and ever-changing manufacturing environment, the inventory problem is becoming more complicated to solve. The incorporation of heuristics methods has become a new trend to tackle the complex problem in the past decade. This article considers a lot-sizing problem, and the objective is to minimise total costs, where the costs include ordering, holding, purchase and transportation costs, under the requirement that no inventory shortage is allowed in the system. We first formulate the lot-sizing problem as a mixed integer programming (MIP) model. Next, an efficient genetic algorithm (GA) model is constructed for solving large-scale lot-sizing problems. An illustrative example with two cases in a touch panel manufacturer is used to illustrate the practicality of these models, and a sensitivity analysis is applied to understand the impact of the changes in parameters to the outcomes. The results demonstrate that both the MIP model and the GA model are effective and relatively accurate tools for determining the replenishment for touch panel manufacturing for multi-periods with quantity discount and batch transportation. The contributions of this article are to construct an MIP model to obtain an optimal solution when the problem is not too complicated itself and to present a GA model to find a near-optimal solution efficiently when the problem is complicated.
Mobile Harbor (MH) is a movable floating platform with a container handling system on board so that it can load/discharge containers to/from an anchored container ship in the open sea. As with typical quay crane opera...
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Mobile Harbor (MH) is a movable floating platform with a container handling system on board so that it can load/discharge containers to/from an anchored container ship in the open sea. As with typical quay crane operation, an efficient schedule for its operation is a key to enhancing its operational productivity. A MH operation scheduling problem is to determine a timed sequence of loading/discharging tasks, assignment of MH units to each task, and their docking position, with an objective of minimizing the makespan of a series of incoming container ships. A mixed integer programming model is formulated to formally define the problem. As a practical solution method to the problem, this paper proposes a rule-based algorithm and a random key based genetic algorithm (rkGA). Computational results show that the rkGA method produces a better-quality solution than the rule-based method, while requiring longer computation time.
Automotive painting shops consume electricity and natural gas to provide the required temperature and humidity for painting processes. The painting shop is not only responsible for a significant portion of energy cons...
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Automotive painting shops consume electricity and natural gas to provide the required temperature and humidity for painting processes. The painting shop is not only responsible for a significant portion of energy consumption with automobile manufacturers, but also affects the quality of the product. Various storage devices play a crucial role in the management of multiple energy systems. It is thus of great practical interest to manage the storage devices together with other energy systems to provide the required environment with minimal cost. In this paper, we formulate the scheduling problem of these multiple energy systems as a Markov decision process (MDP) and then provide two approximate solution methods. Method 1 is dynamic programming with value function approximation. Method 2 is mixed integer programming with mean value approximation. The performance of the two methods is demonstrated on numerical examples. The results show that method 2 provides good solutions fast and with little performance degradation comparing with method 1. Then, we apply method 2 to optimize the capacity and to select the combination of the storage devices, and demonstrate the performance by numerical examples.
In the Prize-Collecting Steiner Tree Problem (PCStT) we are given a set of customers with potential revenues and a set of possible links connecting these customers with fixed installation costs. The goal is to decide ...
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In the Prize-Collecting Steiner Tree Problem (PCStT) we are given a set of customers with potential revenues and a set of possible links connecting these customers with fixed installation costs. The goal is to decide which customers to connect into a tree structure so that the sum of the link costs plus the revenues of the customers that are left out is minimized. The problem, as well as some of its variants, is used to model a wide range of applications in telecommunications, gas distribution networks, protein-protein interaction networks, or image segmentation. In many applications it is unrealistic to assume that the revenues or the installation costs are known in advance. In this paper we consider the well-known Bertsimas and Sim (B&S) robust optimization approach, in which the input parameters are subject to interval uncertainty, and the level of robustness is controlled by introducing a control parameter, which represents the perception of the decision maker regarding the number of uncertain elements that will present an adverse behavior. We propose branch-and-cut approaches to solve the robust counterparts of the PCStT and the Budget Constraint variant and provide an extensive computational study on a set of benchmark instances that are adapted from the deterministic PCStT inputs. We show how the Price of Robustness influences the cost of the solutions and the algorithmic performance. Finally, we adapt our recent theoretical results regarding algorithms for a general class of B&S robust optimization problems for the robust PCStT and its budget and quota constrained variants. (c) 2013 Elsevier B.V. All rights reserved.
With the rapid development in computer technologies, mathematical programming-based technique to solve scheduling problems is significantly receiving attention from researchers. Although, it is not efficient solution ...
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With the rapid development in computer technologies, mathematical programming-based technique to solve scheduling problems is significantly receiving attention from researchers. Although, it is not efficient solution method due to the NP-hard structure of these problems, mathematical programming formulation is the first step to develop an effective heuristic. Numerous comparative studies for variety scheduling problems have appeared over the years. But in our search in literature there is not an entirely review for mathematical formulations of flexible job shop scheduling problems (FJSP). In this paper, four the most widely used formulations of the FJSP are compiled from literature and a time-indexed model for FJSP is proposed. These formulations are evaluated under three categories that are distinguished by the type of binary variable that they rely on for using of sequencing operations on machines. All five formulations compared and results are presented. (C) 2012 Elsevier Inc. All rights reserved.
The Reviewer Assignment Problem is a critical management problem faced by academic journals, conferences, and research funding agencies. Previous relevant literature focuses on performing an optimized assignment of ma...
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The Reviewer Assignment Problem is a critical management problem faced by academic journals, conferences, and research funding agencies. Previous relevant literature focuses on performing an optimized assignment of manuscripts (or proposals) to reviewers. In this paper, we study a group-to-group reviewer assignment problem, where manuscripts and reviewers are divided into groups, with groups of reviewers are assigned to groups of manuscripts. We formulate this problem as a multi-objective mixed integer programming model, which is proven NP-hard. An effective two-phase stochastic-biased greedy algorithm is then proposed to solve the problem. Results of comprehensive experiments demonstrate the effectiveness of the algorithm. The approach is applied to a real application, for which the result receive positive and encouraging feedback from users. (C) 2012 Elsevier Ltd. All rights reserved.
In the paper we prove that any nonconvex quadratic problem over some set with additional linear and binary constraints can be rewritten as a linear problem over the cone, dual to the cone of K-semidefinite matrices. W...
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In the paper we prove that any nonconvex quadratic problem over some set with additional linear and binary constraints can be rewritten as a linear problem over the cone, dual to the cone of K-semidefinite matrices. We show that when K is defined by one quadratic constraint or by one concave quadratic constraint and one linear inequality, then the resulting K-semidefinite problem is actually a semidefinite programming problem. This generalizes results obtained by Sturm and Zhang (Math Oper Res 28:246-267, 2003). Our result also generalizes the well-known completely positive representation result from Burer (Math Program 120:479-495, 2009), which is actually a special instance of our result with K = R-+(n).
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