In this paper, a new mixedinteger mathematical model for a closed-loop supply-chain network that includes both forward and reverse flows with multi-periods and multi-parts is proposed. The proposed model guarantees t...
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In this paper, a new mixedinteger mathematical model for a closed-loop supply-chain network that includes both forward and reverse flows with multi-periods and multi-parts is proposed. The proposed model guarantees the optimal values of transportation amounts of manufactured and disassembled products in a closed-loop supply chain while determining the location of plants and retailers. Finally, computational results are presented for a number of scenarios to show and validate the applicability of the model.
The standard way to represent a choice between n alternatives in mixed integer programming is through n binary variables that add up to one. Unfortunately, this approach commonly leads to unbalanced branch-and-bound t...
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The standard way to represent a choice between n alternatives in mixed integer programming is through n binary variables that add up to one. Unfortunately, this approach commonly leads to unbalanced branch-and-bound trees and diminished solver performance. In this paper, we present an encoding formulation framework that encompasses and expands existing approaches to mitigate this behavior. Through this framework, we generalize the incremental formulation for piecewise linear functions to any finite union of polyhedra with identical recession cones. (C) 2013 Elsevier B.V. All rights reserved.
As computational clouds offer increasingly sophisticated services, there is a dramatic increase in the variety and complexity of virtual machine (VM) placement problems. In this paper, we consider a VM placement probl...
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As computational clouds offer increasingly sophisticated services, there is a dramatic increase in the variety and complexity of virtual machine (VM) placement problems. In this paper, we consider a VM placement problem with a special type of anti-colocation requirements-disk anti-colocation-which stipulate that, for every VM assigned to a PM (physical machine), its virtual disks should be spread out across the physical disks of the PM. Once such a requirement is met, the users of the VM can expect improved disk I/O performance. There will also be improvement in fault tolerance and availability. For scalable solutions, we propose a method that combines hierarchical decomposition with mixed integer programming (MIP), where the basic building blocks are independent, small MIP subproblems. We provide experimental results to demonstrate the effectiveness of the proposed method. We show that it is scalable and achieves high performance with respect to the optimization objective.
mixed integer programming has become a very powerful tool for modeling and solving real-world planning and scheduling problems, with the breadth of applications appearing to be almost unlimited. A critical component i...
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mixed integer programming has become a very powerful tool for modeling and solving real-world planning and scheduling problems, with the breadth of applications appearing to be almost unlimited. A critical component in the solution of these mixedinteger programs is a set of routines commonly referred to as presolve. Presolve can be viewed as a collection of preprocessing techniques that reduce the size of and, more importantly, improve the "strength" of the given model formulation, that is, the degree to which the constraints of the formulation accurately describe the underlying polyhedron of integer-feasible solutions. As our computational results will show, presolve is a key factor in the speed with which we can solve mixedinteger programs and is often the difference between a model being intractable and solvable, in some cases easily solvable. In this paper we describe the presolve functionality in the Gurobi commercial mixed integer programming code. This includes an overview, or taxonomy of the different methods that are employed, as well as more-detailed descriptions of several of the techniques, with some of them appearing, to our knowledge, for the first time in the literature.
The Degree-Corrected Stochastic Block Model (DCSBM) is a popular model to generate random graphs with community structure given an expected degree sequence. The standard approach of community detection based on the DC...
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The Degree-Corrected Stochastic Block Model (DCSBM) is a popular model to generate random graphs with community structure given an expected degree sequence. The standard approach of community detection based on the DCSBM is to search for the model parameters that are the most likely to have produced the observed network data through maximum likelihood estimation (MLE). Current techniques for the MLE problem are heuristics, and therefore do not guarantee convergence to the optimum. We present mathematical programming formulations and exact solution methods that can provably find the model parameters and community assignments of maximum likelihood given an observed graph. We compare these exact methods with classical heuristic algorithms based on expectation-maximization (EM). The solutions given by exact methods give us a principled way of measuring the experimental performance of classical heuristics and comparing different variations thereof.
This survey presents cutting planes that are useful or potentially useful in solving mixedinteger programs. Valid inequalities for (i) general integer programs, (ii) problems with local structure such as knapsack con...
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This survey presents cutting planes that are useful or potentially useful in solving mixedinteger programs. Valid inequalities for (i) general integer programs, (ii) problems with local structure such as knapsack constraints, and (iii) problems with 0-1 coefficient matrices, such as set packing, are examined in turn. Finally, the use of valid inequalities for classes of problems with structure, such as network design, is explored. (C) 2002 Elsevier Science B.V. All rights reserved.
This paper presents a mixed integer programming (MIP) model which succeeds in a system integration of the production planning and shop floor scheduling problems. The proposed advanced planning and scheduling (APS) mod...
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This paper presents a mixed integer programming (MIP) model which succeeds in a system integration of the production planning and shop floor scheduling problems. The proposed advanced planning and scheduling (APS) model explicitly considers capacity constraints, operation sequences, lead times and due dates in a multi-order environment. The objective of the model is to seek the minimum cost of both production idle time and tardiness or earliness penalty of an order. The output of the model is operation schedules with order starting time and finish time. Numerical result shows that the suggested APS model can favorably produce optimal schedules. (c) 2006 Elsevier B.V. All rights reserved.
When market demand exceeds the company's capacity to manufacture, outsourcing is commonly considered as an effective alternative option. In traditional scheduling problems, processing of received orders is just po...
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When market demand exceeds the company's capacity to manufacture, outsourcing is commonly considered as an effective alternative option. In traditional scheduling problems, processing of received orders is just possible via in-house resources, while in practice, outsourcing is frequently found in various manufacturing industries, especially in electronics, motor and printing companies. This paper deals with the scheduling problem, minimising the cost of outsourcing and a scheduling measure represented by weighted mean flow time, in which outsourcing of manufacturing operations is allowed through subcontracts. Each order can be either scheduled for in-house production or outsourced to an outside supplier in order to meet customer due dates. In this problem, not only should the sequence of orders be determined, but also decision on picking the jobs for outsourcing, selecting the appropriate subcontractor, and scheduling of the outsourced orders are considered as new variables. To formulate the given problem, four different outsourcing scenarios are derived and mixed integer programming models are developed for each one separately. Furthermore, to solve the suggested problem, a computationally effective team process algorithm is devised and then a constraint handling technique is embedded into the main algorithm in order to ensure satisfaction of customer due dates. Numerical results show that the suggested approach possesses high global solution rates as well as fast convergence.
Due to the spatial aggregation effect, the amount of zones (AoZ) has a direct influence on the optimality of traffic analysis zone delineation (TAZD) problems. Unlike existing studies, this paper addresses a TAZD prob...
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Due to the spatial aggregation effect, the amount of zones (AoZ) has a direct influence on the optimality of traffic analysis zone delineation (TAZD) problems. Unlike existing studies, this paper addresses a TAZD problem in which both the AoZ and zone partitions are optimized. For the TAZD problem, we propose a mixed integer programming (MIP) model with the optimization objective of minimizing the sum of geographical errors within each zone. To solve the TAZD model, the following works have been done. First, the TAZD model is strengthened by our proposed IR (influence region) construction algorithm. Second, based on the strengthened model, we analyse the lower bound of the optimal AoZ from the theoretical perspective, and then the DRMI (domain reduction method I) is proposed to specify a tighter lower bound. Also, to reduce the amount of decision variables, we put forward the DRMII (domain reduction method II) which enumerates all feasible AoZ values. Third, to settle a non-solution situation, we propose the AHCBHA (aggregation hierarchical clustering based heuristic algorithm) in order to rebuild the solution space. Fourth, we then design two methods to solve the TAZD model. The former method combines the AHCBHA with the DRMI and the latter method combines the AHCBHA with the DRMII. Finally, the performance of the proposed TAZD and the developed methods is explored using a numerical example and a real-world case. The obtained results constitute good solutions. (C) 2014 Elsevier Inc. All rights reserved.
This paper addresses the single-track multi-hoist cyclic scheduling problem. In most existing studies, loaded hoist moves are implicitly or explicitly assumed to start and end within the same cycle. We give a countere...
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This paper addresses the single-track multi-hoist cyclic scheduling problem. In most existing studies, loaded hoist moves are implicitly or explicitly assumed to start and end within the same cycle. We give a counterexample to demonstrate that the optimal solution obtained with such an assumption is not necessarily the best one among all feasible solutions, called globally optimal solution. To obtain a globally optimal solution, we propose an improved mixed integer programming (MIP) approach for the multi-hoist cyclic scheduling problem with relaxation of the above assumption. Computational results on benchmark and randomly generated instances are reported and analyzed. Note to Practitioners-Automated electroplating lines with material handling hoists are widely used in the manufacture of many electronic or mechanical products. The higher productivity of these systems could be achieved by optimizing the sequence of the hoist moves. This paper presents an improved mixed integer programming (MIP) approach for the multi-hoist cyclic scheduling problem. In contrast with most previous approaches, our MIP approach can always find a globally optimal hoist schedule with the maximum productivity. The improved MIP approach can be easily implemented using a commercial optimization software package, such as ILOG CPLEX. The optimal hoist schedule obtained with our approach can be used to control the hoist operations via a programmable logic controller.
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