We review classical valid linear inequalities for mixed-integer programming, i.e., Gomory's fractional and mixed-integer cuts, and discuss their use in branch-and-cut. In particular, a generalization of the recent...
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We review classical valid linear inequalities for mixed-integer programming, i.e., Gomory's fractional and mixed-integer cuts, and discuss their use in branch-and-cut. In particular, a generalization of the recent mixed-integer rounding (MIR) inequality and a sufficient condition for the global validity of classical cuts after branching has occurred are derived.
The risks and uncertainties inherent in most enterprise resources planning (ERP) investment projects are vast. Decision making in multistage ERP projects investment is also complex, due mainly to the uncertainties inv...
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The risks and uncertainties inherent in most enterprise resources planning (ERP) investment projects are vast. Decision making in multistage ERP projects investment is also complex, due mainly to the uncertainties involved and the various managerial and/or physical constraints to be enforced. This paper tackles the problem using a real-option analysis framework, and applies multistage stochastic integerprogramming in formulating an analytical model whose solution will yield optimum or near-optimum investment decisions for ERP projects. Traditionally, such decision problems were tackled using lattice simulation or finite difference methods to compute the value of simple real options. However, these approaches are incapable of dealing with the more complex compound real options, and their use is thus limited to simple real-option analysis. Multistage stochastic integerprogramming is particularly suitable for sequential decision making under uncertainty, and is used in this paper and to find near-optimal strategies for complex decision problems. Compared with the traditional approaches, multistage stochastic integerprogramming is a much more powerful tool in evaluating such compound real options. This paper describes the proposed real-option analysis model and uses an example case study to demonstrate the effectiveness of the proposed approach.
We consider the discrete lot-sizing and scheduling problem with sequence-dependent changeover costs and times and propose solving it as a mixed-integer program using a commercial solver. Our approach is based on the e...
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We consider the discrete lot-sizing and scheduling problem with sequence-dependent changeover costs and times and propose solving it as a mixed-integer program using a commercial solver. Our approach is based on the extension of an existing tight formulation for the case without changeover times. Computational results confirm the benefits of the proposed solution procedure. (C) 2008 Elsevier B.V. All rights reserved.
Borozan and Cornuejols show that valid inequalities for an infinite relaxation for MIPs, relative to some vertex f of the linear relaxation, are determined by maximal lattice-free convex sets containing f. We show tha...
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Borozan and Cornuejols show that valid inequalities for an infinite relaxation for MIPs, relative to some vertex f of the linear relaxation, are determined by maximal lattice-free convex sets containing f. We show that cuts for the original MIP are given by such sets with f in the interior. (C) 2008 Elsevier B.V. All rights reserved.
Finding a feasible solution of a given mixed-integer programming (MIP) model is a very important NP-complete problem that can be extremely hard in practice. Feasibility Pump (FP) is a heuristic scheme for finding a fe...
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Finding a feasible solution of a given mixed-integer programming (MIP) model is a very important NP-complete problem that can be extremely hard in practice. Feasibility Pump (FP) is a heuristic scheme for finding a feasible solution to general MIPs that can be viewed as a clever way to round a sequence of fractional solutions of the LP relaxation, until a feasible one is eventually found. In this paper we study the effect of replacing the original rounding function (which is fast and simple, but somehow blind) with more clever rounding heuristics. In particular, we investigate the use of a diving-like procedure based on rounding and constraint propagation-a basic tool in Constraint programming. Extensive computational results on binary and general integer MIPs from the literature show that the new approach produces a substantial improvement of the FP success rate, without slowing-down the method and with a significantly better quality of the feasible solutions found.
The increase in efficiency of container terminals is addressed via an approach based on the optimisation of logistics operations. Toward this end, a discrete-time dynamic model of the various flows of containers that ...
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The increase in efficiency of container terminals is addressed via an approach based on the optimisation of logistics operations. Toward this end, a discrete-time dynamic model of the various flows of containers that are inter-modally routed from arriving carriers to carriers ready for departure is proposed. On the basis of such a model, the decisions on the allocation of the available handling resources inside a container terminal are made according to the predictive-control approach by minimising a performance cost function over a forward horizon from the current time instant. Since both the dynamic equations and the cost function are in general nonlinear and since binary variables are used to model the departure or stay of a carrier, such decisions result from the on-line solution of a mixed-integer nonlinear programming problem at each time step. To solve this problem, two techniques are proposed that have to deal explicitly with the binary variables and with the nonlinearities of the model and the cost function. The first relies on the application of a standard branch-and-bound algorithm. The second is based on the idea of treating the decisions associated with the binary variables as step functions. Simulation results are reported to illustrate the pros and cons of such methodologies in a case study.
This work is concerned with customer-oriented catalog segmentation that each catalog consists of specific number of products. In this problem, requirements of a specific ratio of customers should be satisfied. Accordi...
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ISBN:
(纸本)9781424448692
This work is concerned with customer-oriented catalog segmentation that each catalog consists of specific number of products. In this problem, requirements of a specific ratio of customers should be satisfied. According to the definition, when a customer is satisfied that at least t required products exist in his/her catalog. The objective of this problem is to minimize the number of catalogs, regarding to minimum number of customers constraint that was comply. In this paper, we present a mixed-integer programming model for this clustering problem. This problem is NP-Hard in large scales and the optimum solution is almost impossible to reach. Hence, a solution procedure is developed based on genetic algorithm. Then, the results of computational experiments are reported, in which the GA solution is compared with exact solution of mixed-integer programming model.
The aim of this paper is to present an industrial application of a new procedure for classification. The problem is solved by minimizing the distance between the components and the centers of the clusters. It is there...
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ISBN:
(纸本)9781424441358
The aim of this paper is to present an industrial application of a new procedure for classification. The problem is solved by minimizing the distance between the components and the centers of the clusters. It is therefore critical to determine the best centers of the clusters. Once the centers of each class are determined, the rule of center neighbourhood is applied to assign an element to a class. The problem of clustering has several applications in various contexts, such as the problems of data mining, bioinformatics and finance. The implementation of the method was applied in the operational process of the Packing Techniques in Cardboard Mayr-Melnhof Packaging firm.
This paper addresses the issues on high operation cost, start up and operation reliability of rapid-start units, such as open cycle gas turbines (OCGTs), for energy scheduling and online/offline reserve allocation in ...
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ISBN:
(纸本)9781424444540
This paper addresses the issues on high operation cost, start up and operation reliability of rapid-start units, such as open cycle gas turbines (OCGTs), for energy scheduling and online/offline reserve allocation in the deregulated electricity market. A probabilistic technique is presented in this paper to assess the un-realised reserve which has been allocated to the rapid-start generators that failed during starting up while considering their response time needed for reserve contribution. This is accomplished by modelling the process in term of expected energy not served (EENS) with an enumerated mathematical formulation. A study on the variation of OCGTs characteristics is performed and the results are compared with those of the 26-thermal unit system from IEEE-RTS integrated with 3 interruptible loads (ILs). Numerical results and discussions documented in this paper may be helpful to provide a guide for economic deployment of rapid-start units for energy and reserve contributions.
We study a production planning problem known as the Discrete Lot-sizing and Scheduling problem with sequence-dependent changeover costs. We consider here the case where there are several identical parallel resources a...
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ISBN:
(纸本)9781424441358
We study a production planning problem known as the Discrete Lot-sizing and Scheduling problem with sequence-dependent changeover costs. We consider here the case where there are several identical parallel resources available for production and we propose solving the resulting optimization problem as a mixed-integer program (MIP) using a commercial solver. This is achieved thanks to the extension of an existing tight MIP formulation for the case of a single resource to the case of parallel resources. The results of our computational experiments show that using the proposed solution approach, we are able to provide guaranteed optimal solutions for instances of medium size with a reasonable computational effort.
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