The integer L-shaped method for stochastic integer programs with complete recourse

Laporte, Gilbert; Louveaux, François

doi:10.1016/0167-6377(93)90002-x

Cited by 604 publications

(360 citation statements)

References 11 publications

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“…In most cases, the minimization of a stochastic functional, such as the expected value, is a very complex operation (even more than exponential), since it often requires to repeatedly solve a deterministic subproblem [12]. The cost of such a procedure is not affordable for hardware design purposes if the deterministic subproblem is by itself NP-hard, which is our case.…”

Section: Allocation Problem Modelmentioning

confidence: 97%

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Stochastic Allocation and Scheduling for Conditional Task Graphs in MPSoCs

Lombardi

Milano

2006

Principles and Practice of Constraint Programming - CP 2006

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Abstract. This paper describes a complete and efficient solution to the stochastic allocation and scheduling for Multi-Processor System-on-Chip (MPSoC). Given a conditional task graph characterizing a target application and a target architecture with alternative memory and computation resources, we compute an allocation and schedule minimizing the expected value of communication cost, being the communication resources one of the major bottlenecks in modern MPSoCs. Our approach is based on the Logic Based Benders decomposition where the stochastic allocation is solved through an Integer Programming solver, while the scheduling problem with conditional activities is faced with Constraint Programming. The two solvers interact through no-goods. The original contributions of the approach appear both in the allocation and in the scheduling part. For the first, we propose an exact analytic formulation of the stochastic objective function based on the task graph analysis, while for the scheduling part we extend the timetable constraint for conditional activities. Experimental results show the effectiveness of the approach.

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Section: Allocation Problem Modelmentioning

confidence: 97%

“…The main approaches are: sampling [11] consisting in approximating the expected value with its average value over a given sample; the l-shaped method [12] which faces two phase problems and is based on Benders Decomposition [13]. The master problem is a deterministic problem for computing the first phase decision variables.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Allocation and Scheduling for Conditional Task Graphs in MPSoCs

Lombardi

Milano

2006

Principles and Practice of Constraint Programming - CP 2006

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“…In studies by Gendreau et al (1995Gendreau et al ( , 1996aGendreau et al ( , 1996b) and Laporte and Louveaux (1993), stochastic vehiclerouting problems were addressed in which some elements of the problem are random. Common examples of the random elements are stochastic demands and stochastic travel times.…”

Section: Introductionmentioning

confidence: 99%

An Auction-Based Dispatching Method for an Electronic Brokerage of Truckload Vehicles

Lee¹,

Kim²

2015

Industrial Engineering and Management Systems

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This study suggests an electronic brokerage system that has the capability of efficiently matching dispatching delivery tasks with trucks. In the brokerage system, individual truck drivers and shippers are allowed to participate in the dispatching process through the internet or wireless communication. An auction-based dispatching method for the electronic brokerage system is suggested. The basic rationale of the auction-based dispatching method-which is a distributed decision-making process-is discussed. The performance of the suggested algorithms is evaluated by a simulation study.

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“…Thus, the standard decomposition approaches that work nicely for stochastic linear programs, break down when second stage integer variables are present. Laporte and Louveaux [15] developed a branch and bound scheme for stochastic integer programs with binary first stage variables. This restriction allows for the construction of optimality cuts that approximate the non-convex objective function at all binary solutions.…”

Section: Computational Challengesmentioning

confidence: 99%

Dynamic Capacity Acquisition and Assignment under Uncertainty

Ahmed

Garcia

2003

Annals of Operations Research

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Given a set of m resources and n tasks, the dynamic capacity acquisition and assignment problem seeks a minimum cost schedule of capacity acquisitions for the resources and the assignment of resources to tasks, over a given planning horizon of T periods. This problem arises, for example, in the integrated planning of locations and capacities of distribution centers (DCs), and the assignment of customers to the DCs, in supply chain applications. We consider the dynamic capacity acquisition and assignment problem in an environment where the assignment costs and the processing requirements for the tasks are uncertain. Using a scenario based approach, we develop a stochastic integer programming model for this problem. The highly non-convex nature of this model prevents the application of standard stochastic programming decomposition algorithms. We use a recently developed decomposition based branch-andbound strategy for the problem. Encouraging preliminary computational results are provided.

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The integer L-shaped method for stochastic integer programs with complete recourse

Cited by 604 publications

References 11 publications

Stochastic Allocation and Scheduling for Conditional Task Graphs in MPSoCs

Stochastic Allocation and Scheduling for Conditional Task Graphs in MPSoCs

An Auction-Based Dispatching Method for an Electronic Brokerage of Truckload Vehicles

Dynamic Capacity Acquisition and Assignment under Uncertainty

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