An Approach to Stochastic Integer Programming Problem with Simple Recourse via Dynamic Slope Scaling Procedure

DOI Web Site 14 References
  • NISHIOKA Ayumi
    Information Processing Solutions Operations, Dai Nippon Printing Co., Ltd.
  • SHIINA Takayuki
    Faculty of Social Systems Science, Chiba Institute of Technology
  • IMAIZUMI Jun
    Faculty of Business Administration, Toyo University
  • MORITO Susumu
    School of Creative Science and Engineering, Waseda University

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Other Title
  • 単純リコースを有する整数確率計画問題のＤｙｎａｍｉｃ　Ｓｌｏｐｅ　Ｓｃａｌｉｎｇ　Ｐｒｏｃｅｄｕｒｅを用いた解法
  • タンジュン リコース オ ユウスル セイスウ カクリツ ケイカク モンダイ ノ Dynamic Slope Scaling Procedure オ モチイタ カイホウ

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Abstract

Mathematical programming has been applied to various fields. However for many actual problems, the assumption that the parameters involved in the problem are deterministic known data is often unjustified. These data contain uncertainty and are thus represented as random variables, since they represent information about the future. Decision-making under conditions of uncertainty involves potential risk. Stochastic programming deals with optimization under uncertainty. A stochastic programming problem with recourse is referred to as a two-stage stochastic problem. We consider the stochastic programming problem with simple integer recourse in which the value of the recourse variable is restricted to a multiple of a nonnegative integer. The algorithm of a dynamic slope scaling procedure to solve the problem is developed by using the property of the expected recourse function. The numerical experiments show that the proposed algorithm is quite efficient. The stochastic programming model defined in this paper is quite useful for a variety of design and operational problems.

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