کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
420391 | 683930 | 2009 | 19 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Polyhedral analysis for the two-item uncapacitated lot-sizing problem with one-way substitution Polyhedral analysis for the two-item uncapacitated lot-sizing problem with one-way substitution](/preview/png/420391.png)
We consider a production planning problem for two items where the high quality item can substitute the demand for the low quality item. Given the number of periods, the demands, the production, inventory holding, setup and substitution costs, the problem is to find a minimum cost production and substitution plan. This problem generalizes the well-known uncapacitated lot-sizing problem. We study the projection of the feasible set onto the space of production and setup variables and derive a family of facet defining inequalities for the associated convex hull. We prove that these inequalities together with the trivial facet defining inequalities describe the convex hull of the projection if the number of periods is two. We present the results of a computational study and discuss the quality of the bounds given by the linear programming relaxation of the model strengthened with these facet defining inequalities for larger number of periods.
Journal: Discrete Applied Mathematics - Volume 157, Issue 14, 28 July 2009, Pages 3133–3151