Abstract
In this paper, we investigate two-period subproblems for big-bucket lot-sizing problems, which have shown a great potential for obtaining strong bounds. In particular, we investigate the special case of zero setup times and identify two important mixed integer sets representing relaxations of these subproblems. We analyze the polyhedral structure of these sets, deriving several families of valid inequalities and presenting their facet-defining conditions. We then extend these inequalities in a novel fashion to the original space of two-period subproblems, and also propose a new family of valid inequalities in the original space. In order to investigate the true strength of the proposed inequalities, we propose and implement exact separation algorithms, which are computationally tested over a broad range of test problems. In addition, we develop a heuristic framework for separation, in order to extend computational tests to larger instances. These computational experiments indicate the proposed inequalities can be indeed very effective improving lower bounds substantially.
Highlights
The lot-sizing problem aims to determine an optimal production plan detailing how much to produce and stock in each time period of the planning horizon, given manufacturing system limitations such as machine capacities and customer orders/forecasted demand
Due to its practical importance and limited knowledge in the literature, we focus in this paper on the multi-item lot-sizing problem with big-bucket capacities, where each resource is shared by multiple items and more than one type of item can be produced in any time period
Facet-defining properties for the relaxations of the two-period subproblem, (ii) novel extensions of these inequalities into the original space of the two-period relaxation, as well as new valid inequalities for the original space, and (iii) exact separation algorithms designed to test the practical strength of the proposed inequalities
Summary
The lot-sizing problem aims to determine an optimal production plan detailing how much to produce and stock in each time period of the planning horizon, given manufacturing system limitations such as machine capacities and customer orders/forecasted demand. Due to its practical importance and limited knowledge in the literature, we focus in this paper on the multi-item lot-sizing problem with big-bucket capacities, where each resource is shared by multiple items and more than one type of item can be produced in any time period. We study this problem from a theoretical perspective, where we analyze a two-period relaxation of this problem and characterize its important properties. Our computational results show that the proposed inequalities have great potential to strengthen the lower bounds significantly
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