Abstract
This study addresses the stochastic multi-item capacitated lot-sizing problem. Here, it is assumed that all items are produced on a single production resource and unmet demands are backlogged. The literature shows that the deterministic version of this problem is NP-Hard. We consider the case where period demands are time-varying random variables. The objective is to determine the minimum expected cost production plan so as to meet stochastic period demands over the planning horizon. We extend the mixed integer programming formulation introduced in the literature to capture the problem under consideration. Further, we propose a fix-and-optimize heuristic building on an item-period oriented decomposition scheme. We then conduct a numerical study to evaluate the performance of the proposed heuristic as compared to the heuristic introduced by Tempelmeier and Hilger [16]. The results clearly show that the proposed fix-and-optimize heuristic arises as both cost-efficient and time-efficient solution approach as compared to the benchmark heuristic.
Highlights
The capacitated lot-sizing problem (CLSP) is concerned with the determination of optimal production schedule and corresponding quantities so as to minimize total cost under given production capacity requirement over a discrete and finite planning horizon
We extend the mixed integer programming (MIP) models provided in [23] and [29] to the setting in which multi-item and backlogging cost are of concern
The MIP models are often fail to solve the problem under consideration within a reasonable time as is the case in the proposed formulation
Summary
The capacitated lot-sizing problem (CLSP) is concerned with the determination of optimal production schedule and corresponding quantities so as to minimize total cost under given production capacity requirement over a discrete and finite planning horizon. The problem under β service level constraints is addressed by Tempelmeier and Hilger [16] once again and a fix-andoptimize heuristic is proposed. It is shown that the fix-and-optimize heuristic outperforms the column generation approach in settings where either production capacity is tight or a limited number of items are of concern. It should be remarked that there are number of recent studies addressing the stochastic multi-item CLSP with setup carryovers ( [25]), energy concerns ( [26]), and rolling horizon framework under service level constraints ( [27], [28]).
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