Decentralized multi-level unconstrained lot-sizing

Problem description

This web site deals with the Multi-Level Unconstrained Lot-Sizing Problem (MLULSP) which can be described as follows: given an uncapacitated manufacturing production system, external demand for end products over a T-period planning horizon, a product structure for each end product, find a production plan for all items, i.e. end products, intermediate products and components, such that the total inventory holding and setup cost are minimized (Yelle 1979). The MLULSP is often used in material requirements planning systems and is therefore of great practical importance (Voß and Woodruff 2006; Pitakaso et al. 2007).

In this web site the MLULSP is reformulated as a coordination problem on the basis of a facility-based decomposition where the production of subassemblies is spread across multiple facilities searching for a mutually agreeable production plan. Each facility has the objective to minimize its individual sum of setup and holding cost. Following the idea of Dudek and Stadtler (2007) we choose the objective of coordination to minimize the sum of inventory holding and setup cost.

On the web site three classes of relevantly known benchmark instances of the MLULSP are given as well as new generated instances of the reformulated model. The three original MLULSP classes differ from each other in particular with regard to the number N of items, the number T of periods to be planned, the product structure, and the external demand. Class 1 covers 96 small scale problem instances (numbered from s-1 to s-96)1 and was developed by Coleman and McKnew (1991) on the basis of work by Veral and LaForge (1985) and Benton and Srivastava (1985). Class 2 covers 40 medium scale problem instances (numbered from m-1 to m-40). Class 3 covers the 40 large scale problem instances (numbered from l-1 to l-40) generated by Dellaert and Jeunet (2000). With the aim to generate instances of the reformulated MLULSP, two multi-facility instances are derived from each MLULSP instance, in which the items are distributed alternatively to n, n = 2, 5, facilities.

Download instance files

In the table below multiple download options are given. The files for each problem class can be downloaded individually or as an all-in-one package.
The "Distributed" packages contain modified versions of the instances that include distribution schemes for 2 and 5 agents. The modification contains an additional paragraph at the end of the file for each case (n=2 or n=5). One paragraph contains either the distribution of items to the agents (random distribution) or the notice “uniform distribution”. The presence of this notice means that each agent receives the same number of items. For a detailed explanation see the readme file.