AN INVESTIGATION OF MULTIPLE LEVEL LOT SIZING PROCEDURES IN A MATERIAL REQUIREMENTS PLANNING ENVIRONMENT

Since its introduction around 1960, material requirements planning (MRP) has gained considerable acceptance as a tool for managing production and raw materials procurement in the manufacturing industry. In the literature, the bulk of the research on MRP has been devoted to the issue of lot sizing. Little research has been done, however, that combines the following features for lot sizing: (1) consideration of problems with multiple items and multiple parents; (2) lot sizing rules that explicitly consider multiple levels; and (3) techniques that are computationally feasible for this class of general problems. The object of this study is to develop and evaluate simple multiple level lot sizing heuristics that can be implemented easily on current MRP systems.; Four heuristics for modifying the setup to inventory holdings costs ratios are proposed, and these are combined with the least total cost method to determine the lot sizes for all items. The proposed heuristics are closest in approach to a heuristic presented by McLaren and Whybark.; To evaluate the proposed heuristics, the experimental design includes: (1) a 52-period time horizon; (2) six demand patterns for the end items, ranging from level to lumpy demand; (3) six production levels or stages, ranging from two to seven levels; and (4) four degrees of item commonality, or common usage of a component item by several parent items. The performance criteria are: (1) the sum of the setup and inventory holding costs; and (2) the CPU execution time.; The best of these four heuristics, the Simple Average heuristic, is compared for the same experimental design with: (1) the well known single level optimal method of Wagner and Whitin; and (2) a multi-level heuristic proposed by McLaren and Whybark.; Results indicate that for problems with two or three levels, the Wagner-Whitin method resulted in 2 to 5% lower costs than the proposed heuristics that performed best. As the number of levels increased, however, the heuristic produced up to 15% lower costs. The heuristic resulted in lower costs of about 5% on the overall average.The execution time, using the Wagner-Whitin method, was three times that taken by the heuristic for 2-level problems, and increased to a factor of eight for 7-level problems.; Total costs and execution times did not differ significantly when the Simple Average heuristic was compared with the one proposed by McLaren and Whybark. The Simple Average heuristic however, is simpler to follow.; The Simple Average heuristic is also compared with: (1) the optimal solution, obtained by solving the mixed integer linear programming problem; and (2) the multiple pass heuristic proposed by Graves. This comparison was limited to a 6-period time horizon and fewer number of items, because of the large computational requirements of these techniques. The Simple Average heuristic resulted in 13% higher costs than the optimal solution, while the Graves heuristics yielded 9% higher costs. Computationally, however, the Simple Average heuristic was more than 16 times faster than the Graves heuristic, and 7000 times faster than the optimal solution.