A Technique for Order Placement and Sizing

A Technique for Order Placement and Sizing This article presents a unique heuristic model for purchased item lot-sizing. The model subsequently is tested using 20 historically popular sample problems. The development of heuristic lot-sizing models was initiated as a result of difficulties identified during evaluation of the multi-level lot-sizing problem encountered in using material requirements planning systems. The "technique for order placement and sizing" (TOPS) is based on the logic of the "incremental part-period algorithm," and incorporates four distinct phases. It compares incremental costs and benefits of revising an initial order release schedule by inserting new orders or shifting existing ones. Results of an experimental process exhibited single-line optimal solutions for all test cases. Additionally, execution times were similar to much simpler but less accurate techniques than those of the optimizing Wagner-Whitin routine. INTRODUCTION AND REVIEW The popularity of dynamic lot-sizing rules and associated research evaluating their effectiveness has risen with the increased implementation of requirements planning systems, which often generate a demand for purchased parts that is highly variable over the planning horizon. The Wagner-Whitin (WW) dynamic programming algorithm guarantees optimality on a single-item basis, but because of computational difficulty, its use has been relatively sparse.[1] Given the disadvantages of WW for order-sizing, especially in MRP environments in which many items must be considered, the more popular applications have therefore been heuristic approaches such as the economic order quantity (EOQ), periodic order quantity (POQ), part-period balancing/least total cost (PPB/LTC), incremental part-period algorithm (IPPA), Silver-Meal (SM), and lot-for-lot (LFL).[2] In most cases, however, the potential deviation from optimality for these methods is significant. This error component is particularly pronounced when such rules are used to sequentially determine lot-sizes for manufactured finished goods or components throughout a bill of materials (multi-level lot-sizing). This is even true for the WW algorithm, for which the computational issue is correspondingly multipled.[3] The purpose of the research reported in this article was to develop a more effective and computationally inexpensive order-sizing method, which could not only better approximate single item optimal solutions with little effort, but would be structured for easy modification for improved multi-level lot-sizing. The result is the algorithm proposed here. Its incremental nature, near-optimal single-item results, and small computational requirements can be exploited in further applications to the more difficult multi-level case. This article has the dual objective of defining the new heuristic--and then demonstrating its effectiveness versus previous algorithms for purchased (single) item lot-sizing. Its worthiness for addressing multi-level lot-sizing problems is left for future evaluation. ALGORITHM DEFINITION The technique for order placement and sizing (TOPS) is an incrementally-based approach which incorporates four distinct steps, and is based on the incremental part period algorithm (IPPA). IPPA, which has been recognized as an effective single-level rule in the literature, nevertheless fails to consider what can be called a "diminishing returns" principle.[4] Specifically, lumping a requirement two periods ahead into an order is less advantageous than lumping an identically-sized requirement that is only one period distant. The same order cost is saved in each instance, but a larger holding cost is incurred in the former case. IPPA does not recognize this property; its logic forces it to lump a requirement into the present order as long as the incremental holding cost to carry that lot is less than the order cost. However, at some point it may become advantageous to not lump such a lot, to instead place a new order in that lot's period, and to lump subsequent lots into the new and nearer order. …