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Lot-sizing rules have tended to exclude the possibility of backorders. In part, this may be due to a widespread perception that backordering is always a more expensive option. However, recent attention has been directed to a backorder version of the Wagner-Whitin algorithm 8!. A computationally simpler approach to lot sizing with backorders has since been introduced 3!. This approach, referred to as the Gupta-Brennan (G-B) algorithm, has demonstrated to be of comparable performance to Wagner-Whitin with backorders for single-level lot sizing. The advantage of these two backorder algorithms is that while they allow more solution combinations, the non-backorder case is also permitted. By choosing the right shortage cost, solutions can be produced with no backorders.
The objective of this article is to evaluate the performance of the G-B algorithm with several of the existing traditional lot-sizing algorithms as well as the backorder version of the EOQ algorithm (referred to as EQS) in the multi-level environment. Simulation is used as a tool to study the performance of the lotsizing rules by varying demand streams, product structures and configurations, and cost parameters.
LOT-SIZING TECHNIQUES
Lot sizing is concerned with the timing and magnitude of orders to satisfy demand. Traditionally, the focus has been on lot-sizing techniques with no consideration of backorders. However, as pointed out by Webster 8!, this is often considered a limitation of the lot-sizing techniques. Two lot-sizing techniques which incorporate consideration of backorders are evaluated and compared with the eight traditional lot-sizing techniques listed later.
The benchmark of the lot-sizing techniques with no backorders has long been the Wagner-Whitin algorithm. However, because of its complex solution procedure involving dynamic programming, it has not been widely implemented in practice. This complexity argument has been addressed by Fordyce and Webster 2! who have presented the Wagner-Whitin algorithm in a simple, straightforward computational style.
Lot Sizing with Backorders
There are times when backordering might be beneficial or even necessary. Backordering may be unavoidable because of unanticipated demand surges or defaulting suppliers. Space limitations may dictate backordering. For perishable and/or high-value goods in volatile markets, backordering may be invoked as a hedging procedure to prevent either too little or too much inventory. Because backordering can sometimes give rise to larger lot sizes, this can lead to reduced...
