The Performance of a Simple Incremental Lot‐sizing Rule in a Multilevel Inventory Environment

Abstract

A simple incremental cost approach to lot sizing was tested in a multilevel inventory environment. The incremental approach has not previously been tested in a large-scale study involving multiple product-structure levels. Using the Wagner-Whitin (WW) algorithm as a benchmark, the simple incremental rule (IPPA) was compared to three heuristic procedures (LFL, EOQ and POQ) frequently used in material requirements planning (MRP) lot-sizing research. The incremental rule consistently generated lower total order/setup and carrying costs than the three heuristics across the 3,200 multilevel test situations examined. In many of the test situations, the incremental rule also outperformed the WW benchmark. Subject Alms. Materhl Requirements Phnnhg, Inventory Management, and P I V~Ction/Oprmtions Management. Deckion Sciences Pol. 16 that lot sizes for items near the top of the product structure influence the quantity and time phasing of virtually all component parts at lower levels. Some researchers have studied lot sizing within this hierarchical framework [2] [4] [7] [8] [9] (101 1151 [161 1241 [251 [271 [30] [33] [351 [381, but much of the work published has concerned the minimization of inventory-related costs associated with a single item having the lumpy demand pattern typically generated by MRP [ 5 ] [ l 11 [18] [I91 POI [211 1221 [231 [291 [MI. An important performance measure in multilevel lot sizing is setup and carrying cost for the entire inventory system. Several multilevel studies published since 1980 have used total setup and carrying cost as the sole criterion variable for assessing the performance of lot-sizing methods [41 [91 [lo] (241 (251 [331 [351 [381. Recent research has attempted to broaden that criterion by including a simulation of the shop performances that would result from the lot sizes chosen [2] [7] [8] Decision Sciences [Vol. 16

Evolutionary algorithms for solving unconstrained multilevel lot-sizing problem with series structure

“…On the other hand, although almost all practical problems are multi-item and multilevel, the polyhedral results concerning such models are limited. As MLLS problem is so common in practice, many approaches have been described in the literature, starting off with a simple "heuristic" solution which is gained by the sequential application of singlelevel lot-sizing models to each component of the product structure [28,32] . Later, the multilevel nature of the problem has been explicitly considered in many heuristic algorithms.…”

A variable neighborhood search based approach for uncapacitated multilevel lot-sizing problems

“…The first set consists of 96 smallsize MLLS problems involving 5-item assembly structure over a 12-period planning horizon, which was developed by Coleman and McKnew (1991) on the basis of Veral and LaForge (1985) and Benton and Srivastava (1985), and also used by Dellaert and Jeunet (2000). In the 96 small-size problems, four typical product structures with a one-to-one production ratio are considered, and the leading times of all items are zero.…”

“…Other approaches involve the branch and bound algorithms (Afentakis, Gavish, & Kamarkar, 1984, 1986) that used a converting approach to change the classical formulation of the general structure into a simple but expanded assembly structure. As the MLLS problem is so common in practice and the solution plays a fundamental role in MRP system, many heuristic approaches have also been developed, consisting first of the sequential application of the single-level lot-sizing models to each component of the product structure (Veral & LaForge, 1985;Yelle, 1979), and later, of the application of the multilevel lot-sizing models. The multilevel models quantify items interdependencies and thus perform better than the single-level based models (Blackburn & Millen, 1982Coleman & McKnew, 1991).…”

Time-phased reorder models for non-instantaneous receipt

“…The literature on discrete, single-stage lot sizing under conditions of instantaneous receipt contains a number of recent studies t h a t advocate a n incremental, Downloaded by [University of Glasgow] at 16:19 20 December 2014 R. L. LaForge and S. B a m a n or marginal cost, approach to the lot-sizing logic (Boe and Yilmaz 1983, Freeland and Colley 1982, Gaither 1983, Groff 1979, Karni 1981, LaForge 1982, Silver and Meal 1973, Veral and LaForge 1985, Wemmerlov 1982. Instead of measuring total inventory a c c~m u l a t i o~ associated with a trial lot size, a marginal cost approach to PPR would only consider the incremental inventory accumulation created by the last period's requirement that was added to the lot.…”