Effects of Product Structure Complexity on Multi-level Lot Sizing*

As an input to the materials requirement planning (MRP) process, the product structure interacts with the lot-sizing rules to affect inventories, materials flow, and production costs. Despite engineering constraints, considerable latitude is still available to construct alternate product structures for the same product. An important concern of MRP managers and designers is the impact of product structure complexity on the cost performance of the lot-sizing rules. To date, there exists no detailed research that provides managers with guidelines that relate the lot-sizing rules to individual product structure parameters. We report on an extensive experiment to test the effects of individual product structure parameters on the relative cost performance of 11 lot-sizing rules. Three parameters—the number of items, number of levels, and commonality index—are proposed to characterise product structure complexity and used as factors in an experiment involving a large variety of product structures. The results indicate that all three parameters affect the relative cost differences but not the ranking of the rules. The overall best lot-sizing rule is Bookbinder and Koch's [11] rule.     

PRODUCT STRUCTURE COMPLEXITY AND MULTILEVEL LOT SIZING USING ALTERNATIVE COSTING POLICIES*

This research evaluates the effect of product structure complexity on the performance of several lot-sizing procedures in a multilevel manufacturing environment. The experiment compares two different costing policies, full value added (FVA) and marginal value added (MVA), for calculating inventory holding cost. The major finding of the research is that product structure complexity has very little effect on the performance of various lot-sizing procedures. A second finding is that when product structures with varying components per parent and stocking points for a particular end item are present, the MVA costing policy emerges as the policy of choice because it favors slightly the Silver-Meal (SM)/least-total-cost (LTC) procedures over the Wagner-Whitin (WW)/LTC procedures.     

Coordinated deterministic dynamic demand lot-sizing problem: A review of models and algorithms

Due to their importance in industry and mathematical complexity, dynamic demand lot-sizing problems are frequently studied. In this article, we consider coordinated lot-size problems, their variants and exact and heuristic solutions approaches. The problem class provides a comprehensive approach for representing single and multiple items, coordinated and uncoordinated setup cost structures, and capacitated and uncapacitated problem characteristics. While efficient solution approaches have eluded researchers, recent advances in problem formulation and algorithms are enabling large-scale problems to be effectively solved. This paper updates a 1988 review of the coordinated lot-sizing problem and complements recent reviews on the single-item lot-sizing problem and the capacitated lot-sizing problem. It provides a state-of-the-art review of the research and future research projections. It is a starting point for anyone conducting research in the deterministic dynamic demand lot-sizing field.     

COST INCREASES DUE TO DEMAND UNCERTAINTY IN MRP LOT SIZING

This paper analyzes the cost increases due to demand uncertainty in single-level MRP lot sizing on a rolling horizon. It is shown that forecast errors have a tremendous effect on the cost effectiveness of lot-sizing techniques even when these forecast errors are small. Moreover, the cost differences between different techniques become rather insignificant in the presence of forecast errors. Since most industrial firms face demand uncertainty to some extent, our findings may have important managerial implications. Various simulation experiments give insight into both the nature and the magnitude of the cost increases for different heuristics. Analytical results are developed for the constant-demand case with random noise and forecasting by exponential smoothing. It is also shown how optimal buffers can be obtained by use of a simple model. Although the analysis in this paper is restricted to simplified cases, the results merit further consideration and study. This paper is one of the first to inject forecast errors into MRP lot-sizing research. As such it attempts to deal with one of the major objections against the practical relevance of previous research in this area.     

Master Scheduling in Assemble-To-Order Environments: A Capacitated Multiobjective Lot-Sizing Model

Basic characteristics of an assemble-to-order environment make effective master scheduling extremely difficult. Limited resource capacities and dynamic customer end-item demand contribute to the complexity of the master production scheduling problem. To gain flexibility and responsiveness within this system, the master production schedule (MPS) focuses at the component level. This research proposes a master scheduling technique for manufactured components which combines a multiobjective capacitated multi-item/multi-stage lot-sizing model with an interactive multiple objective optimization solution procedure. To evaluate the model's performance as a realistic and practical master scheduling tool, this study focuses on the National Cash Register (NCR) electronics manufacturing facility in Columbia, South Carolina.     

Integrative Cycle Scheduling Approach for a Capacitated Flexible Assembly System*

This study revisits the traditional single stage, multi-item, capacitated lot-sizing problem (CLSP) with a new integrative focus on problem structuring. Unlike past research, we develop integrative cycle scheduling approaches which simultaneously address lot-sizing, capacity, and sequencing issues. Our purposes are to (1) explore the effect of sequencing on inventory levels, (2) examine the problem of infeasibility in the economic lot scheduling problem (ELSP), and (3) provide a simple methodology of generating low-cost cycle schedules in an environment with discrete shipping, dynamic demands, limited capacity, zero setup cost, and sequence-independent setup times. Our procedures are compared to benchmark cycle scheduling approaches in terms of both inventory cost and computation time under different demand scenarios, using the operating data from a flexible assembly system (FAS) at the Ford Motor Company's Sandusky, Ohio plant.     

The two-level lot-sizing problem with outbound shipment

We consider the two-level lot-sizing problem for the integrated replenishment and dispatch plan of a third-party logistics company and distribution center. Each outbound shipment for a dispatch involves cargos that incur a stepwise transportation cost. To increase the effect of shipment consolidation, the distribution center allows backlogging. This problem has the characteristics of capacitated and uncapacitated lot-sizing. A forward dynamic program is applied to exploit the beneficial characteristic of the uncapacitated problem. The forward dynamic program is implemented using Zangwill partitions to decrease the number of computational parameters with legitimacy checks to guarantee optimality. Employing these techniques, we provide an O(T⁴) algorithm, which serves as an improvement on the O(T⁶) algorithm of previous research. Moreover, computational results from actual implementations show that our algorithm is significantly faster than that of prior research.     

HEURISTIC LOT-SIZING PERFORMANCE IN A ROLLING-SCHEDULE ENVIRONMENT*

This paper examines the impact of a rolling-schedule implementation on the performance of three of the better known lot-sizing methods for single-level assembly systems——Part-Period-Cost-Balancing, Silver-Meal, and Wagner-Whitin algorithms—and a modified version of the Silver-Meal procedure. The main finding is that under certain conditions the computationally simpler Silver-Meal heuristic can provide cost performance superior to that of the Wagner-Whitin algorithm.     

On the Joint Lot-Sizing Problem with Zero Setup Costs

In a recent paper, Pinto and Mabert [5] presented a lot-sizing rule and an improvement procedure for the joint lot-sizing problem with zero setup costs. We show that this procedure often yields infeasible schedules. We also present and discuss two interesting properties of the joint lot-sizing problem with zero setup costs. A numerical example to illustrate the second property is provided.     

THE PERFORMANCE OF A SIMPLE INCREMENTAL LOT-SIZING RULE IN A MULTILEVEL INVENTORY ENVIRONMENT

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.     

Efficient Heuristics for MRP Lot Sizing with Variable Production/Purchasing Costs*

Two heuristics based on branch and bound (B&B) are developed to solve closed-loop material requirements planning (MRP) lot-sizing problems that have general product structures and variable costs. A “look ahead method'’(LAM) heuristic allows for variable production/purchasing costs and uses a single-level B&B procedure to rapidly improve lower bound values; thus, LAM efficiently uses computer-storage capacity and allows solution of larger problems. The “total average modification'’(TAM) heuristic uses B&B, applied level by level, and modified setup and carrying costs to solve the variable production/purchasing costs MRP lot-sizing problem. LAM and TAM are tested on problems and compared to heuristics in the literature. TAM may be used to solve large MRP lot-sizing problems encountered in practice.     

A Simple Heuristic for Lot Sizing with Setup Times

This paper presents an easily understood and computationally efficient heuristic algorithm for the capacitated lot sizing problem (CLSP), the single machine lot-sizing problem, with nonstationary costs, demands, and setup times. The algorithm solves problems with setup time or setup cost. A variation of the algorithm can solve problems when limited amounts of costly overtime are allowed. Results of experimentation indicate that the most significant effects on solution quality are due to the level of setup costs relative to holding costs and the size of the problems as determined by the number of items. Also affecting solution quality are tightness of the capacity constraint and variability of demand in a problem. When the capacity constraint is extremely tightly binding, it sometimes has difficulty finding solutions that do not require overtime.     

An Efficient Zero-One Formulation of the Multilevel Lot-Sizing Problem

This paper presents a zero-one linear formulation of the multilevel lot-sizing problem for materials requirement planning systems without capacity constraints. The model is an efficient statement of the problem and has a structure that is particularly convenient for research work. In addition, it is demonstrated that the relaxed linear programming solution to this formulation will always be integer. The results of a rather large computational history are reported along with a variable reduction methodology that allows for the solution of reasonably sized research problems.     

REPETITIVE LOTS: FLOW-TIME REDUCTIONS THROUGH SEQUENCING AND DYNAMIC BATCH SIZING

This paper presents a new integrative concept for job sequencing, dispatching, and lot sizing. The interrelation between these procedures and their impact on flow-time performance is examined in a capacitated production environment. Generally, lot-sizing decisions are made without regard to shop conditions and do not consider their impact on job sequencing procedures. The repetitive lots (RL) concept (developed and tested in this paper) attempts to integrate these decision processes. RL uses a number of features which have not been considered jointly in either the lot-sizing or job-dispatching/sequencing literature. These include operation batch sizes which vary by operation, transfer of work within the shop in quantities less than operation batch size, and the use of overlapped operations. A simulation model is used to analyze flow-time characteristics in a hypothetical production system. Traditional measures of flow-time performance are compared to a set of nontraditional measures which capture the interaction between lot sizing and the sequencing procedure used.     

COMMENTS ON “COST INCREASES DUE TO DEMAND UNCERTAINTY IN MRP LOT SIZING”: A VERIFICATION OF ORDERING PROBABILITIES

In a recent article in this journal, De Bodt and Van Wassenhove [1] presented analytic derivations related to lot-sizing behavior under uncertainty. Although their models appear to have been verified in the aggregate by simulation experiments, detailed justifications for several of the derivations are missing. The present paper looks at De Bodt and Van Wassenhove's analysis and provides verifications of (and corrections to) the ordering probabilities and order cycles used by the authors to estimate the cost effects of forecast errors in the particular operating environment studied. The probabilities simulated in this study also generate additional insight into the “system nervousness” caused by lot-sizing and forecast errors.     

A Note on “An Efficient Zero-One Formulation of the Multilevel Lot-Sizing Problem”

In a recent paper, McKnew, Saydam, and Coleman [3] presented a novel zero-one integer programming formulation of the multilevel dynamic, deterministic lot-sizing problem in assembly systems. They stated that “the relaxed linear programming solution to this formulation will always be integer’ [3, p. 280] since the constraint matrix is totally unimodular. In this note, we point out that the constraint matrix is not totally unimodular and therefore the authors’claim that a linear relaxation of the zero-one integer formulation always yields an integer solution is not true.     

Replenishment Analysis in Distribution Requirements Planning*

Most research on lot sizing has been for the case of a manufacturing system. In this paper, analogous issues are studied for a distribution network. Specifically, we consider the choice of shipment quantities within distribution requirements planning (DRP). A simulation model of DRP in a multi-echelon, rolling-schedule environment is used to examine, in conditions of both certain and uncertain demand, the performance of five lot-sizing rules. We conducted a full-factorial experiment in which four additional parameters were varied: distribution network structure (two options), demand distribution (three options), forecast error distribution (three options), and ordering cost (three values), as suggested by the consulting study which motivated our research. We found that for DRP, contrary to the “shop floor” wisdom on MRP, the choice of lot-sizing method can be important. Generally the Silver-Meal and Bookbinder-Tan heuristics were significantly better than the other methods.     

Classifying Revenue Management: A Taxonomy to Assess Business Practice*

As revenue management (RM) techniques evolve there is a need to take stock of how organizations practice RM and the interactions among techniques. This would help practitioners and researchers better understand how RM practice is influenced by the business setting, including those not traditionally associated with advanced RM techniques. Also, it would facilitate investigations of which practices lead to better outcomes in different contexts. Research to date has focused on individual techniques within individual business settings, with limited attention to the range of environments in which RM practice occurs. This suggests a need for a common framework to classify and assess differences in practice. In this article, we present a taxonomy which comprises (i) seven indicators of practice and (ii) a decision tree to measure RM across diverse businesses. We test the classification system in a survey of 232 businesses. Results show the taxonomy provides a comprehensive view of RM practice, with meaningful discrimination across settings. Findings also offer insight into how practices vary across different settings. Our taxonomy contributes to future research by facilitating systematic comparisons of RM practices, the settings in which it is adopted, and its impact on performance.     

求解大规模生产批量问题的启发式算法

企业资源优化模型是多物料、多层、受多种能力约束、有启动时间和启动成本的生产批量问题,该问题是NP完全问题,求解十分困难。为此我们提出了一个新的启发式方法,通过交互求解线性规划松弛问题并应用改进的Silver-Meal方法处理批量来近似求解生产批量问题,并第一次将影子价格引入Silver-Meal方法的批量决策,数值实验表明新算法在不同规模问题上的有较好的表现。