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.     

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.     

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.     

Discrete time-varying demand lot-sizing models with learning and forgetting effects

This paper deals with the problem of incorporating both learning and forgetting effects into discrete timevarying demand lot-sizing models to determine lot sizes. Forgetting is retrogression in learning which causes a loss of labour productivity due to breaks between intermittent production runs. Formulae are derived for calculating the production cost required to produce the first unit of each successive lot over a finite planning horizon. An optimal lotsizing model and three heuristic models are developed by extending the existing models without learning and forgetting considerations. Numerical examples and computational experience indicate that larger lot sizes are needed when the phenomenon of learning and forgetting exists. Several important conclusions are drawn from a comparison of the three heuristic solutions with the optimal solution, and suggestions for future research and for lot-size users to choose an appropriate lot-sizing technique are made.     

A Comparative Analysis of the Relative Effectiveness of Four Dynamic Lot-Sizing Techniques on Return on Investment

The relative performance of dynamic lot-sizing techniques has been of considerable interest to researchers in recent years. While research has addressed performance in terms of cost-effectiveness, researchers have not determined the impact of dynamic lot-sizing techniques on return on investment (ROI) as it applies to finished goods' schedules. The purpose of this research is to explore the relative performance of four dynamic lot-sizing techniques with regard to ROI, namely the Wagner-Whitin, Incremental Part Period, Silver-Meal, and Groff techniques. Computer graphics are employed to analyze the relative ROI effectiveness.     

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.     

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.     

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。     

Coordinated Capacitated Lot‐Sizing Problem with Dynamic Demand: A Lagrangian Heuristic

Coordinated replenishment problems are common in manufacturing and distribution when a family of items shares a common production line, supplier, or a mode of transportation. In these situations the coordination of shared, and often limited, resources across items is economically attractive. This paper describes a mixed‐integer programming formulation and Lagrangian relaxation solution procedure for the single‐family coordinated capacitated lot‐sizing problem with dynamic demand. The problem extends both the multi‐item capacitated dynamic demand lot‐sizing problem and the uncapacitated coordinated dynamic demand lot‐sizing problem. We provide the results of computational experiments investigating the mathematical properties of the formulation and the performance of the Lagrangian procedures. The results indicate the superiority of the dual‐based heuristic over linear programming‐based approaches to the problem. The quality of the Lagrangian heuristic solution improved in most instances with increases in problem size. Heuristic solutions averaged 2.52% above optimal. The procedures were applied to an industry test problem yielding a 22.5% reduction in total costs.     

The Performance of MRP Purchase Lot-Size Procedures Under Actual Multiple Purchase Discount Conditions

Several heuristic procedures for purchase lot sizing in material requirements planning (MRP) systems were tested with actual data from manufacturing companies. Information provided by the companies for each purchased item included the estimated requirements and costs, the price discount structure from the vendor, and the actual company ordering policy. Simulation tests for each purchased item involved comparisons of several purchase lot-size procedures from the research literature along with the actual procedure used by the company providing the data. Results indicate that one of the heuristic lot-size procedures from the literature consistently outperformed the company policies as well as all other models tested. Another noteworthy result is that, in some cases, the actual company order policy was more cost-effective than some of the models from the research literature.     

A new MRP/GT lot sizing heuristic: A simulation study

This paper studies the lot-sizing problem in Material Requirements Planning/Group Technology (MRP/GT) systems. A GT production cell is designed to produce many families of components. A major setup is required when switching from manufacturing one family of components to another family, and a minor setup is needed when switching from manufacturing a component type to another component type within the same family. Inventory holding cost is incurred if inventory level is positive, and inventory shortage cost is incurred if inventory level is negative, that is, backordering. The objective of the proposed lot-sizing problem is to minimize the sum of major and minor setup costs, holding and shortage costs, and regular production cost, and to meet simultaneously the demand requirements. The proposed problem is modelled into a linear integer program, a heuristic method to solve the problem is proposed, and a simulation experiment conducted to evaluate the performance of the proposed heuristic and some existing heuristics. The computational results show that the proposed heuristic is useful to reduce the total cost significantly over a wide variety of simulated environments.     

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.     

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.     

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.     

A SIMPLE HEURISTIC FOR DYNAMIC ORDER SIZING AND SUPPLIER SELECTION WITH TIME‐VARYING DATA

In this paper we consider the problem of supplier selection and purchase order sizing for a single item under dynamic demand conditions. Suppliers offer all‐units and/or incremental quantity discounts, which may vary over time. Although the problem refers to a typical planning task of a purchasing agent, which is often solved without algorithmic assistance, in an eBusiness (b2b) environment, the need for the integration of an automatic performance of this planning task into a web‐based procurement process becomes evident. A new model formulation for this problem is developed, and a simple but easily extendible heuristic procedure is presented and tested. The heuristic is implemented as part of the Advanced Planner and Optimizer (apo) software of SAP AG, Walldorf, Germany.     

Concepts,Theory, and Techniques A JOINT LOT-SIZING RULE FOR FIXED LABOR-COST SITUATIONS

Many American firms are implementing just-in-time production in order to minimize inventories, reduce flow time, and maximize resource utilization. These firms recognize that, in the short run, setup costs really are fixed expenses and it is available capacity which is the critical factor in determining production-run quantities. We propose using available capacity to increase the number of setups and reduce lot-size inventories. This results in improved relevant cost performance. Sugimori, Kusunoki, Cho, and Uchikawa [16] in their paper on the Toyota kanban system developed a relationship for lead time but failed to use it for lot sizing. We use this relationship to develop the joint lot-sizing rule. The efficacy of our proposed rule is demonstrated by applying it to lot-size scheduling problems at the John Deere Engine Works [14]. Extensions of the proposed rule to undercapacity situations with material-wastage costs in the setup processes and to multistate production inventory systems also are discussed.     

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.     

A LOWER BOUND FOR THE SINGLE-LEVEL DYNAMIC HORIZON LOT-SIZING PROBLEM

Conventional production planning methods assume the existence of a medium- or longrange demand horizon. However, demand usually is known over a much shorter range; scheduling decisions must be made within this “decision window,” which rolls forward in time. This paper presents a new lower bound for lot-sizing heuristics in a rolling-horizon framework and compares it to the well-known Wagner-Whitin bound. The new bound indicates heuristic schedules that have costs close to the optimum. Rolling-horizon schedule costs are compared to corresponding static-horizon schedule costs (assuming the whole horizon is known in advance), using the ratio of decision-window size to the natural order cycle as a parameter. For values below unity, the rolling-horizon policy is significantly more costly. For values above one, the two policies have similar costs and actually converge as the parameter value increases.     

Setups and effective capacity: the impact of lot sizing techniques in an MRP environment

This study investigates how lot sizing techniques influence the profit performance, inventory level, and order lardiness of an assembly job shop controlled by MRP. Four single-level lot sizing techniques are compared by simulation analysis under two levels of master schedule instability and two levels of end item demand. A second analysis investigates the influence of a multilevel lot sizing technique, the generalized constrained-K (GCK) cost modification, on the four single-level techniques at low demand and low nervousness. The analyses reveal a previously unreported phenomenon. Given the same inventory costs, the single-level lot sizing techniques generate substantially different average batch sizes. The lot sizing techniques maintain the following order of increasing average batch size (and decreasing total setup time):

economic order quantity (EOQ)

period order quantity (POQ)

least total cost (LTC)

Silver-Meal heuristic (SML)

The causes for different average batch sizes among the lot sizing techniques are analysed and explained. Demand lumpiness, inherent in multilevel manufacturing systems controlled by MRP, is found to be a major factor. The number of setups each lot sizing technique generates is the primary determinant of profit performance, inventory level, and order tardiness. EOQ, a fixed order quantity technique, is less sensitive to nervousness than the discrete lot sizing techniques. EOQ_, however, generates the smallest average batch size, and, therefore, the most setups. Since setups consume capacity, EOQ, is more sensitive to higher demand. SML generates the largest average batch sizes, and is, therefore, less sensitive to increased demand. At low demand, the other lot sizing techniques perform better on all criteria. They generate smaller batches and, therefore, shorter actual lead times. The GCK cost modification increases the average batch size generated by each lot sizing technique. GCK improves the profit and customer service level of EOQ the lot sizing technique with the smallest batches. GCK causes the other lot sizing techniques to generate excessively large batches and, therefore, excessively long actual lead times.     

Revenue Management in Order‐Driven Production Systems

This article investigates the effectiveness of a tactical demand‐capacity management policy to guide operational decisions in order‐driven production systems. The policy is implemented via a heuristic that attempts to maximize revenue by selectively accepting or rejecting customer orders for multiple product classes when demand exceeds capacity constantly over the short term. The performance of the heuristic is evaluated in terms of its ability to generate a higher profit compared to a first‐come‐first‐served (FCFS) policy. The policies are compared over a wide range of conditions characterized by variations in both internal (firm) and external (market) factors. The heuristic, when used with a Whole Lot order‐processing approach, produces higher profit compared to FCFS when profit margins of products are substantially different from each other and demand exceeds capacity by a large amount. In other cases it is better to use the heuristic in conjunction with the Split Lot order‐processing approach.