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.     

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.     

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 New Framework for Manufacturing Planning and Control Systems*

This paper presents a new framework for manufacturing planning and control systems which we call iterative manufacturing planning in continuous time (IMPICT) that appears to have several advantages over the well-known material requirements planning (MRP) framework. IMPICT explicitly considers capacity constraints and total system cost (including tardiness) to determine order sizes, order release/due dates, and operation schedules in a deterministic, multi-level, finite horizon, dynamic demand environment. Continuous time scheduling variables allow setups to be carried over from one period to the next. Three new heuristics built on the IMPICT framework are presented and tested in a simulation-based, full-factorial experiment with a wide variety of problem environments. The benchmark for the experiment was materials requirements planning with operations sequencing (MRP/OS) implemented with best-case, fixed planned lead times. The experiment showed that all three heuristics were statistically better than MRP/OS. The total cost for the order merging (OM) heuristic was 25 percent better than the total cost for MRP/OS. Computational times for OM were substantially larger than for MRP/OS; however, the computational times in the experiment suggest that OM is still computationally viable for large-scale batch manufacturing environments found in industry. IMPICT is superior to standard MRP systems because it explicitly considers capacity constraints and total system costs when it creates a materials plan. IMPICT is superior to linear programming-based approaches to finite loading and scheduling found in the literature because it allows setups to be carried over from one period to another and because it is computationally viable for realistic-sized problems.     

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.     

Freezing the master production schedule in multilevel material requirements planning systems under deterministic demand

This paper extends the studies by Sridharan, Berry, and Udayabhanu from single-level MPS systems to multilevel material requirements planning (MRP) systems, and examines the impact of product structure, lot-sizing rules and cost parameters upon the selection of MPS freezing parameters under deterministic demand. A model is built to simulate the master production scheduling and material requirements planning operations in a make-to-order environment. The results show that all the MPS freezing parameters studied have a significant impact upon total inventory costs and schedule instability in multilevel MRP systems. First, the order-based freezing method is preferable to the period-based method. Secondly, the study finds that increasing the freezing proportion reduces both total inventory costs and schedule instability. This finding contradicts the finding by Sridharan et al. in single-level systems. Thirdly, the study finds that a higher replanning periodicity results in both lower total inventory cost and lower schedule instability. The study also indicates that the product structure and lot-sizing rules do not significantly influence the selection of MPS freezing parameters in a practical sense under most situations. However, the cost parameter seems to significantly influence the selection of replanning periodicity.     

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.     

The effect of MRP lot sizing on actual cumulative lead times in multi-level systems

This study investigates how different lot sizing techniques influence the cumulative lead time for multi-level production-inventory systems controlled by material requirements planning (MRP). Theoretical approaches, a numerical example, as well as simulation are used to analyse and illustrate the combined effect of lot sizing at different product structure levels. It is shown that lot-sizing requirements for more than a single period, such as fixed period requirements, period under quantity, Silver Meal algorithm, as well as economic order quantity will lead to longer actual cumulative lead times than would be expected, when taking the item lead times along the critical path through the product structure into account. Consequently, MRP will underestimate the cumulative lead time and will require a longer planning horizon. We show that the extension of the cumulative lead techniques covering the time is a lot-sizing related phenomenon and cannot be accounted for by, e.g. using safety lead time. Lot-sizing techniques with multi-period coverage will only occasionally provide the 'expected' cumulative lead time. We also show that average and maximum throughput times, as well as throughput time variability increases with increasing time-period coverage of lots.     

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.     

Resource-constrained materials requirements planning- MRP rc

Computerized MRP systems used in industrial practice have been criticized by researchers as well as industrial users with respect to their limited ability to generate feasible production schedules. In this paper the lot size planning stage of a typical MRP system is considered. Several modelling alternatives for multi-level lot sizing are discussed with the help of a small example. A resourceconstrained approach to lot sizing- called MRP rc- is presented that cooperates with standard production planning and control systems. In this approach the item-by-item lot size planning is substituted by the heuristic solution of a multi-level multi-item dynamic capacitated lot sizing problem with setup times for general product structures.     

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.     

A modified hierarchical production planning system integrated with MRP: A case study

In this paper, a hierarchical planning system is proposed which integrates aggregate capacity planning with MRP. This system is to be implemented in a metal box manufacturing company which multi-user MRP system covering manufacturing activities as well as procurement sales order processing and accounting systems. The hierarchical planning system includes a medium-range aggregate planning model adapted to the firm's requirements and strategies. The model consists of a mathematical formulation which covers labour capacity has already installed a constraints and includes certain cost estimations in the objective function. The planning horizon of the medium range planning is taken as twelve months in order to cover sales seasonality. The aggregate production quantities resulting from the optimized medium-range planning model are disaggregated according to procedures already found in the literature. Furthermore, the theoretical infeasibilities pertaining to the disaggregation procedures are also resolved in an heuristic manner. Using the latter modified disaggregation procedure, a feasible disaggregated plan is generated for the whole planning horizon. The proposed plan is compared with the current production policy of the firm and it is observed that the proposed plan leads to backorder reduction.     

AN ANALYSIS OF CAPACITY PLANNING PROCEDURES FOR A MATERIAL REQUIREMENTS PLANNING SYSTEM*

This paper is concerned with planning work-center capacity levels in manufacturing firms that employ a material requirements planning (MRP) system. It presents four procedures for developing work-center capacity plans designed to insure the production of components and assemblies as specified by the MRP plan and the master production schedule (MPS). These procedures (capacity planning using overall factors, capacity bills, resource profiles, and capacity requirements planning) are compared using simulation analysis. The results indicate that the performance of a procedure when measured against the MPS depends on the operating conditions of the manufacturing system. The results also indicate that the choice of a particular procedure often represents a compromise among the benefits of improved MPS performance, the costs of preparing and processing data, and the premium expenses required for more frequent adjustments in work-center capacity levels.     

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.     

THE COEFFICIENT OF VARIATION AS A FACTOR IN MRP RESEARCH

This paper investigates the use of the coefficient of variation (CV) as a measure of requirements lumpiness (the amount of variation in requirements from period to period) in material requirements planning (MRP) research. CV is used as a factor in MRP research even though it is limited as a measure. Any sequence of requirements will have a unique CV, but any CV can represent a variety of requirements sequences. This limitation raises questions concerning the robustness of CV as a measure. In this paper, two other aspects of the requirements sequence for a given CV are investigated: the procedure used to generate the requirements and the manner in which the requirements are grouped. A simulation comparison of selected lot-sizing techniques is used to conduct the investigation. With respect to these two (new) aspects of the requirements sequence, CV appears to be a robust measure.     

AN EVALUATION OF FORECAST ERROR IN MASTER PRODUCTION SCHEDULING FOR MATERIAL REQUIREMENTS PLANNING SYSTEMS.

Typical forecast-error measures such as mean squared error, mean absolute deviation and bias generally are accepted indicators of forecasting performance. However, the eventual cost impact of forecast errors on system performance and the degree to which cost consequences are explained by typical error measures have not been studied thoroughly. The present paper demonstrates that these typical error measures often are not good predictors of cost consequences in material requirements planning (MRP) settings. MRP systems rely directly on the master production schedule (MPS) to specify gross requirements. These MRP environments receive forecast errors indirectly when the errors create inaccuracies in the MPS. Our study results suggest that within MRP environments the predictive capabilities of forecast-error measures are contingent on the lot-sizing rule and the product components structure When forecast errors and MRP system costs are coanalyzed, bias emerges as having reasonable predictive ability. In further investigations of bias, loss functions are evaluated to explain the MRP cost consequences of forecast errors. Estimating the loss functions of forecast errors through regression analysis demonstrates the superiority of loss functions as measures over typical forecast error measures in the MPS.     

Economic Production Lot Sizing with Periodic Costs and Overtime*

Traditional approaches for modeling economic production lot‐sizing problems assume that a single, fixed equipment setup cost is incurred each time a product is run, regardless of the quantity manufactured. This permits multiple days of production from one production setup. In this paper, we extend the model to consider additional fixed charges, such as cleanup or inspection costs, that are associated with each time period's production. This manufacturing cost structure is common in the food, chemical, and pharmaceutical industries, where process equipment must be sanitized between item changeovers and at the end of each day's production. We propose two mathematical problem formulations and optimization algorithms. The models' unique features include regular time production constraints, a fixed charge for each time period's production, and the availability of overtime production capacity. Experimental results indicate the conditions under which our algorithms' performance is superior to traditional approaches. We also test the procedures on a set of lot‐sizing problems facing a national food processor and document their potential economic benefit.