Simple policies in the economic lot scheduling problem with zero setup costs

The economic lot scheduling problem is analysed for the case when the cost of setups, but not their duration, is assumed to be zero. This would be the case when setups are performed by the machine operators, or when management's goal is holding-cost reduction. Theoretical results are presented describing when the common cycle solution of producing one lot of every item every cycle is optimal or near optimal. Computational results using simulated data are then presented which show that the common cycle solution is nearly optimal in a wide range of practical situations.     

Process Mean Determination with Quantity Discounts in Raw Material Cost*

Setting the mean (target value) for a container-filling process is an important decision for a producer when the material cost is a significant portion of the production cost. Because the process mean determines the process conforming rate, it affects other production decisions, including, in particular, the production setup and raw material procurement policies. In this paper, we consider the situation in which quantity discounts exist in the raw material acquisition cost, and incorporate the quantity-discount issue into an existing model that was developed for simultaneously determining the process mean, production setup, and raw material procurement policies for a container-filling process. The product of interest is assumed to have a lower specification limit, and the items that do not conform to the specification limit are scrapped with no salvage value. The production cost of an item is proportional to the amount of the raw material used in producing the item. A two-echelon model is formulated for a single-product production process, and an algorithm is developed for finding the optimal solution. A sensitivity analysis is performed to study the effects of the model parameters on the optimal solution.     

The Impact of Imperfect Processes on Production Run Times

This paper investigates the interaction between the economics of production and imperfections in the production process. Specifically, this paper is the first to devise a model in an attempt to provide managers with guidelines to choose the appropriate production run times to buffer against both the production of defective items and stoppages occurring due to machine breakdowns. In addition to providing several structural properties of the model, we show that a manager will always incur a cost penalty when (s)he uses the results of two oft‐cited models‐the EMQ (Economic Order/Manufacturing Quantity) and the NR‐E (No‐Resumption, Exponential machine breakdown)‐to determine production run times.     

Models and Methods to Support a New Type of Inventory Performance Measure: The ESWSO

When analyzing a reorder point, order quantity (r, Q) inventory systems, one important question that often gets very little, if any, attention is: When a stockout occurs, how large is it? This paper is directed at researchers and practicing inventory planners with two objectives. First, we provide several models and algorithms to compute the Expected Shortages When a Stockout Occurs (ESWSO) for a variety of stochastic environments. We show that when ESWSO, is used in conjunction with the traditional fill rate measures it greatly enhances a planners ability to plan for shortages. Second, we develop two cost‐minimizing inventory models—one addressing the backorder and the other the shortage scenario—to show how the ESWSO can be seamlessly integrated into an inventory‐cost framework to specify lot sizes and safety stocks.     

The effects of the warranty cost on the imperfect EMQ model with general discrete shift distribution

In this paper, we investigate the effect of the warranty cost on optimization of the economic manufacturing quality (EMQ). This is done for a deteriorating process where the production process shifts from the in-control state to the out-of-control state following a general discrete probability distribution. Once the production process goes out of control, the production process produces some defective items. The defective item cost includes reworking and warranty costs. Thus, in order to economically operate a production-inventory system with products sold under warranty, the tradeoffs among the production setup, inventory, and defective item cost, including the reworked cost before sale and the warranty cost after sale, needed to be analysed. This objective in this paper is to determine the production lot size while minimizing the total cost per unit of time per unit of time. Various special cases are presented. Two of them are extensions of results obtained previously in the literature. Finally, a numerical example is given which uses a discrete Weibull probability distribution. Sensitivity analysis of the model with respect to cost and time parameters is also performed.     

Optimal Purchase and Transportation Cost Lot Sizing for a Single Item

A review of the literature indicates that the traditional approach for evaluating quantity discount offerings for purchased items has not adequately considered the effect that transportation costs may have on the optimal order quantity; despite the general fact that purchased materials must bear transportation charges. The transportation cost structure for less-than-truckload (LTL) shipments reflects sizable reductions in freight rates when the shipment size exceeds one of the nominal rate breakpoints. However, the shipper must also be aware of the opportunity to reduce total freight costs by artificially inflating the actual shipping weight to the next rate breakpoint, in order that a lower marginal tariff is achieved for the entire shipment. Such over-declared shipments result in an effective freight rate schedule that is characterized by constant fixed charge segments in addition to the nominal marginal rates. Over-declared shipments are economical when the shipment volume is less than the rate breakpoint, but greater than a cost indifference point between the two adjacent marginal rates. This paper presents a simple analytical procedure for finding the order quantity that minimizes total purchase costs which reflect both transportation economies and quantity discounts. After first solving for the series of indifference points that apply to a particular freight rate schedule, a total purchase cost expression is presented that properly accounts for the actual transportation cost structure. The optimal purchase order quantity will be one of the four following possibilities: (1) the valid economic order quantity (EOQ), QC; (2) a purchase price breakpoint in excess of QC; (3) a transportation rate breakpoint in excess of QC; and (4) a modified EOQ which provides an over-declared shipment in excess of QC. Finally, an algorithm which systematically explores these four possibilities is presented and illustrated with a numerical example.     

A new prototype system for optimized job shop scheduling

Optimal scheduling of shopfloor activities in an environment of discrete part manufacturing is discussed. The scheduling problem is a well known NP complete one. The main part, the sequencing problem, has been tackled using two techniques: virtual resources identification and taboo search heuristics. The first approach allowed the authors to reduce the complexity of the sequencing from a job shop to a general flow shop problem. On the other hand, the search for an optimal solution, with respect to a fixed strategy, has been achieved via the taboo search. A synthesis of the results of a large number of tests is presented as well as the results of an application to a real case. The latter is shown in comparison with the output of the system being presently used in the examined factory.     

Design and implementation of an integrated production planning system for a pharmaceutical manufacturing concern in India

SmithKline Beecham (SBPI) is a major player in the Indian pharmaceutical industry. Though relatively small in terms of turnover, it has performed Pharmaceuticals (India) exceptionally well in terms ofprofitability and growth rate. The firm has substantial cash reserves. However, the firm operates in 'mass production' mode at present, with the established finished goods inventory norms being in the range of 1 to 1.5 months. Competitive pressure on the firm is now forcing it to move towards world class manufacturing and the application of concepts from MRP II, JIT and OPT is under consideration. This paper describes the considerations that went into the justification, design and implementation of an integrated production planning and control system in this situaion.     

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.     

Evaluation of scheduling strategies for a dynamic job shop in a tool-shared,flexible manufacturing environment

A two-phase approach is used to examine the impact of job scheduling rules and tool selection policies for a dynamic job shop system in a tool-shared, flexible manufacturing environment. The first phase develops a generalized simulation model and analyses 'simple' job scheduling rules and tool selection policies under various operating scenarios. The results from this investigation are then used to develop and analyse various bi-criteria rules in the second phase of this study. The results show that the scheduling rules have the most significant impact on system performance, particularly at high shop load levels. Tool selection policies affect some of the performance measures, most notably, proportion of tardy jobs, to a lesser degree. Higher machine utilizations can be obtained at higher tool duplication levels but at the expense of increased tooling costs and lower tool utilization. The results also show that using different processing time distributions may have a significant impact on shop performance.     

A SIMULATION ANALYSIS OF THE JAPANESE JUST-IN-TIME TECHNIQUE (WITH KANBANS) FOR A MULTILINE,MULTISTAGE PRODUCTION SYSTEM

The Japanese “just-in-time with kanban” technique reduces in-process inventory to absolute minimal levels, in concert with the Japanese belief that inventory is an unnecessary evil. Due to the success of Japanese firms that employ this type of system, American firms would like to import this technique and emulate Japanese successes. But this Japanese success may be attributable not only to the just-in-time with kanban technique but also to the production environment in which the technique is employed. This paper simulates the just-in-time with kanban technique for a multiline, multistage production system in order to determine its adaptability to an American production environment that might include such characteristics as variable processing times, variable master production scheduling, and imbalances between production stages. The results have practical implications for those firms considering adoption of the Japanese technique.     

Analysis of justification problems in CIMS review and projection

Attempts to study justification problems related to advanced manufacturing systems such as CIMS are made. Such systems conceptually promise industries many significant advantages, but many justification procedures that are used in appraising such system proposals remain ill-suited because of their failure to incorporate multifaceted strategic and tactical issues. The aim in this paper is to review some of these procedures and finally propose a total systems approach. The objective is to make a prognosis of the issues to prepare a projective base for organizational decision support. Two case studies from Indian industries where CIMS have been tried out are also described.     

Solving the Economic Lot-Scheduling Problem Using the Method of Prime Subperiods

In recent years the reported successes of Japanese production systems, particularly the just-in-time approach to inventory control, has caused managers to focus more of their attention on efficient decision-making procedures for determining production schedules that minimize inventory costs. One such potential area of attention is the economic lot-scheduling problem (ELSP), which occurs in a variety of manufacturing environments where machining operations are prevalent. The economic lot-scheduling problem addresses the determination of lot sizes for N products with constant demand (and cycled through one machine with a given production rate) to minimize setup and inventory costs. The most successful solution approaches to the ELSP have been based on the concept of a basic period that is of sufficient length for the production of all items, even though each item might not be produced during each repetition of the basic period. This paper proposes a heuristic approach to the solution of the ELSP (referred to as the method of prime subperiods), which is an extension of the basic period approaches. The procedure is described and demonstrated via an example and then tested using a set of six example problems previously employed in the literature related to the ELSP. The results indicate as good or superior performance by the proposed method of prime subperiods.     

Recursive Behavior of Safety Stock Reduction: The Effect of Lead‐Time Uncertainty

Motivated by a recent paper on the effect of lead‐time variability reduction on safety stocks, we provide evidence of the recursive nature of safety stock changes. When lead times follow a gamma distribution we demonstrate that, for cycle service levels between .60 and .70, the reduction of lead‐time variability will first increase safety stock and then either recursively decrease safety stock or make it remain constant. We also numerically show the existence of the recursive effect. A two‐by‐two matrix is introduced to assist managers in making decisions regarding safety stock policy.     

The Value of Supplier Information to Improve Management of a Retailer's Inventory

The distribution of lead time demand is essential for determining reorder points in inventory systems. Usually, the distribution of lead time demand is approximated directly. However, in some cases it may be worthwhile to take the demand per unit time and lead time into account, particularly when specific information is available. This paper deals with the situation where a supplier, who produces on order in fixed production cycles, provides information on the status of the coming production run. The retailer can use this information to gain insight into the lead-time process. A fixed order (s_vQ) strategy is presented, with a set of reorder points s_v depending on the time t until the first possible delivery, which is determined by the information of the supplier. A Markov model that analyzes a given (s_vQ) strategy is used to quantify the value of the information provided by the supplier. Some numerical examples show that the approach may lead to considerable cost savings compared to the traditional approach that uses only one single reorder point, based on a two-moments approximation. Using this numerical insight, the pros and cons of a more frequent exchange of information between retailers and suppliers can be balanced.     

A Comparison of Three Joint Ordering Inventory Policies*

This paper evaluates the performance of a joint ordering inventory policy which was first suggested and characterized by Renberg and Planche [14]. This paper shows that the policy is easily characterized for Poisson demands. This policy is then compared with two other joint ordering policies—the well-known (S, c, s) or can-order policy of Balintfy [3] and the recent periodic policies suggested by Atkins and lyogun [2]. For a continuous review operating environment, the Renberg and Planche policy utilizes a group reorder point and a combined order quantity (Q), with each item maintaining an order-up-to level (S). For the can-order policy, each item in the product group has a must-order point (s), a can-order point (c) and an order-up-to level (S). The periodic policies require that item orders be grouped at some fixed scheduled intervals. Using long-run total average costs as the basis, it is shown that no one policy is superior to the others in all the examples tested. In some cases, the Renberg and Planche policy performs surprisingly well.     

The Effect of Lead Time Uncertainty on Safety Stocks

The pressure to reduce inventory investments in supply chains has increased as competition expands and product variety grows. Managers are looking for areas they can improve to reduce inventories without hurting the level of service provided. Two areas that managers focus on are the reduction of the replenishment lead time from suppliers and the variability of this lead time. The normal approximation of lead time demand distribution indicates that both actions reduce inventories for cycle service levels above 50%. The normal approximation also indicates that reducing lead time variability tends to have a greater impact than reducing lead times, especially when lead time variability is large. We build on the work of Eppen and Martin (1988) to show that the conclusions from the normal approximation are flawed, especially in the range of service levels where most companies operate. We show the existence of a service‐level threshold greater than 50% below which reorder points increase with a decrease in lead time variability. Thus, for a firm operating just below this threshold, reducing lead times decreases reorder points, whereas reducing lead time variability increases reorder points. For firms operating at these service levels, decreasing lead time is the right lever if they want to cut inventories, not reducing lead time variability.     

Inventory Positioning/Partitioning for Backorders Optimization for a Class of Multi-Echelon Inventory Problems*

Inventory management has undergone significant philosophical changes in recent decades such as the advent of the zero inventory concept. However, as attractive as the concept of minimal inventories may be, it is often unrealistic in application. Attention to basic features of inventory control systems such as order quantities, base stock levels, and reorder points remain crucial to ensure customer service at minimal cost. A nonlinear optimization model for determining base stock levels in a multi-echelon inventory network is presented. Lagrangian relaxation results in (1) newsboy-style relations that provide the optimal solutions, and (2) instantaneous shadow prices for the budget constraint. Sensitivity analysis of this model will facilitate making decisions concerning the desired investment in inventory for the entire system. This model may be solved on standard nonlinear programming software and is generalizable to problems in both production and distribution settings.     

Determining the Critical Elements of Just-In-Time Implementation

There are a limited number of papers dealing primarily with the implementation aspect of JIT. While the literature shows almost general agreement on the critical elements of JIT implementation, few empirical studies exist to support the proposed elements. The purpose of this study is to identify the elements of JIT implementation that are required to ensure successful implementation. A number of implementation elements were identified and subsequently grouped into a hierarchical structure consisting of four broader elements. Criteria were selected as measures of the level of implementation success. Analysis revealed that only a few of the identified elements were indeed required for successful JIT implementation.