Farrokh Nasri

Setup cost reduction in an inventory model with finite-range stochastic lead times

SUMMARY Traditionally, upon solution, independent demand inventory models result in the determination of a closed form for the economic lot size. Generally, this is obtained from the result that holding costs and setup costs are constant and equal at the optimum. However, the experience of the Japanese indicates that this need not be the case. Specifically, setup cost may be reduced by investing in reduced setup times resulting in smaller lot sizes and increased flexibility. Various authors have investigated the impact of such investment on classical lot sizing formulas which has resulted in the derivation of modified relationships. A common assumption of this research has been that demand and lead time are deterministic. This paper extends this previous work by considering the more realistic case of investing in decreasing setup costs where lead time is stochastic. Closed form relationships for optimal lot size, optimal setup cost, optimal total cost, etc. are derived. Numerical results are presented for...

Defective units in a continuous review (s, Q) system

This paper considers the number of defective items in a lot to be a random variable and derives a modified (s, Q) model with stochastic demand and constant lead time. The paper develops explicit results for the case of exponential and uniform demand during lead time when the number of defective items in a lot follows a binomial process. It also investigates the effect of lower setup costs on the operating characteristics of the model. A numerical example is given and sensitivity analysis is performed.

Quality improvement and setup reduction in the joint economic lot size model

Abstract The co-maker concept has become accepted practice in many successful global business organizations. This fact has resulted in a class of inventory models known as joint economic lot size (JELS) models. Heretofore such models assumed perfect quality production on the part of the vendor. This paper relaxes this assumption and proposes a quality-adjusted JELS model. In addition, classical optimization methods are used to derive models for the cases of setup cost reduction, quality improvement, and simultaneous setup cost reduction and quality improvement for the quality-adjusted JELS. Numerical results are presented for each of these models. Comparisons are made to the basic quality-adjusted model. Results indicate that all three policies exhibit significantly reduced total cost. However, the simultaneous model results in the lowest cost overall and the smallest lot size. This suggests a synergistic impact of continuous improvement programs that focus on both setup and quality improvement of the vendors production process. Sensitivity analysis indicates that the simultaneous model is robust and representative of practice.

Environmental versus quality standards ‐ an overview and comparison

Considers the series of environmental standards known as ISO 14000. Presents an overview of the organization‐processes group of these standards, and a comparison with the existing quality standards ‐ ISO 9000 and the Malcolm Baldrige National Quality Award. ISO 14000 is concerned with establishing guidelines and principles for the management of environmental matters by organizations, through the establishment and operation of an environmental management system (EMS). Finds there is synergy between a quality management system (QMS) and an EMS; that like a QMS, an EMS must be an integral part of an organization’s overall management system; and that like a QMS, the design of an EMS is an ongoing process of continuous improvement. Concludes with several proposed research questions.

Lead-time variability reduction in stochastic inventory models

Abstract This research is motivated by the realization that Japanese manufacturers have devoted much time and effort to establish a long term partnership with their suppliers in order to reduce lead-time uncertainty. It is very common for a Japanese manufacturer to advance money to finance its suppliers and help them meet the rigid delivery standards imposed. However, there have been very few mathematical analyses of the advantages of investing in such efforts. The main objective of this paper is to provide an analytical model to quantify the tradeoffs associated with lower lead-time uncertainty. In particular, we consider the option of investing in order to reduce the lead-time variance in an inventory model with stochastic lead time. The paper also considers the option of investing in both setup cost and lead-time variability reduction. Numerical results are presented to demonstrate the use of the models. Sensitivity analysis is performed to indicate under what conditions investment is warranted.

A comparison of alternative joint vendor-purchaser lot-sizing models

Abstract This paper provides a comparative analysis of two sets of alternative joint lot-sizing models for the general one-vendor, many-nonidentical-purchasers case. Specifically, the basic joint economic lot size (irJELS) and individually responsible and rational decision (IRDD) models, and the simultaneous setup cost and order cost reduction versions are explored. Models for the latter situation are derived by the use of classical optimization techniques. A numerical example is presented which provides the basis for comparison of the models with the results of independent optimization (IO). For the basic models the previously reported advantages of IRRD are refuted. In the simultaneous investment case both the vendor and the purchasers realize significant savings over IO when the JELS policy is followed. This is not true for IRRD. This suggests that when an environment of co-operation between the parties has been established the JELS is a superior policy.

Quality improvement in an inventory model with finite-range stochastic lead times

Typically, traditional inventory models operate under the assumption of perfect quality. In this paper we modify an inventory model with finite-range stochastic lead time to allow for a random number of defective units in a lot. However, there is an extra cost for holding the defective items in the lot for the period before it is returned to the supplier. This paper also considers the option of investment to improve quality. Closed-form relationships are obtained for a quality-adjusted model as well as a quality improvement model. Numerical examples confirm that the option of investment in quality improvement results in significant cost savings. Sensitivity analysis shows that the quality improvement model is robust.

Investing in Lead-Time Variability Reduction in a Quality-Adjusted Inventory Model with Finite-Range Stochastic Lead-Time

We study the impact of the efforts aimed at reducing the lead-time variability in a quality-adjusted stochastic inventory model. We assume that each lot contains a random number of defective units. More specifically, a logarithmic investment function is used that allows investment to be made to reduce lead-time variability. Explicit results for the optimal values of decision variables as well as optimal value of the variance of lead-time are obtained. A series of numerical exercises is presented to demonstrate the use of the models developed in this paper. Initially the lead-time variance reduction model (LTVR) is compared to the quality-adjusted model (QA) for different values of initial lead-time over uniformly distributed lead-time intervals from one to seven weeks. In all cases where investment is warranted, investment in lead-time reduction results in reduced lot sizes, variances, and total inventory costs. Further, both the reduction in lot-size and lead-time variance increase as the lead-time interval increases. Similar results are obtained when lead-time follows a truncated normal distribution. The impact of proportion of defective items was also examined for the uniform case resulting in the finding that the total inventory related costs of investing in lead-time variance reduction decrease significantly as the proportion defective decreases. Finally, the results of sensitivity analysis relating to proportion defective, interest rate, and setup cost show the lead-time variance reduction model to be quite robust and representative of practice.

Yield improvement and yield variability reduction in an EOQ model with planned shortages and random yield

Three models for improving yield rate and reducing yield variability are developed.The optimal values of the policy variables and costs are presented in explicit form.In all three models investment programs lead to yield improvement and cost savings. This paper reports the results of an investigation of a set of continuous time, constant demand inventory models under the condition of yield uncertainty. Specifically, the impact of yield improvement programs on lot size, backorder level, and the resulting costs are examined. Models for improving yield rate and reducing yield variability are developed and examined through a series of numerical exercises. In addition, a model for the simultaneous improvement of yield rate and yield variability is presented for the case where there is a relationship between the mean and variance of the yield distribution. In all cases, investment programs improve the picture with respect to manufacturing yield for processes which are not necessarily under statistical control.

An analysis of setup cost reduction in a two stage system with power investment function

Recently, a framework for analyzing investment decisions as they relate to setup cost reduction in two stage production processes has appeared in the literature. Closed form results were developed for the case of logarithmic investment function. This paper extends the results to the case of power investment function. We present an algorithm for calculating the optimal values of the decision variables. A numerical example is utilized to reveal some interesting aspects of this system.