A NOTE ON INTEGRATING INVENTORY AND PRODUCT SALES-MIX MODELS

In a recent issue of Decision Sciences, Raiborn and Harris [2] discussed the integration of inventory and product sales-mix models. While they formulated a model which reflected some of the interactions between product sales-mix and inventory decisions, the purpose of this note is to point out deficiencies in their decision rule analysis for solving such integrated models.     

PRODUCT LINE AND INVENTORY STRATEGY

The problem of optimal variety in inventory heretofore has been approached on an individual item basis. This paper demonstrates the analysis of aggregate inventory through the use of the log-normal distribution. The theory and application of this distribution to inventory problems are reviewed. This distribution is then applied to the problem of optimal variety, measuring the impact on sales and cost of deletion of slow-moving items in order to determine the optimal assortment for profitability. This then leads to analysis of optimal margin determination for slow-moving items. The final part of the discussion deals with inventory characteristics of the distribution channel, utilizing the characteristics of the log-normal distribution.     

ON-LINE QUALITY MANAGEMENT: INTEGRATION OF PRODUCT INSPECTION AND PROCESS CONTROL

A growing recognition that quality management is an important factor in defining a firm's competitive position has led to renewed attention to this function and has resulted in implementation of elaborate systems for on-line quality control comprising product inspection and process control. Traditionally, these functions have been treated independently, with very little interaction. In this paper we examine, in detail, a scheme that integrates the two functions, and we demonstrate that such an approach can result in significant cost savings. The motivation for this work comes from our experience in a wafer fabrication facility that suggested that exchange of quality information between different stages of production could result in significant performance improvements. To illustrate this approach, we consider a specific environment characterized by a single-stage continuous production process whose status is monitored by an X̄ control chart. We assume that quality-related costs may be described as a function of the process output. This is analogous to Taguchi's quality loss function and may be interpreted as a generalization of conventional classification of process output as either acceptable or defective units. The integrative scheme essentially relies on utilization of the process status information (based on process control) in making product inspection decisions. For this system we derive a cost model and develop a solution procedure to determine optimal decision parameters. Limited computational results indicate that the scheme has significant potential for reducing quality-related costs.     

AN EMPIRICAL EVALUATION OF CONSTANT AND ADAPTIVE COMPUTER FORECASTING MODELS FOR INVENTORY CONTROL

This study compares the performance of one constant model with two adaptive models. MAD and bias were used as criteria for evaluating performance. The results of testing the adaptive models with the constant model were contrary to the expected better performance of the adaptive models; no significant differences were found between the models over known horizontal, trend, and seasonal demand patterns. However, some of the practical advantages of adaptive forecasting models in business suggest their continued use.     

AN APPLICATION OF INVENTORY THEORETICAL MODELS TO CASH COLLECTION

A problem common to all companies operating widely dispersed revenue-generating outlets is that of transferring these revenues to central accounts. Company funds held in local banks represent an unusable asset that, in view of the high opportunity cost of money, may substantially increase operating costs. A wide variety of systems can be devised to effect this transfer process. As an example of such systems, this paper examines a transfer procedure that uses depository transfer checks. It is shown that a simple (s, S) policy characterizes the optimal transfer policy.     

INCREMENTAL (MARGINAL) ANALYSIS OF BASIC INVENTORY MODELS

For simple inventory models with linear costs and stochastic demands, the technique of incremental analysis is applied to the problem of determining both the optimum number of units to stock and the associated expected profit. The cases where there are shortage costs and where reordering is possible are covered. Sensitivity analysis of optimum solutions is shown to be useful and straightforward. Problems involving cost minimization, rather than profit maximization, are discussed. The emphasis is on discrete probability distributions of demand, but the extensions to continuous probability distributions are clearly indicated.     

INVENTORY MODELS: OPTIMIZATION BY GEOMETRIC PROGRAMMING

Geometric programming is a mathematical programming technique that is designed to determine the constrained minimum value of a generalized polynomial objective function. To date, most applications of the technique have been restricted to certain classes of engineering problems. This paper presents a brief summary of geometric programming and then illustrates its application to managerial problems by applying it to three well-known inventory models.     

THE INTERACTION OF TRANSPORTATION AND INVENTORY DECISIONS

The management of inventories and determination of transportation policy are normally carried out by different groups of people in an organization. These activities interact, however, when the transportation is used to replace inventory and when the transportation alternatives have different speed, reliability, and cost characteristics. This paper presents exact and heuristic procedures for jointly determining the inventory reorder points, order quantities, and transportation alternatives that provide minimum total transportation and inventory costs. The effectiveness of each procedure is demonstrated for a broad range of problems. The heuristic procedure was also applied to actual company data to determine the potential for cost savings. The results showed that savings were possible both from improving the current procedures and from applying the procedure developed in this study.     

OPTIMALITY OF STATE-DEPENDENT (s,S) POLICIES IN INVENTORY MODELS WITH MARKOV-MODULATED DEMAND AND LOST SALES

Markov-modulated processes have been used in stochastic inventory models with setup costs for modeling demand under the influence of uncertain environmental factors, such as fluctuating economic and market conditions. The analyses of these models have been carried out in the literature only under the assumption that unsatisfied demand is fully backlogged. The lost sales situation occurs in many retail establishments such as department stores and supermarkets. We use the analysis of the Markovian demand model with backlogging to analyze the lost sales case; in particular, we establish the optimality of an (s, S)-type policy under fairly general conditions.     

BAYESIAN MODELS FOR NEW PRODUCT PRICING

This paper develops an information decision system for new product pricing based on Bayesian updating of prior estimates of demand distribution parameter values and on optimization by dynamic programming. The model considers the interaction of production and pricing decisions and emphasizes the simultaneous making of both decisions. After presentation of the basic model, approximate techniques are introduced which obtain most of the benefit of the approach while requiring only a fraction of the computer cost and input data. Numerical examples using growing demand and price sensitivity are given to demonstrate the high computer cost of the first model and the relative performance (on a profit basis) of the approximate techniques.     

RETURN ON INVESTMENT AS A CRITERION FOR INVENTORY MODELS

In the past most inventory formulations have utilized cost minimization or profit maximization as an optimizing criterion. When viewed from the standpoint of the owner or investor, maximizing the return on investment (ROI) is an appropriate criterion for many types of inventories. This paper proposes ROI as a criterion for inventory models and derives optimal reorder rules for some common assumptions. An economic order quantity that differs greatly from the traditional formulas is discussed. The paper also enumerates the conditions under which ROI is an appropriate criterion and contrasts it to the traditional cost minimization and profit maximization criteria.     

SIMPLE MODELS FOR MONITORING NEW PRODUCT PERFORMANCE

Several studies have shown that consumers trying a new brand of frequently purchased consumer goods behave differently from repeat buyers. The “customer mix” for a new brand changes over time. Early in a new brand's life, most of the buyers are triers, while later in its life, a significant portion of the buyers are repeaters. The study presented here tests the hypothesis that an aggregate sales forecast, “averaging” the behaviors of triers and repeaters, would be outperformed by a model that treats them separately. A new product model, giving separate consideration to triers and repeaters, is developed. This model is tested on predictive ability against a widely used single-equation aggregate model. Consumer panel purchase diaries and data on advertising in measured media, covering a period of 42 months following introduction of a major brand of cold tablets, serve as the proving grounds. Data for the early part of this period serve as the data base for both models, while data for the rest of the period serve to test the predictive ability of both models. The disaggregate model is shown to perform significantly better than the aggregate model in terms of predictive accuracy. It also offers several other advantages in use as a decision aid, both for GO-NO decisions and for marketing mix decisions. Finally, several problems in the implementation of the proposed model and implications for research strategy are discussed.     

PRICE‐DEPENDENT INVENTORY MODELS WITH DISCOUNT OFFERS AT RANDOM TIMES*

We consider an inventory model with a supplier offering discounts to a reseller at random epochs. The offer is accepted when the inventory position is lower than a threshold level. We compare three different pricing policies in which demand is induced by the resellers price variation. Policy 1 is the EOQ policy without discount offers. Policy 2 is a uniform price, stock‐independent policy. Policy 3 is a stock level‐dependent, discriminated price policy. Assuming constant demand rates, expressions are obtained for the optimal order quantities, prices, and profits. The numerical experiments show that if it is better to accept a suppliers discount, then it benefits the reseller to transfer the discount to downstream customers.     

SPECIFICATION AND ESTIMATION OF LOGICALLY CONSISTENT LINEAR MODELS

The implications of constrained dependent and independent variables for model parameters are examined. In the context of linear model systems, it is shown that polyhedral constraints on the dependent variables will hold over the domain of the independent variables when a set of polyhedral constraints is satisfied by the model parameters. This result may be used in parameter estimation, in which case all predicted values of the dependent variables are consistent with constraints on the actual values. Also, the implicit constraints that define the set of parameters for many commonly used linear stochastic models with an error term yield values of the dependent variables consistent with the explicit constraints. Models possessing these properties are termed “logically consistent”.     

COMPUTER-INTEGRATED MANUFACTURING: A TAXONOMY OF INTEGRATION AND RESEARCH ISSUES

The past decade has seen an upsurgence in the number of manufacturing companies that are attempting to transform into computer-integrated enterprises. However, much of the computer-based integration efforts in these manufacturing organizations have been limited in scope and localized within certain areas of the organization (particularly, technology-intensive areas such as the shop floor). Such compartmentalized and myopic approaches to the development of computer-integrated manufacturing (CIM) systems undermine the ability of these systems to reach their fullest potential. CIM is much larger in scope and can impact an organization along various dimensions and at various levels. The fact that no completely integrated manufacturing enterprise has been developed to date can be attributed, in part, to a lack of understanding of the scope and implications of CIM. The purpose of this paper is, therefore, twofold. First, the paper presents a meta-schema (called TRIAD) for multidimensional and multilevel integration of a manufacturing system. Second, on the basis of the proposed meta-schema, the paper develops a taxonomical framework for defining key integration issues in CIM system design and discusses critical research needs that exist in this area. It is hoped that this paper will serve as a road map for research efforts that will enable the emergence of comprehensive CIM systems.     

DEEP FINANCIAL INTEGRATION AND VOLATILITY

We investigate the relationship between foreign direct ownership of firms and firm‐ and region‐level output volatility using a novel panel data set for European countries. We document a positive, highly robust, relationship between firm‐level foreign ownership and volatility of value added. This relationship holds cross‐sectionally and in panels with firm fixed effects where the relationship captures within‐firm variation over time. Considering domestic firms with assets in foreign countries, we document that it is international diversification, rather than the nationality of the owner, that explains this positive correlation. Our results can also be found at the aggregate level, where we show that region‐level volatility is correlated positively with foreign investment in the region. We show that this positive relation between aggregate volatility and foreign investment can be explained by the granularity of the firm size distribution and the fact that foreign ownership is concentrated among the largest firms.     

MULTI-MACHINE,MULTI-PRODUCT PRODUCTION SCHEDULING AND INVENTORY CONTROL

This paper deals with a multi-machine, multi-product lot size determination and scheduling problem. The model developed here considers not only the usual inventory-related operational cost, but also the costs that depend on under- or over-utilization of available men and machines. It penalizes overtime or idle time at any facility. The solution minimizes the inventory and resource-related costs and not just inventory costs. A heuristic is developed to determine the solution from the model and to modify it, as necessary, to obtain a conflict-free, repetitive, and cyclic production schedule for an infinite horizon. Although this model is developed for a manufacturing situation, the words machine, job, and machine shop are used in a symbolic sense, and hence the model can be used in practice in a variety of circumstances.     

SHAREHOLDER LIMITED LIABILITY AND MEAN-VARIANCE MODELS OF CAPITAL STRUCTURE*

This paper demonstrates that shareholder limited liability imposes a restriction on corporate borrowing and that failure to incorporate this restriction into the analysis yields the “reductio ad absurdum” argument against mean-variance models of optimal capital structure. With corporate income taxes and costless bankruptcy, the firm's value is a monotonically increasing function of debt as long as the amount of debt does not exceed the upper limit imposed by shareholder limited liability. As a result, the introduction of costly bankruptcy into the mean-variance framework is justified.