THE CLASSIC ECONOMIC PRODUCTION QUANTITY MODEL WITH SETUP COST AS A FUNCTION OF CAPITAL EXPENDITURE*

The formulation of the classic economic production quantity (EPQ) model is extended to include setup cost as a function of capital expense. Additional capital will buy reduced setup cost. Thus, the objective now is to balance holding, setup, and capital expenses. This new formulation is solved under conditions where setup cost varies exponentially and linearly as a function of capital expense. Decision rules are formulated to indicate under what conditions setup cost reduction reduces total cost. For the linear function, it is shown that once the decision to reduce setup cost is justified, the optimal choice is the minimum setup cost that is technologically feasible.     

MAXIMIZING THE PROBABILITY OF ACHIEVING A TARGET PROFIT IN A TWO-PRODUCT NEWSBOY PROBLEM*

This paper explores the two-product newsboy problem. Solution procedures are developed to find the optimal production quantities of each product that will maximize the probability of achieving a profit target. The problem is shown to be surprisingly challenging, and numerical results obtained for only the more restrictive cases exhibit interesting behavior with important decision implications. For example, the results suggest that, if a firm has two single-product divisions and each will receive a bonus for achieving a profit target, it is beneficial for the two divisions to cooperate if the targets are lax and the profit margins are high, but not if the targets are tight and the profit margins low. Also, between two products having different profit margins, one should produce more of the product with the lower profit margin if the target is sufficiently lax. This exploration motivates further efforts in solving the two-product problem for the more general cases and also in extending the problem to three or more products.     

TOTAL SETUP LOT SIZING WITH QUANTITY DISCOUNTS*

Often, order quantity decisions are made by purchasers facing a price schedule of quantity discounts. Traditional solution procedures have consisted of the evaluation of total cost at numerous price-break points in search of the lowest total cost. This approach is tedious and not particularly informative, especially when one is faced with lengthy schedules. This paper presents a total setup lot-sizing model that reduces the computations required to find the least-total-cost quantity, given parameters from a supplier's price schedule. The parameters are first obtained by simple regression (graphical or computer) and in themselves can provide valuable insight for the purchaser's decision making. A total setup lot-sizing model is next developed to define a “critical interval” that contains the solution. The model and algorithm are tested under a variety of conditions. Their application offers the decision maker a convenient alternative to determine the best quantity to order from a tendered price schedule.     

Some Comments on the Validity of EOQ Formula under Inflationary Conditions

In an earlier issue of Decision Sciences, Jesse, Mitra, and Cox [1] examined the impact of inflationary conditions on the economic order quantity (EOQ) formula. Specifically, the authors analyzed the effect of inflation on order quantity decisions by means of a model that takes into account both inflationary trends and time discounting (over an infinite time horizon). In their analysis, the authors utilized two models: Current-dollars model and Constant-dollars model. These models were derived, of course, by setting up a total cost equation in the usual manner then finding the optimum order quantity that minimizes the total cost. Jesse, Mitra, and Cox [1] found that EOQ is approximately the same under both conditions; with or without inflation. However, we disagree with the conclusion drawn by [2] and show that EOQ will be different under inflationary conditions, provided that the inflationary conditions are properly accounted for in the formulation of the total cost model.     

Generalizing the Announced Price Increase Problem*

This paper generalizes the announced price increase problem to consider a variety of practical concerns arising out of applications ranging from foreign exchange fluctuations to upper limits on the purchase of discounted supermarket items. These include limitations on the amount that can be purchased at the old price and/or on the length of the grace period, within which buyers may take advantage of this lower price. These constraints give rise to 16 possible situations. For each situation purchasing and inventory decision rules are developed. A numerical example is discussed to highlight the main features of the models.     

CHEXPEDITE: A COMPUTER-BASED APPROACH TO THE BANK COURIER PROBLEM

This paper presents a successful computer-based approach to scheduling courier vehicles for the check collection system in multibranch commercial banks. The approach has been adopted by six large banks in the United States and has achieved dramatic cost savings at several of these banks. This paper begins by describing the bank courier problem and reviewing several approaches to the problem that have been proposed in the literature. A practical, computer-based approach to the bank courier problem is then presented. Finally, implementation experience at several banks is overviewed.     

Determining Optimal Selling Price and Lot Size When the Supplier Offers All-Unit Quantity Discounts*

This paper is concerned with finding the optimal price and lot size for a retailer purchasing a product for which the supplier offers all-unit quantity discounts. Demand for the product is assumed to be a decreasing function of price, and a procedure is developed for finding the optimal price and lot size for a class of demand functions. The procedure then is applied to two common demand functions: (1) the constant price-elasticity function, and (2) the linear demand function.     

A MATHEMATICAL PROGRAMMING APPROACH TO SENSITIVITY ANALYSIS IN SINGLE-STAGE DECISION MAKING

This paper presents sensitivity analyses for a single-stage decision problem where an action which will maximize the expected payoff must be chosen from a finite number of actions given the states of nature, their probabilities, and the payoffs corresponding to each action and state of nature. Three types of sensitivity analysis are developed: (1) sensitivity analysis on the probabilities keeping the payoff numbers fixed, (2) sensitivity analysis on the payoffs keeping the probabilities fixed, and (3) joint sensitivity analysis on the payoffs and the probabilities. The approach is illustrated with an example. Quite often the sensitivity analysis can be conducted by solving an appropriate linear or quadratic programming problem.     

Multiechelon (R,S) Inventory Model*

Most studies in multiechelon inventory systems have concentrated on understanding the specific aspects of a system's behavior. The problem of optimal policy computation has largely been ignored. In this paper, we investigate a two-echelon inventory system experiencing stochastic demand and a pull system of inventory allocation. Both echelons use an order-up-to-level type control policy. A mathematical model is developed to determine the optimal order level at all echelons and validated through simulation. Two simple algorithms to locate the optimum solution are presented. The use of graphical tools in optimal policy calculation is also discussed.     

A PRACTICAL APPROACH TO THE LARGE-SCALE FOREST SCHEDULING PROBLEM*

A large-scale forest cutting schedule problem involving 1166 forest units to be cut over a 24–year planning period is discussed. The problem is formulated as a generalized version of the basic transportation problem. The conversion procedure for such a problem to the standard transportation format is outlined. The proposed approach is then compared with a linear programming decomposition approach on the basis of operating results obtained and computer time required by each approach. It is shown that this new approach will solve a real world problem about 40 times faster than the usual linear programming decomposition approach.     

Notes and Communications A NON-DUAL APPROACH TO SENSITIVITY ANALYSIS—THE RIGHT-HAND-SIDE CASE

Linear programming and sensitivity analysis in linear programming have long been integral parts of business school curricula, both at the undergraduate and graduate levels. Most business school students are required to take an introductory course in management science emphasizing linear programming and sensitivity analysis. This note is educational and presents a non-dual approach to restoring the optimal solution to a linear program when changes in the right-hand-side vector render the current solution infeasible and thus nonoptimal.     

A NOTE ON HOLDING COSTS AND LOT-SIZE ERRORS

This note examines the sensitivity of the basic economic-order-quantity inventory model to lot-size errors when holding costs are assumed to be a strictly increasing (though not necessarily linear) function of average inventory. In particular, we show that the penalty associated with ordering either too much or too little is a function not only of the size of the error but of the shape of the holding-cost curve as well. We demonstrate that, under certain conditions, even relatively small lot-size errors can be extremely costly.     

A CONJUNCTIVE-COMPENSATORY APPROACH TO THE SELF-EXPLICATION OF MULTIATTRIBUTED PREFERENCES*

Consumer choice among multiattributed products is modeled as a two-stage process in which a conjunctive stage (that eliminates products with one or more “totally unacceptable” attribute levels) is followed by a compensatory stage (that trades off remaining products on multiple attributes). A self-explicated preference measurement procedure based on the two-stage model yielded a slightly larger predictive validity compared to conjoint analysis.     

Designing Distribution Systems to Support Vendor Strategies in Supply Chain Management*

The interactions among a firm's distribution strategy, market share, and distribution costs are an important consideration in the design of supply chain networks. However, these interactions are largely ignored by existing distribution system design methodologies, which assume demand is constant regardless of the firm's distribution strategy. This paper describes a multidisciplinary framework that considers these interactions in the design of “profit maximizing” distribution networks. The framework employs two major decision support methodologies: (1) binary logit models for estimating market share considering various demand-influencing parameters such as product price and distribution service, and (2) a mixed-integer programming (MIP) model for finding optimal distribution network designs. We applied the framework to an actual design problem facing a national distributor of industrial chemical products. The test results verify the framework's large-scale capability and the potential benefit of the integrated solution methodology.     

DEGENERACY AND THE (MIS)INTERPRETATION OF SENSITIVITY ANALYSIS IN LINEAR PROGRAMMING

Under conditions of degeneracy, sensitivity analysis information such as cost and right-hand-side ranges, which are produced by standard linear programming procedures used in commercial codes, can be misleading. From a managerial perspective, the interpretation of such information can be erroneous. In this paper we present these problems, explain their occurence with elementary examples, and discuss procedures for their resolution.     

“A JOINT ECONOMIC-LOT-SIZE MODEL FOR PURCHASER AND VENDOR”: A COMMENT*

Banerjee [1] developed a joint economic-lot-size model for the case where a vendor produces to order for a purchaser on a lot-for-lot basis under deterministic conditions. The assumption of lot-for-lot bases is restrictive in nature. In this note, a more general joint economic-lot-size model is suggested and it is shown to provide a lower or equal joint total relevant cost as compared to the model of Banerjee.     

A SYSTEMS PERSPECTIVE ON MATERIAL REQUIREMENTS PLANNING*

For many companies, the implementation of material requirements planning systems has failed to produce the expected improvements in manufacturing efficiency. This paper shows that MRP failure can occur in the common situation in which MRP is installed in a manufacturing environment that has evolved around manual methods of material control. A system dynamics simulation model is used to interrelate decision functions (policies) of a manufacturing firm. Simulation runs of the model operating with manual methods of material control show six- to seven-year fluctuations in production, ordering, and labor. A modified version of the model, changed only by the introduction of a requirements explosion to represent MRP, shows that MRP can actually cause more severe production fluctuations, resulting in lower average labor productivity and higher manufacturing costs. The major practical implication of the analysis is that the organizational environment that suits MRP (and utilizes its inherent strengths) is different from the environment that is likely to prevail at the time of implementation.     

Optimal Policy for a Reseller When the Supplier Offers a Temporary Reduction in Price*

A common practice in product distribution is the case in which the supplier offers a temporary reduction in price. It is suggested in the literature that in such situations, the reseller may engage in forward buying (i.e., purchasing additional stock at the reduced price offered by the supplier for later sale at the regular selling price). In this paper, a model is formulated of the reseller's response when the supplier offers a temporary reduction in price. It is assumed that the market demand for the product is elastic with respect to the selling price the reseller sets. A procedure for determining the optimal response of the reseller is developed. The model presented in this paper can easily be adapted to the case in which the reseller faces a permanent increase in the price charged by the supplier.