Optimal lot sizing under continuous price decrease

An important characteristic of high-tech industries is decreasing component prices over time. In the personal computer industry, some component prices decline at a rate of 1% per week. This paper develops an inventory model for products experiencing continuous decrease in unit price. We develop an accurate closed-form approximate solution to the model. Our results indicate that declining prices lead to substantial decrease in the optimal cycle time and much frequent ordering. This explains the heavy emphasis on just-in-time inventory management practiced by successful companies in high-tech industries. While previous models attributed the success of just-in-time policies to reduced holding cost and improved quality, under declining prices a substantial source of savings becomes lower costs of raw materials which is significant part of cost in these industries. We illustrate the results of the model with a numerical example and perform sensitivity analysis.     

Acquisition of Telecommunications Bandwidth Under Economies of Scale in Size and Duration of Contracts*

Significant advances in information technology have brought about increased demand for bandwidth. Buyers of bandwidth often encounter bandwidth prices that are decreasing over time. Additionally, bandwidth prices at any point in time are decreasing in total bandwidth purchased and length of contracts. Therefore, buyers face complex decisions in terms of the number of contracts to buy, their bandwidth, and their lengths. In this article, we formulate models for the acquisition of bandwidth from a buyer's perspective. We begin with a model that allows varying contract durations under deterministic demand and without allowing shortages or overlapping contracts. We then formulate a simpler model, which restricts contract lengths over the planning horizon to be equal. We also solve the problem under probabilistic demand and allowing for shortages, which are satisfied by buying additional bandwidth at a premium. We perform numerical sensitivity analysis to compare the results of the models and illustrate the results with numerical examples. The numerical analyses illustrate that using relatively simple equal‐length contracts produces approximately the same results as the more complicated unequal‐length contract strategy.     

A comparison between genetic algorithms and the RAND method for solving the joint replenishment problem

The purpose of this paper is to compare the performance of genetic algorithms (GAs) and the best available heuristic, known as the RAND, for solving the joint replenishment problem (JRP). An important feature of the JRP which makes it suitable for GAs is that it can be formulated as a problem having one continuous decision variable and a number of integer decision variables equal to the number of products being produced or ordered. Experiments on randomly generated problems indicate that GAs can provide better solutions to the JRP than the RAND for some problems, and at worst can almost match the performance of the RAND from a practical point of view for the rest of the problems. GAs never converged to solution with a total cost of more than 0.08% of the total cost of the RAND for 1600 randomly generated problems. In addition, GAs have the advantages of: (i) being easy to implement (e.g. less than 200 lines of code); (ii) having a code which is easy to understand and modify; and (iii) dealing easily with constrained JRPs which are neglected by most of the available methods including the RAND, in spite of their importance in practice.     

A free gift card alternative to price discounts in the newsvendor problem

In this paper, we develop a newsvendor model in which the retailer gives “free” gift cards to consumers who purchase a regularly priced product at the end of the selling season instead of discounting the product. The model is developed for a market with patient consumers. We derive the sufficient optimality condition for the retailer's stocking level in the first period and the optimal gift card value in the second period. We also investigate the conditions under which giving gift cards results in higher expected profits than discounting the product. We find that five factors determine the effectiveness of gift cards. The first three factors are consumers' valuation per $1 of gift card, gift card redemption rates, and the average gross margin of the retailer. The last two factors are the degree to which consumers use gift cards to pay for products which they would have purchased from the retailer in the future with cash, and the additional spending above the gift card value consumers make when they redeem the card. The last two factors have a strong interaction. We also find that gift cards can be profitable when patient consumers consistently value each $1 by their redemption probability, even with 100% redemption. Numerical analysis shows that in the presence of patient consumers, increases in the redemption rate may lead to an increase in the expected profit. Similar counter-intuitive behavior of the expected profit occurs with changes in other problem parameters. The analysis also shows that gift cards' profit advantage over discounting increases with the variability of demand. The analysis also indicates that gift cards are most effective for low to medium priced products sold by high margin retailers.     

The Effect of Delayed Incentives on Supply Chain Profits and Consumer Surplus

We examine the use of consumer cash mail‐in rebates offered by a manufacturer in a Stackelberg game where the manufacturer is the leader and the retailer is the follower. Our analysis indicates that rebates are profitable for manufacturers if consumers are inconsistent in the sense that their rebate valuation when they make purchase decisions is independent of their redemption probabilities when they make redemption decisions. If the manufacturer keeps the wholesale price unchanged, then the rebate increases the retailer's profit by a larger amount than the increase in the manufacturer's profit. If the manufacturer jointly optimizes the wholesale price and rebate, then the increase in the manufacturer's profit is twice the increase in the retailer's profit. The retailer responds to rebates by increasing the retail price, which increases the margin paid by consumers who do not redeem the rebate. On average, consumer surplus decreases when it is optimal for manufacturers to offer rebates. We suggest incentive schemes that make it worthwhile for retailers to limit the price increase. In these incentive schemes, the manufacturer imposes a negative relationship between the rebate value and the retail price. We show that such incentives increase supply chain profits.     

An aggregate production planning framework for the evaluation of volume flexibility

Flexibility in manufacturing has been identified as one of the key factors to success in the marketplace. Many types of flexibility have been identified in the literature among which volume flexibility is one of the most important. Volume flexibility of a manufacturing system is defined as its ability to be operated profitably at different overall output levels. Volume flexibility permits a manufacturing system to adjust production upwards or downwards within wide limits. In this paper, we develop an aggregate production planning model for volumeflexible production systems. The model can be used with a Monte Carlo simulation to evaluate the optimal level of investment in volume flexibility for a firm operating under a given set of market conditions. In addition, the model can be used to develop some conclusions about the relationship between the value of volume flexibility and the cost of holding inventory, the cost of shortage, forecast accuracy, and the length of the planning horizon.