Sampath Rajagopalan

Make to Order or Make to Stock: Model and Application

Some firms make all their products to order while others make them to stock. There are a number of firms that maintain a middle ground, where some items are made to stock and others are made to order. This paper was motivated by a consumer product company faced with the decision about which items to make to stock and which ones to make to order, and the inventory and production policy for the make-to-stock items. The production environment is characterized by multiple items, setup times between the production of consecutive items, limited capacity, and congestion effects. In such an environment, making an item to order reduces inventory costs for that item, but might increase the lot size and inventory costs for the items made to stock. Also, lead times increase because of congestion effects, resulting in higher safety stocks for make-to-stock items and lower service levels for make-to-order items, thus leading to a complex trade-off. We develop a nonlinear, integer programming formulation of the problem. We present an efficient heuristic to solve the problem, which was motivated by key results for a special case of the problem without congestion effects that can be solved optimally. We also develop a lower bound to evaluate the performance of the heuristic. A computational study indicates that the heuristic performs well. We discuss the application of the model in a large firm and the resulting insights. We also provide insights into the impact of various problem parameters on the make-to-order versus make-to-stock decisions using a computational study. In particular, we find that the average number of setups of an item selected for make-to-stock production is always less than half the average number of setups of the item if it were to be made to order. Also, factors other than an items demand, such as its setup time, processing time, and unit holding cost, impact the make-to-order versus make-to-stock decision.

Have U.S. Manufacturing Inventories Really Decreased? An Empirical Study

Numerous normative models have been developed to determine optimal inventory levels, and several articles and case studies have been written about the concerted efforts and practices adopted by manufacturing firms in the United States to reduce inventories. But little is known about whether inventories have indeed decreased in U.S. manufacturing and whether such a decrease has been restricted to a few well-publicized firms or is true at an industry level. Using data published by the U.S. Census Bureau, the authors study trends in materials, work-in-process, and finished-goods inventory ratios during the period 1961 to 1994 in 20 manufacturing industry sectors and the total U.S. manufacturing sector to determine whether a significant decrease was seen in these ratios. Further, since a great deal of momentum for inventory reduction began in the early 1980s, the authors investigate whether greater improvement was seen in the post-1980 period as compared with the pre-1980 period. We find that material and work-in-process inventories did decrease in a majority of the two-digit industry sectors from 1961 to 1994 and showed greater improvement in about half the sectors in the post-1980 period relative to the pre-1980 period. Finished-goods inventories did decrease in some industry sectors and increase in a few others but did not show a significant trend in more than half the sectors. Total manufacturing inventory ratios decreased from 1961 to 1994 at all three stages--material, work-in-process, and finished goods. However, total manufacturing inventory ratios did not improve at a higher rate during the post-1980 period as compared with the pre-1980 period in any of the three stages. Overall, the analysis provides an encouraging but somewhat mixed picture about the results of U.S. manufacturing inventory-reduction efforts.

Capacity Expansion and Equipment Replacement: a Unified Approach

Businesses frequently have to decide which of their existing equipment to replace, taking into account future changes in capacity requirements. The significance of this decision becomes clear when one notes that expenditure on new plant and equipment is a significant proportion of the GDP in the United States. The equipment replacement literature has focused on the replacement issue, usually ignoring aspects such as future demand changes and economies of scale. On the other hand, the capacity expansion literature has focused on the expansion of equipment capacity to meet demand growth, considering economies of scale but ignoring the replacement aspect. This paper attempts to unify the two streams of research by developing a general model that considers replacement of capacity as well as expansion and disposal, together with scale economy effects. Even special cases of the problems discussed here, such as the parallel machine replacement problem, have been considered difficult so far. However, we show that the problem can be solved efficiently by formulating it in a novel, disaggregate manner and using a dual-based solution procedure that exploits the structure of the problem. We also provide computational results to affirm that optimal or near-optimal solutions to large, realistic problems can be determined efficiently. We demonstrate the robustness of this approach by showing how other realistic features such as quantity discounts in purchases, alternative technology types or suppliers, and multiple equipment types can be incorporated.

Revenue Sharing and Information Leakage in a Supply Chain

This work explores the potential of revenue-sharing contracts to facilitate information sharing in a supply chain and mitigate the negative effects of information leakage. We consider a supplier who offers a revenue-sharing contract to two competing retailers, one of whom has private information about uncertain market potential and orders first. This order information may be leaked to the uninformed retailer by the supplier to realize higher profits. We show that the incentives of the supplier and retailers are better aligned under a revenue-sharing contract, as opposed to under a wholesale-price contract, reducing the suppliers incentive to leak. This is true for a wide range of wholesale prices and revenue-share percentages and is more likely when the revenue-share percentage is higher and when variation in demand is greater. Preventing information leakage may result in higher profits not only for the informed retailer and supplier but surprisingly even for the uninformed retailer. Our results are robust when the model is generalized along various dimensions. This paper was accepted by Yossi Aviv, operations management.

The impact of quality on learning

Abstract The strategic importance of learning curves has been recognized for a long time both in industry and in academia, but little is known about the huge difference in rates at which different firms learn. Recent theoretical studies and anecdotal evidence from Japanese manufacturing firms suggest that quality-related activities may be one major factor explaining the difference in learning rates. When the impact of quality on learning is considered, three important questions arise: (1) How well does cumulative output of defective or good units explain learning curve effects? (2) Do defective units explain learning curve effects better than good units? (3) How should cumulative experience be represented in the learning curve model when the quality level may have an impact on learning effects? This paper presents, to our knowledge, the first empirical study addressing these questions. Using time series data from two manufacturing firms, we find that cumulative output of defective or good units is statistically significant in explaining learning curve benefits. However, defective and good units do not explain learning curve effects equally as is implicitly assumed in traditional learning curve models. In particular, defective units are statistically more significant than good units in explaining learning curve effects.

Inventory Models for Substitutable Products: Optimal Policies and Heuristics

In this paper, we examine the nature of optimal inventory policies in a system where a retailer manages substitutable products. We first consider a system with two products 1 and 2 whose total demand is D and individual demands are negatively correlated. A fixed proportion of the unsatisfied customers for an item will purchase the other item if it is available in inventory. For the single-period case, we show that the optimal inventory levels of the two items can be computed easily and follow what we refer to as “partially decoupled” policies, i.e., base stock policies that are not state dependent, in certain critical regions of interest both when D is known and random. Furthermore, we show that such a partially decoupled base-stock policy is optimal even in a multiperiod version of the problem for known D for a wide range of parameter values and in an N-product single-period model under some restrictive conditions. Using a numerical study, we show that heuristics based on the decoupled inventory policy perform well in conditions more general than the ones assumed to obtain the analytical results. The analytical and numerical results suggest that the approach presented here is most valuable in retail settings for product categories where the level of substitution between items in a category is not high, demand variation at the aggregate level is not high, and service levels or newsvendor ratios are high.

A Coordinated Production Planning Model with Capacity Expansion and Inventory Management

Motivated by a problem faced by a large manufacturer of a consumer product, we explore the interaction between production planning and capacity acquisition decisions in environments with demand growth. We study a firm producing multiple items in a multiperiod environment where demand for items is known but varies over time with a long-term growth and possible short-term fluctuations. The production equipment is characterized by significant changeover time between the production of different items. While demand growth is gradual, capacity additions are discrete. Therefore, periods immediately following a machine purchase are characterized by excess machine capacity. We develop a mathematical programming model and an effective solution approach to determine the optimal capacity acquisition, production and inventory decisions over time. Through a computational study, we show the effectiveness of the solution approach in terms of solution quality and investigate the impact of product variety, cost of capital, and other important parameters on the capacity and inventory decisions. The computational results bring out some key insights--increasing product variety may not result in excessive inventory and even a substantial increase in set-up times or holding costs may not increase the total cost over the horizon in a significant manner due to the ability to acquire additional capacity. We also provide solutions and insights to the real problem that motivated this work.

A learning curve model with knowledge depreciation

Abstract Empirical studies in several industries have verified that unit costs decline as organizations gain experience or knowledge in production, which is referred to as the learning curve effect. In the past two decades, there has also been analytical work on the relationship between a firms learning curve effects and its pricing and output decisions. Learning rates differ significantly across firms in the same industry and recent empirical evidence has shown that knowledge depreciation may be an important reason for these differences. We propose and analyze a learning curve model with knowledge depreciation and provide several new insights. First, we show that there exists a steady state where knowledge level and unit cost remain constant over time and there exists an optimal path to this steady state. Many empirical researchers have observed this ‘plateau’ phenomenon, whereby unit costs decline but reach saturation after some time. While this has been traditionally modeled exogenously in the learning curve literature by assuming that cost reduction stops at some level of knowledge through a convex, decreasing unit cost function, we provide an alternative endogenous explanation. We are also able to show that, unlike in the model without knowledge depreciation, the production rate along the optimal path to the steady state may decrease over time. Also, the knowledge level along the optimal path may actually decline over time. Finally, we show that the optimal production rate decreases at higher interest rates and increases at higher knowledge depreciation rates. In turn, this implies that a high interest rate environment discourages firms from achieving high knowledge levels and results in higher prices. On the other hand, higher knowledge depreciation rates result in higher production rates and lower prices.

Standard vs. Custom Products: Variety, Lead Time, and Price Competition

In this paper, we study the standardization and customization decisions of two firms in a competitive setting, along with variety, lead time, and price decisions. We incorporate consumer heterogeneity both in firm preference (or store convenience) and in product attribute preferences. We find that the equilibrium outcome depends on the cost efficiencies of the production technologies as well as the consumer sensitivity to product fit and lead time. We develop an index that signifies the relative attractiveness of the standardization and customization strategies, and the potential outcomes. We identify the strategic roles of product variety and lead time in the competition. In contrast to the previous literature, we find that increasing the variety will not intensify the price competition if there is sufficient firm differentiation. Rather, it relieves the price pressure for the firm as it satisfies consumer needs better and enables higher price premiums. We also analyze the impact of asymmetric variable costs, fixed costs, and brand reputation on the equilibrium decisions.

Capacity planning with congestion effects

Abstract Important operational performance measures for a successful firm include not only price and quality, but also fast and on time delivery of customer orders. Capacity is a key issue in determining the lead time from customer order to delivery. However, capacity planning models seldom consider the impact of capacity levels on lead time performance. An important characteristic of this paper is the incorporation of congestion effects and their impact on lead time in making capacity acquisition decisions. It is especially important in a make-to-order environment, where customer orders arrive randomly and lead to high variability and congestion. This work was motivated by our observations of such tradeoffs at firms in several industries. We present a model to make equipment choice decisions in a multi-product, multi-machine, and single-stage production environment with congestion effects. The model is a nonlinear integer program. We present a heuristic solution procedure for this problem, which is based on a lower bound for the formulation that can be solved efficiently. The computational study shows that the solution procedure is quite effective in solving industry size problems. We illustrate the application of the model using data from a chemical-testing laboratory. We also discuss various extensions of the model.