Panos Kouvelis

Robust scheduling of a two-machine flow shop with uncertain processing times

This paper focuses on manufacturing environments where job processing times are uncertain. In these settings, scheduling decision makers are exposed to the risk that an optimal schedule with respect to a deterministic or stochastic model will perform poorly when evaluated relative to actual processing times. Since the quality of scheduling decisions is frequently judged as if processing times were known a priori, robust scheduling, i.e., determining a schedule whose performance (compared to the associated optimal schedule) is relatively insensitive to the potential realizations of job processing times, provides a reasonable mechanism for hedging against the prevailing processing time uncertainty. In this paper we focus on a two-machine flow shop environment in which the processing times of jobs are uncertain and the performance measure of interest is system makespan. We present a measure of schedule robustness that explicitly considers the risk of poor system performance over all potential realizations of job processing times. We discuss two alternative frameworks for structuring processing time uncertainty. For each case, we define the robust scheduling problem, establish problem complexity, discuss properties of robust schedules, and develop exact and heuristic solution approaches. Computational results indicate that robust schedules provide effective hedges against processing time uncertainty while maintaining excellent expected makespan performance

Financing the Newsvendor: Supplier vs. Bank, and the Structure of Optimal Trade Credit Contracts

We consider a supply chain with a retailer and a supplier: A newsvendor-like retailer has a single opportunity to order a product from a supplier to satisfy future uncertain demand. Both the retailer and supplier are capital constrained and in need of short-term financing. In the presence of bankruptcy risks for both the retailer and supplier, we model their strategic interaction as a Stackelberg game with the supplier as the leader. We use the supplier early payment discount scheme as a decision framework to analyze all decisions involved in optimally structuring the trade credit contract (discounted wholesale price if paying early, financing rate if delaying payment) from the suppliers perspective. Under mild assumptions we conclude that a risk-neutral supplier should always finance the retailer at rates less than or equal to the risk-free rate. The retailer, if offered an optimally structured trade credit contract, will always prefer supplier financing to bank financing. Furthermore, under optimal trade credit contracts, both the suppliers profit and supply chain efficiency improve, and the retailer might improve his profits relative to under bank financing (or equivalently, a rich retailer under wholesale price contracts), depending on his current “wealth” (working capital and collateral).

Supply chain capacity and outsourcing decisions: the dynamic interplay of demand and supply uncertainty

We study the interplay of demand and supply uncertainty in capacity and outsourcing decisions in multi-stage supply chains. We consider a firms investment in two stages of a supply chain (Stage 1 models the “core” activities of the firm, while Stage 2 are the “non-core” activities). The firm invests in these two stages in order to maximize the multi-period, discounted profit. We consider how non-stationary stochastic demand affects the outsourcing decisions. We also consider how investment levels are affected by non-stationary stochastic supply when the market responds to the firms investments. We characterize the optimal capacity investment decisions Tor the single- and multi-period versions of our model and focus on how changes in supply and demand uncertainly affect the extent of outsourcing. We find that as the responsiveness of the market to investments made by the firm increases, the reliance on outsourcing generally increases. While greater supply and greater demand have the expected effect on investments, decreases in variability are not as straightforward. Greater supply uncertainty increases the need for vertical integration while greater demand uncertainty increases the reliance on outsourcing. In the multi-period model, we find that the nature of adjustments in capacity based on changes in demand or supply follows from the comparative statics of the single-period model, although whether outsourcing increases or decreases depends on the costs of adjusting capacity.

Dynamic Pricing and Inventory Control of Substitute Products

We study dynamic pricing and inventory control of substitute products for a retailer who faces a long supply lead time and a short selling season. Within a multinomial logit model of consumer choice over substitutes, we develop a stochastic dynamic programming formulation and derive the optimal dynamic pricing policy. We prove that dynamic pricing converges to static pricing as inventory levels of all variates approach the number of remaining selling periods (assuming at most one customer arrival within each period). Our extensive numerical study of the effects of time and inventory depletion on the optimal pricing reveals two fundamental underlying driving forces of the complex price behavior: the level of inventory scarcity and the quality difference among products. We also compare the performance of three restricted pricing strategies: static, unified dynamic, and mixed dynamic pricing. We find that full-scale dynamic pricing is of great value in the presence of inventory scarcity, and initial inventory decisions are quite robust in the pricing scheme employed in the selling season. Based on the above insights, we propose a computationally efficient approach to the initial inventory decision, which delivers close-to-optimal inventory levels for all testing cases.

Order Quantity and Timing Flexibility in Supply Chains: The Role of Demand Characteristics

We study how differences in product demand characteristics affect the strategic value of different types of supply chain flexibility for accurate response. We propose a single-period inventory modelling framework with two ordering opportunities. The second order reflects updated demand information and potentially capitalizes on supply chain flexibility. We consider two complementary forms of flexibility: quantity flexibility in production and timing flexibility in scheduling. In this framework, we analyze the total inventory cost of a firm for alternate demand types. We model functional products through the standard assumption of independent demand over the period, fashion-driven innovative products through a Bayesian model, and innovative products with evolving demand through a Martingale process. The three demand processes exhibit very different behavior with respect to the value of the alternate forms of flexibility. We observe that quantity flexibility is of moderate value for functional goods and of high value for fashion-driven products for all lead times. Quantity flexibility is of low value for goods with evolving demand with long lead times but of high value for short lead times. Alternately, we observe timing flexibility is of highest value for functional goods, especially for cases of high holding cost, and is of lesser value for fashion-driven goods. It is of least value for goods with evolving demand. Both quantity and timing flexibility capabilities are required to significantly reduce the relevant supply chain costs for evolving-demand innovative goods when the lead times are long.

Exchange Rates and the Choice of Ownership Structure of Production Facilities

The aim of this research is to study the effects of real exchange rates on the long-term ownership strategies of production facilities of firms entering foreign markets. Among the strategies considered are exporting (EXP), joint ventures with local partners (JV), and wholly owned production facilities (WOS) in the foreign country. Our research takes a first step in modeling the influence of exchange rates on the choice and dynamic adjustment of such strategies. The insights obtained from our modeling analysis are then translated into testable hypotheses and empirically verified with the use of firm level data from U.S. multinational corporations (both at the firm and a more aggregate level). An insightful result of our model is the identification of a hysteresis phenomenon that characterizes switching behavior between strategies in the presence of switchover cost. The magnitude of the hysteresis band, which is a measure of the inertia associated with keeping the current ownership structure, is affected by a multiplicity of factors such as exchange rate volatility and market power of the entering firm. Analytical and numerical results on the effects of such factors on the hysteresis band are provided. The four testable hypotheses generated from our modeling analysis are rigorously tested with the use of a multinomial logit model on data obtained from the Harvard Multinational Enterprise database, and a data set maintained by the Bureau of Economic Analysis, the U.S. Department of Commerce. The empirical results strongly support our insights that relatively depreciated real exchange rates (i.e., weak home currency) favor (a) the JV over the WOS and (b) EXP mode over the WOS or JV. Finally, we summarize our results into useful guidelines for global production managers.

Quality-Based Competition, Profitability, and Variable Costs

We consider the impact of variable production costs on competitive behavior in a duopoly where manufacturers compete on quality and price in a two-stage game. In the pricing stage, we make no assumptions regarding these costs---other than that they are positive and increasing in quality---and no assumptions about whether or not the market is covered. In the quality stage, we investigate a broad family of variable cost functions and show how the shape of these functions impacts equilibrium product positions, profits, and market coverage. We find that seemingly slight changes to the cost functions curvature can produce dramatically different equilibrium outcomes, including the degree of quality differentiation, which competitor is more profitable (the one offering higher or lower quality), and the nature of the market itself (covered or uncovered). Our model helps to predict and explain the diversity of outcomes we see in practice---something the previous literature has been unable to do.

On the Complementary Value of Accurate Demand Information and Production and Supplier Flexibility

We study the value of information, production flexibility, and supplier flexibility for a good for which an initial and a subsequent order may be placed. We consider a Bayesian model of demand in which the unknown mean demand rate is assumed to have a prior, which is a mixture of two normal distributions corresponding to the demand forecast for an innovative (fashion) good. We develop three models of production flexibility: a static model requiring initial placement of both orders, a partially dynamic model requiring a fixing of the time that the second order will be made, and a fully dynamic model with no restrictions on ordering. Supplier flexibility is modeled through supply lead times. We observe that the magnitude of the savings from the static to the fully flexible model, corresponding to the sum of the values of information and production flexibility, reflects all sources of variability: differences between demand means of the prior mixture, variability within each prior, and variability about the observed mean. We observe that as the difference between high and low demand cases increases, the value of information increases, though for long lead times, production flexibility is required to take advantage of the updated information. Further, we observe that the greater the uncertainty within each prior distribution, the greater the value of information relative to the value of production flexibility, particularly for long lead times. However, the greater the uncertainty around the mean demand, which is the uncertainty that cannot be resolved through observation, the lower the value of information. Finally, we observe that the value of supply flexibility grows initially in a concave then convex manner as a function of the supply lead times.

Marketing/manufacturing trade-offs in product line management

A critical decision facing firms across industries is the selection of a mix of products to offer in the marketplace. Both in practice and in the academic literature, the product line design problem has typically been considered from a marketing perspective, with a focus on how alternative sets of products interact and compete in the marketplace. The operational implications of product line decisions have been largely ignored, even while the importance and complexity of interactions among products in the manufacturing environment increase with broadening product lines. Furthermore, consideration of manufacturing synergies among products in product line design is increasingly beneficial given efforts in many industries to improve co-ordination of manufacturing activities across products. In this work we examine the benefits of integrating marketing implications of product mix with more detailed manufacturing cost implications. Traditional product line models are extended to capture both individual product costs and relevant cost interactions among products. The relevant marketing and manufacturing elements are considered in a mathematical programming formulation that identifies a profit maximizing mix of products. The resulting normative model of the product line design problem is used to generate insights into important cross-functional issues in product line management. Specifically, we examine the impact of alternative manufacturing environment characteristics on the composition of the optimal product line.

Global Sourcing Strategies Under Exchange Rate Uncertainty

Firms competing in the “global” marketplace have to take into account the comparative advantages of various countries in forming their manufacturing and sourcing strategies. Developing countries, for instance, have advantages over the developed nations in terms of low labor and raw material costs. Such cost advantages provide strong motivation for multinational firms to seek offshore sourcing arrangements in developing countries. In other cases, critical technological components and/or process equipment are available only from few foreign sources, which are in many cases located in technologically advanced countries other than the firm’s home country. In such cases the firm has no choice but to look at these foreign suppliers for its sourcing needs. Because of these reasons, global sourcing is increasingly emerging as a key strategy for companies seeking competitive advantages, and it represents a sizable amount of the economic activities cf multinational firms. Nearly 10 percent of Chrysler’s