Roman Kapuscinski

Value of Information in Capacitated Supply Chains

We incorporate information flow between a supplier and a retailer in a two-echelon model that captures the capacitated setting of a typical supply chain. We consider three situations: (1) a traditional model where there is no information to the supplier prior to a demand to him except for past data; (2) the supplier knows the (s, S) policy used by the retailer as well as the end-item demand distribution; and (3) the supplier has full information about the state of the retailer. Order up-to policies continue to be optimal for models with information flow for the finite horizon, the infinite horizon discounted and the infinite horizon average cost cases. Study of these three models enables us to understand the relationships between capacity, inventory, and information at the supplier level, as well as how they are affected by the retailers (S - s) values and end-item demand distribution. We estimate the savings at the supplier due to information flow and study when information is most beneficial.

Coordinating Contracts for Decentralized Supply Chains with Retailer Promotional Effort

In this paper, a risk-neutral manufacturer sells a single product to a risk-neutral retailer. The retailer chooses inventories ex ante and promotional effort ex post. If the wholesale price exceeds marginal production cost, the retailer orders fewer than the joint profit-maximizing inventories. If the manufacturer attempts to coordinate inventories by buying back unsold units, then the retailers promotional incentives are dulled. Under very general assumptions on the form of the effort function, we show that buy-backs adversely affect supply chain profits, and higher buy-back prices imply lower profits. Also, while a buy-back alone cannot coordinate the channel, coupling buy-backs with promotional cost-sharing agreements (if effort cost is observable), offering unilateral markdown allowances ex post (if demand is observable but not verifiable), or placing additional constraints on the buy-back (if demand is observable and verifiable) does result in coordination. This problem is not limited to returns policies but is shown to hold for a much larger set of contracts. The results are quite robust (e.g., when the retailer chooses effort before observing demand), but coordinating contracts become more problematic if, for example, the retailer also stocks substitutes for the manufacturers product. Other model extensions are also discussed.

Coordinating Production and Delivery Under a (z, Z)-Type Vendor-Managed Inventory Contract

This paper models a type of vendor-managed inventory (VMI) agreement that occurs in practice called a (z, Z) contract. We investigate the savings due to better coordination of production and delivery facilitated by such an agreement. The optimal behavior of both the supplier and the retailer are characterized. The optimal replenishment and production policies for a supplier are found to be up-to policies, which are shown to be easily computed by decoupling the periods when the supplier outsources from those when the supplier does not outsource. A simple application of the newsvendor relation is used to define the retailers optimal policy. Numerical analysis is conducted to compare the performance of a single supplier and a single retailer operating under a (z, Z) VMI contract with the performance of those operating under traditional retailer-managed inventory (RMI) with information sharing. Our results verify some observations made in industry about VMI and show that the (z, Z) type of VMI agreement performs significantly better than RMI in many settings, but can perform worse in others.

Optimal Policies for a Capacitated Two-Echelon Inventory System

This paper demonstrates optimal policies for capacitated serial multiechelon production/inventory systems. Extending the Clark and Scarf (1960) model to include installations with production capacity limits, we demonstrate that a modified echelon base-stock policy is optimal in a two-stage system when there is a smaller capacity at the downstream facility. This is shown by decomposing the dynamic programming value function into value functions dependent upon individual echelon stock variables. We show that the optimal structure holds for both stationary and nonstationary stochastic customer demand. Finite-horizon and infinite-horizon results are included under discounted-cost and average-cost criteria.

Existence of Coordinating Transshipment Prices in a Two-Location Inventory Model

We consider a two-location production/inventory model where each location makes production decisions and is subject to uncertain capacity. Each location optimizes its own profits. Transshipment (at a cost) is allowed from one location to another. We focus on the question of whether one can globally set a pair of coordinating transshipment prices, i.e., payments that each party has to make to the other for the transshipped goods, that induce the local decision makers to make inventory and transshipment decisions that are globally optimal. A recent paper suggests, for a special case of our model, that there always exists a unique pair of coordinating transshipment prices. We demonstrate through a counterexample that this statement is not correct and derive sufficient and necessary conditions under which it would hold. We show that in some conditions, coordinating prices may exist for only a narrow range of problem parameters and explore conditions when this can happen. Finally, we study the effects of demand and capacity variability on the magnitude of coordinating transshipment prices.

Optimal Policies and Simulation-Based Optimization for Capacitated Production Inventory Systems

The motivation for this stream of research has come from problems faced by diverse set of companies, such as IBM, AMD, Allegheny Ludlum, GE, Proctor and Gamble, Westinghouse, Intel, American Standard, McDonald’s, and Caterpillar. Smaller local (to Pittsburgh) companies such as Sintermet, Blazer Diamond, ASKO and Northside Packing have also provided several interesting issues to pursue. At the heart of many of the problems is the interaction between demand variability and non-stationarity, available production capacity, holding costs of inventory (at different locations), lead times and desired service levels. The central goal of this research stream is to understand the interactions in simple single and multiple stage settings and to provide insights and implementable solutions for managing inventories in a cost-effective manner for complex systems. The goal of this chapter is to introduce in a systematic manner some recent advances in ‘Discrete-time, Capacitated Production-Inventory Systems facing Stochastic Demands’ and we limit ourselves to single product setting. The material here is collected from papers that have appeared in the literature: [31, 22, 23, 48, 49].

Optimal Joint Inventory and Transshipment Control Under Uncertain Capacity

In this paper, we address the optimal joint control of inventory and transshipment for a firm that produces in two locations and faces capacity uncertainty. Capacity uncertainty (e.g., due to downtime, quality problems, yield, etc.) is a common feature of many production systems, but its effects have not been explored in the context of a firm that has multiple production facilities. We first characterize the optimal production and transshipment policies and show that uncertain capacity leads the firm to ration the inventory that is available for transshipment to the other location and characterize the structure of this rationing policy. Then, we characterize the optimal production policies at both locations, which are defined by state-dependent produce-up-to thresholds. We also describe sensitivity of the optimal production and transshipment policies to problem parameters and, in particular, explain how uncertain capacity can lead to counterintuitive behavior, such as produce-up-to limits decreasing for locations that face stochastically higher demand. We finally explore, through a numerical study, when the optimal policy is most likely to yield significant benefits compared to simple policies.

Reliable Due-Date Setting in a Capacitated MTO System with Two Customer Classes

We study a finite-horizon discrete-time model of due-date setting (equivalently, reserving capacity) in a make-to-order setting, where demands arrive from two different classes of customers. Demands in each period are stochastic. The two customer classes penalize with different margins the lead times quoted to them, which (once quoted) are to be satisfied reliably. We first derive the optimal policy for reserving capacity that maps to quoted due dates. We use the insights from its structure to develop a novel approximation that provides near-optimal solutions quickly. Currently available heuristics are tested and are found to be considerably less effective than the above approximation.

Strategic waiting for consumer-generated quality information: : Dynamic pricing of new experience goods

In this paper, we study the impact of consumer-generated quality information (e.g., consumer reviews) on a firms dynamic pricing strategy in presence of strategic consumers. Such information is useful, not only to the consumers that have not yet purchased the product, but also to the firm. The informativeness of the consumer-generated quality information depends, however, on the volume of consumers who share their opinions and, thus, depends on the initial sales volume. Hence, via its initial price, the firm not only influences its revenue but also controls the quality information flow over time. The firm may either enhance or dampen the quality information flow via increasing or decreasing initial sales. The corresponding pricing strategy to steer the quality information flow is not always intuitive. Compared to the case without consumer-generated quality information, the firm may reduce the initial sales and lower the initial price. Interestingly, the firm may get strictly worse off due to the consumer-generated quality information. Even when the firm benefits from consumer-generated quality information, it may prefer less accurate information. Finally, consumer surplus can also decrease due to the consumer-generated quality information, contrary to the conventional wisdom that word-of-mouth should help consumers.

Timing Successive Product Introductions with Demand Diffusion and Stochastic Technology Improvement

This paper considers a firms decisions on the introduction timing for successive product generations. We examine the case where a firm introduces multiple generations of a durable product for which demand is characterized by a demand diffusion process. Under fixed introduction costs, we consider the case where available product technology improves stochastically. As such, delaying introduction to a later date may lead to the capture of further technology improvements, potentially at the cost of slowing sales for the existing product (and a decline in market potential for the product to be introduced, given our focus on durable products). We specify a state-based model of demand diffusion and construct a decision model to solve the firms introduction timing problem. By incorporating technology improvement in our model, we prove the optimality of a state-dependent threshold policy governing the firms product-introduction decisions. Numerical analysis reveals the influence of key model parameters on the pace of product introduction. Our model helps to explain the product-introduction behavior of firms and provides an alternative to previous explanations of IBMs introduction timing decisions for successive generations of its mainframe computers.