Gregory A. DeCroix

Inventory management under random supply disruptions and partial backorders

We explore the management of inventory for stochastic-demand systems, where the products supply is randomly disrupted for periods of random duration, and demands that arrive when the inventory system is temporarily out of stock become a mix of backorders and lost sales. The stock is managed according to the following modified (s, S) policy: If the inventory level is at or below s and the supply is available, place an order to bring the inventory level up to S. Our analysis yields the optimal values of the policy parameters, and provides insight into the optimal inventory strategy when there are changes in the severity of supply disruptions or in the behavior of unfilled demands.

Optimal Shared Savings Contracts in Supply Chains: Linear Contracts and Double Moral Hazard

In many supply chains consumption of indirect materials, sold by a supplier to a customer for use in her production process, can be reduced by efforts exerted by either party. Since traditional supply contracts provide no incentive for the supplier to exert such effort, shared-savings contracts have been proposed as a way to improve incentives in the channel, leading to more efficient effort choices by the two parties. Such shared-savings contracts typically combine a fixed service fee with a variable component based on consumption volume. We formalize this situation using the double moral hazard framework, in which both parties decide how much effort to exert by trading off the cost of their effort against the benefits that they will obtain from reduced consumption. We also extend the double moral hazard framework to analyze a broader class of cost-of-effort functions than considered so far, including the linear cost-of-effort functions commonly found in practice. We show that the supplier can still always induce the optimal second-best equilibrium with a linear shared-savings contract. Under this broader class of functions, however, the behavior of the optimal contract as a function of the problem parameters becomes more complex. We illustrate how small changes in the problem parameters can turn profits from being a well-behaved to a poorly-behaved function of the contract, and provide some theoretical characterization of this phenomenon. The practical significance of this is that simple (linear) contracts are sufficient in many double moral hazard contexts, even for the broader class of functions we consider, but care must be taken in selecting the optimal contract parameters.

Optimal Policy for a Multiechelon Inventory System with Remanufacturing

We analyze a multiechelon inventory system with inventory stages arranged in series. In addition to traditional forward material flows, used products are returned to a recovery facility, where they can be stored, disposed, or remanufactured and shipped to one of the stages to re-enter the forward flow of material. This system combines the key elements of two simpler systems: the series system studied by Clark and Scarf (1960) and the single-stage remanufacturing systems studied by Simpson (1978) and Inderfurth (1997). We focus on identifying the structure of the optimal remanufacturing/ordering/disposal policy for such a system. In particular, we investigate whether the optimal policy inherits the basic structural properties of the simpler systems. We show that if remanufactured items flow into the most upstream stage, then this is the case. Specifically, the system can be solved by decomposition into a sequence of single-stage systems, with each downstream stage following an echelon base-stock policy and the most upstream stage following a three-parameter policy with a simple (and intuitive) structure. We show that similar results hold when remanufactured products flow into a downstream stage; however, in this case some modifications must be made. In particular, the definition of echelon inventory must be adjusted for stages upstream of the remanufacturing stage, and disposal of used items can no longer be allowed. We also compare the information required for managing this system to that required in the Clark and Scarf or Inderfurth settings, and we point out how the requirements are somewhat different depending on whether remanufacturing occurs upstream or downstream.

Inventory Management for an Assembly System with Product or Component Returns

This paper considers an inventory system with an assembly structure. In addition to uncertain customer demands, the system experiences uncertain returns from customers. Some of the components in the returned products can be recovered and reused, and these units are returned to inventory. Returns complicate the structure of the system, so that the standard approach (based on reduction to an equivalent series system) no longer applies in general. We identify conditions on the item-recovery pattern and restrictions on the inventory policy under which an equivalent series system does exist. For the special case where only the end product (or all items used to assemble the end product) is recovered, we show that the system is equivalent to a series system with no policy restrictions. For the general case, we explain how and why the system becomes more problematic and propose two heuristic policies. The heuristics are easy to compute and practical to implement, and they perform well in numerical trials. Based on these numerical trials, we obtain insights into the impact of various factors on system performance. For example, we find that holding and backorder costs tend to increase when the average return rate, the variability of returns, or the number of components recovered increases. However, neither the product architecture nor the specific set of components being recovered seems to have a significant impact on these costs. Whether product recovery reduces total system costs depends on the magnitude of the additional holding and backorder costs relative to potential procurement cost savings.

Decentralized Pricing and Capacity Decisions in a Multitier System with Modular Assembly

We model a modular assembly system in which a final assembler outsources some of the assembly task to first-tier suppliers (subassemblers), who produce modules made up of multiple components. The assembler sets module prices it will pay to the subassemblers, the subassemblers set component prices they will pay to suppliers, and then all players choose how much capacity to install, with the minimum capacity choice determining system capacity. Finally, stochastic end-product demand is observed and all players produce (and are paid for) the same number of units-the minimum of demand and system capacity. We characterize equilibrium price and capacity choices, and then use that characterization to derive results regarding higher-level structural choices by the assembler-such as how to group components into modules and which suppliers to choose as subassemblers. We also compare performance of the system to a traditional assembly system with an assembler and suppliers but without subassemblers.

Make-to-order versus make-to-stock in a production-inventory system with general production times

We study the optimality of make-to-order (MTO) versus make-to-stock (MTS) policies for a company producing multiple heterogeneous products at a shared manufacturing facility. Manufacturing times are general i.i.d. random variables, and different products may have different manufacturing-time distributions. Demands for the products are independent Poisson processes with different arrival rates. The costs of managing the production-inventory system are stationary and include inventory holding and backordering costs. Backordering costs may be

A Series System with Returns: Stationary Analysis

per unit or

Inventory Policies in a Decentralized Assembly System

per unit per unit time. We derive optimality conditions for MTO and MTS policies. We also study the impact of several managerial considerations on the MTO versus MTS decision.

Inventory Management for an Assembly System Subject to Supply Disruptions

This paper analyzes a series inventory system with stationary costs and stochastic demand over an infinite horizon. A distinctive feature is that demand can be negative, representing returns from customers, as well as zero or positive. We observe that, as in a system with nonnegative demand, a stationary echelon base-stock policy is optimal here. However, the steady-state behavior of the system under such a policy is different from that in systems with nonnegative demands. We present an exact procedure and several approximations for computing the operating characteristics and system costs for any stationary echelon base-stock policy, and also describe an algorithm for computing a good policy. As an alternative to the echelon base-stock policy, we discuss a policy that uses only local information. Finally, we describe how to extend the analysis to the case where returns occur at multiple stages instead of just at the stage closest to demand, and the case where returns require a recovery lead time.

The Impact of Demand Aggregation Through Delayed Component Allocation in an Assemble-to-Order System

We consider a system in which a single finished good is assembled from two components. Demand for the finished product is stochastic and stationary, and procurement and assembly lead times are constant. Unsatisfied demand is backordered. The inventory of each component or assembly is controlled by a separate firm using a base-stock policy. Each firm is charged holding costs on its own inventory, plus a share of the shortage cost due to backorders of the finished product. We investigate the equilibrium base-stock levels that arise in this system under both echelon and local base-stock policies. In both cases, the component firms base-stock levels are economic complements. We then examine the effect on system performance when one firm uses information about other firms pipeline inventory. We find that, under echelon base-stock policies, all firms benefit with the use of pipeline information. In contrast, under local policies, using pipeline information may actually increase costs for some firms (including the firm that makes direct use of the information). Also, we compare the behavior of the decentralized system with that of the assembly system under centralized control. Finally, we describe a payment scheme between the final assembler and the suppliers that allows the decentralized system to achieve the centralized solution.