Rodney P. Parker

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.

Managing a Noncooperative Supply Chain with Limited Capacity

We consider a two-stage serial supply chain with capacity limits, where each installation is operated by managers attempting to minimize their own costs. A multiple-period model is necessitated by the multiple stages, capacity limits, stochastic demand, and the explicit consideration of inventories. With appropriate salvage value functions, a Markov equilibrium policy is found. Intuitive profit dominance allows for existence of a unique equilibrium solution, which is shown to be a modified echelon base-stock policy. This equilibrium policy structure is sustained in the infinite horizon. A numerical study compares the behavior of the decentralized system with the first-best integrated capacitated system. The performance of this decentralized system relative to the integrated system across other parameters can be very good over a broad range of values. This implies that an acceptable system performance may be attained without the imposition of a contract or other coordinating mechanism, which themselves may encounter difficulties in implementation in the form of negotiation, execution, or enforcement of these agreements. We find instances where tighter capacities may actually enhance channel efficiency. We also examine the effect of capacity utilization on the system suboptimality.

On Hospice Operations Under Medicare Reimbursement Policies

This paper analyzes the United States Medicare hospice reimbursement policy. The existing policy consists of a daily payment for each patient under care with a global cap of revenues accrued during the Medicare year, which increases with each newly admitted patient. We investigate the hospice’s expected profit and provide reasons for a spate of recent provider bankruptcies related to the reimbursement policy; recommendations to alleviate these problems are given. We also analyze a hospice’s incentives for patient management, finding several unintended consequences of the Medicare reimbursement policy. Specifically, a hospice may seek short-lived patients (such as cancer patients) over patients with longer expected length-of-stay and the effort with which they seek-out, or recruit, such patients will vary during the year. Further, the effort they apply to actively discharge patients whose condition has stabilized may also depend on the time of year. These phenomena are unintended and undesirable but are a direct consequence of the Medicare reimbursement policy. We propose an alternative reimbursement policy which ameliorates these shortcomings.

Dynamic inventory competition with stockout-based substitution

This paper continues the stream of literature observed in Olsen and Parker (2008) where retailers compete under a Markov equilibrium solution concept. In this presentation, we consider a duopoly where retailers compete by providing inventory under the circumstances where unsatisfied customers may seek satisfaction elsewhere or leave. A very general framework is formulated to address a variety of customer avenues when stock is unavailable. We find a base-stock inventory policy is the equilibrium policy in the infinite horizon (open loop) under several mild conditions; this models solution is known as an equilibrium in stationary strategies (ESS). We consequently determine conditions under which the parsimonious base-stock policy is the Markov equilibrium (closed loop) in a discrete-time dynamic game for a general time horizon, coinciding with the ESS base-stock levels. Importantly, when these conditions do not apply, we have counterexamples where a firm has a unilateral incentive to deviate from the ESS, stocking at a higher level. These examples demonstrate a value of inventory commitment, where the retailer may extract a benefit over multiple periods through committing to a higher stocking level and forcing her rival to understock. Our conclusion is that when the Markov solution is base-stock, it coincides with the ESS, but other Markov solutions also exist.

Innovation and technology diffusion in competitive supply chains

Abstract Innovations in consumer products frequently rely on technological advances across multiple tiers in a supply chain. Considering the consumer market demand and downstream investment conditions as input, we model a game in a two-tier supply chain where downstream firms choose to adopt different levels of an upstream technology and an upstream technology leader determines its pricing policy. We identify two necessary but distinct elements for the successful development, adoption, and diffusion of upstream technologies that are sold to lower tiers as components within final products. (1) The level of technology demanded by the market: We develop a measure, Technological Potential, which describes the highest level of an upstream technology demanded by consumer markets. (2) A sufficiently rich return to an upstream innovator, as a function of different levels of technology. From these two elements, we show that the relative magnitudes of two competing sets of consumer market factors determine the Technological Potential whereas the overall magnitude of the factors in both sets determines the return to the upstream developer. We discuss how this difference in consumer market factors’ influence on these two elements may determine how different technologies fare in the supply chain. Our results have managerial implications for: investors in research and development project selection in identifying profitable technologies that are also demanded at higher capability levels; and for governments in defining more targeted public policies – for example in choosing the right tier of a supply chain to provide subsidies – to encourage market support for certain technologies.