We analyze a joint pricing and inventory control problem for a perishable product with a fixed lifetime over a finite horizon. In each period, demand depends on the price of the current period plus an additive random term. Inventories can be intentionally disposed of, and those that reach their lifetime have to be disposed of. The objective is to find a joint pricing, ordering, and disposal policy to maximize the total expected discounted profit over the planning horizon taking into account linear ordering cost, inventory holding and backlogging or lost-sales penalty cost, and disposal cost. Employing the concept of L -concavity, we show some monotonicity properties of the optimal policies. Our results shed new light on perishable inventory management, and our approach provides a significantly simpler proof of a classical structural result in the literature. Moreover, we identify bounds on the optimal order-up-to levels and develop an effective heuristic policy. Numerical results show that our heuristic policy performs well in both stationary and nonstationary settings. Finally, we show that our approach also applies to models with random lifetimes and inventory rationing models with multiple demand classes.
We consider a joint inventory-pricing control problem for a periodic-review, single-stage inventory system with a positive order leadtime and a linear order cost. Demands in consecutive periods are independent, but their distributions depend on the price in accordance with a stochastic demand function of additive form. Pricing and ordering decisions are made simultaneously at the beginning of each period. The objective is to maximize the total expected discounted profit over a finite horizon. We partially characterize the structure of the optimal joint ordering and pricing policies. We also show that our structural analysis can be extended to a multistage (or serial) inventory system with constant or stochastic leadtimes and an assemble-to-order system with price-sensitive demand.
A common technical challenge encountered in many operations management models is that decision variables are truncated by some random variables and the decisions are made before the values of these random variables are realized, leading to non-convex minimization problems. To address this challenge, we develop a powerful transformation technique which converts a non-convex minimization problem to an equivalent convex minimization problem. We show that such a transformation enables us to prove the preservation of some desired structural properties, such as convexity, submodularity, and L-convexity, under optimization operations, that are critical for identifying the structures of optimal policies and developing efficient algorithms. We then demonstrate the applications of our approach to several important models in inventory control and revenue management: dual sourcing with random supply capacity, assemble-to-order systems with random supply capacity, and capacity allocation in network revenue management.
I n recent years, the performance-based approach to contracting for medical services has been gaining popularity across different healthcare delivery systems, both in the United States (under the name of "pay for performance") and abroad ("payment by results" in the United Kingdom). The goal of our research is to build a unified performance-based contracting (PBC) framework that incorporates patient access-to-care requirements and that explicitly accounts for the complex outpatient care dynamics facilitated by the use of an online appointment scheduling system. We address the optimal contracting problem in a principal-agent framework where a service purchaser (the principal) minimizes her cost of purchasing the services and achieves the performance target (a waiting-time target) while taking into account the response of the provider (the agent) to the contract terms. Given the incentives offered by the contract, the provider maximizes his payoff by allocating his outpatient service capacity among three patient groups: urgent patients, dedicated advance patients, and flexible advance patients. We model the appointment dynamics as that of an M/D/1 queue and analyze several contracting approaches under adverse selection (asymmetric information) and moral hazard (private actions) settings. Our results show that simple and popular schemes used in practice cannot implement the first-best solution and that the linear performance-based contract cannot implement the second-best solution. To overcome these limitations, we propose a threshold-penalty PBC approach and show that it coordinates the system for an arbitrary patient mix and that it achieves the second-best performance for the setting where all advance patients are dedicated.
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