Abstract:In this article, we consider a classic dynamic inventory control problem of a self-financing retailer who periodically replenishes its stock from a supplier and sells it to the market. The replenishment decisions of the retailer are constrained by cash flow, which is updated periodically following purchasing and sales in each period. Excess demand in each period is lost when insufficient inventory is in stock. The retailer's objective is to maximize its expected terminal wealth at the end of the planning horizon. We characterize the optimal inventory control policy and present a simple algorithm for computing the optimal policies for each period. Conditions are identified under which the optimal control policies are identical across periods. We also present comparative statics results on the optimal control policy.

Very few stochastic systems are known to have closed-form transient solutions. In this article we consider an immigration birth and death population process with total catastrophes and study its transient as well as equilibrium behavior. We obtain closed-form solutions for the equilibrium distribution as well as the closed-form transient probability distribution at any time t ≥ 0. Our approach involves solving ordinary and partial differential equations, and the method of characteristics is used in solving partial differential equations.

We develop the first approximation algorithms with worst-case performance guarantees for periodic-review perishable inventory systems with general product lifetime, for both backlogging and lost-sales models. The demand process can be nonstationary and correlated over time, capturing such features as demand seasonality and forecast updates. The optimal control policy for such systems is notoriously complicated, thus finding effective heuristic policies is of practical importance. In this paper, we construct a computationally efficient inventory control policy, called the proportional-balancing policy, for systems with an arbitrarily correlated demand process and show that it has a worst-case performance guarantee less than 3. In addition, when the demands are independent and stochastically nondecreasing over time, we propose another policy, called the dual-balancing policy, which admits a worst-case performance guarantee of 2. We demonstrate through an extensive numerical study that both policies perform consistently close to optimal.

Product returns have become a significant feature of many manufacturing systems. Because products are returned under different operational conditions, they usually require different remanufacturing effort/costs. Motivated by a project with a major energy company that manages its inventory through options of ordering and remanufacturing returned products (cores) in various condition, in this paper, we study a single-product, periodic-review inventory system with multiple types of cores. The serviceable products used to fulfill stochastic customer demand can be either manufactured from new parts or remanufactured from the cores, and the objective is to minimize the expected total discounted cost over a finite planning horizon. We show that the optimal manufacturing-remanufacturing-disposal policy has a simple structure and can be completely characterized by a sequence of constant control parameters when manufacturing and remanufacturing leadtimes are the same. To demonstrate the value of the optimal policy, we conduct a numerical study that compares its performance with two simple heuristics, namely, pull policy without and with sorting. The results show that the reduction in system cost by using the optimal policy can be significant. When manufacturing and remanufacturing leadtimes are different, we develop a heuristic method for computing the near-optimal control policy that performs quite well as demonstrated numerically.inventory system, product returns, reverse logistics, remanufacturing, optimal manufacturing and remanufacturing strategies, base-stock policies

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