Research

We study an infinite-horizon periodic-review remanufacturing inventory system with random demand and product return. The quantity of returned products each period depends on historical demands following a distributed lag model. A firm operating the system remanufactures product returns into a serviceable product to fulfill customer demand. When needed, the serviceable product can also be manufactured or ordered. Manufacturing and remanufacturing have different lead times. The firm decides the manufacturing quantity each period to minimize the expected long-run average cost of inventory holding, demand backlogging, and manufacturing.

We first establish the existence of a stationary optimal policy under the long-run average-cost criterion using the vanishing discount factor approach together with a coupling argument. Via state-space reduction, we further prove that the optimal policy is a forecast-adjusted base-stock (FABS) policy when the maximum return lag is shorter than the manufacturing lead time. When the maximum return lag is longer than the manufacturing lead time, the optimal policy becomes a state-dependent base-stock policy. For the latter case, we show that the FABS policy becomes asymptotically optimal as the unit backlogging cost becomes large.

We further develop simple approximate base-stock levels for implementing the FABS policy and numerically demonstrate their effectiveness. Two extensions are examined: one with random coefficients in the return model and another with separate core inventory and remanufacturing decisions.

We study periodic-review backlogging inventory systems with exogenous stochastic lead times. Although base-stock (BS) policies that maintain a constant inventory position are optimal when orders do not cross in transit, their performance under lead-time processes that permit crossover remains poorly understood.

We provide new insights into the effectiveness of BS policies in such settings. First, we derive an upper bound on the optimality gap of a BS policy that explicitly captures the impact of order crossover. The bound implies that the BS policy is optimal when order crossover is absent or when demand is bounded and the unit backlogging cost is sufficiently large. Second, under a mild regularity condition, we establish the asymptotic optimality of the BS policy as the unit backlogging cost grows large. Third, we show that the difference between the optimality gaps of the optimal BS policy under stochastic and deterministic demand is bounded by a term proportional to the coefficient of variation of demand.

We develop an analytical model in which a firm chooses the price of a blind box and the probabilities of drawing either of two horizontally differentiated items. Customers have heterogeneous preferences and receive a set bonus from completing the collection. They may make repeated purchases and, when a secondary market exists, anticipate subsequent trading opportunities. We characterize purchasing strategies and market equilibrium using optimal stopping and linear programming, and compare outcomes with and without a secondary market.

It is widely believed that secondary markets help customers obtain preferred items and complete collections. However, we find that a secondary market reduces the firm’s profit if and only if customer preferences are highly polarized and the set bonus is positive but small. Despite improving allocation for a given supply, a secondary market can reduce both firm profit and social welfare. The firm may optimally raise its price and reduce sales, leaving fewer customers with complete collections. When the set bonus is sufficiently large, an optimal selling policy allows all customers to complete their collections and achieves maximum social welfare. These findings inform whether firms should facilitate secondary trading and how they can adjust pricing and product design in response to its presence.

We study the operational decisions of a smallholder agricultural aggregator, including collection, processing, and selling decisions under supply, quality, and price uncertainty.