Mismatch between supply and demand when the uncertainty of the demand is high and the supply lead time is relatively long, such as seasonal good markets, can result in high overstocking and understocking costs. In this paper we propose transshipment as a powerful mechanism to mitigate the mismatch between the supply and demand. We consider a finite horizon multi-period inventory system where in each period two retailers have the option to replenish their inventory from a supplier (if there is any supply) or via transshipment from the other retailer. Each retailer observes nonnegative stochastic demand with general distribution in each period and incurs overstocking/understocking costs as well as costs for replenishment and transshipment that may be time dependent. We study a stochastic control problem where the objective is to determine the optimal joint replenishment and transshipment policies so as to minimize the total expected cost over the season. We characterize the structure of the optimal policy and show that unlike the known order-up-to level inventory policy, the optimal ordering policy in each period is determined based on two switching curves. Similarly, the optimal transshipment policy is also identified by two switching curves. These four curves together partition the optimal joint ordering and transshipment polices to eight regions where in each region the optimal policy is an order-up-to-curve policy. We demonstrate that the structure of the optimal policy holds for any known sequence and combination of ordering and transshipment over time.

P references for different ages of perishable products exist in many applications, including grocery items and blood products. In this paper, we study a multi-period stochastic perishable inventory system with multiple priority classes that require products of different ages. The firm orders the product with a positive lead time and sells it to multiple demand classes, each only accepting products with remaining lifetime longer than a threshold. In each period, after demand realization, the firm decides how to allocate the on-hand inventory to different demand classes with different backorder or lost-sale cost. At the end of each period, the firm can dispose inventory of any age. We formulate this problem as a Markov decision process and characterize the optimal ordering, allocation, and disposal policies. When unfulfilled demand is backlogged, we show that the optimal order quantity is decreasing in the inventory levels and is more sensitive to the inventory level of fresher products, the optimal allocation policy is a sequential rationing policy, and the optimal disposal policy is characterized by n À 1 thresholds. For the lost-sale case, we show that the optimal allocation and disposal policies have the same structure but the optimal ordering policy may be different. Based on the structure of the optimal policy, we develop an efficient heuristic with a cost that is at most 4% away from the optimal cost in our numerical examples. Using numerical studies, we show that the ordering and allocation policies are close to optimal even if the firm cannot intentionally dispose products. Moreover, ignoring the differences between demand classes and using simple allocation policy (e.g., FIFO) can significantly increase the total cost. We examine how the firm can improve the control of perishable items and show that the benefit of decreasing the lead time is more significant than that of increasing the lifetime of the products or that of decreasing the acceptance threshold of the demand. The analysis is extended to systems with age dependent disposal cost and with stochastic supply.

In this study, we examine whether it is optimal to use electric vehicles (EVs) in the car sharing market and investigate the environmental impact of pulling the EVs from the market. We develop a model consisting of a profit‐maximizing car sharing company (CSC) and a population of utility‐maximizing customers. The CSC sets the number of EVs, the number of fuel vehicles (FVs), and the rental price jointly to maximize its profit. Customers decide whether to use EVs, FVs, or public transportation to complete their trips considering the rental price. We show that it is optimal to use EVs only if the charging speed, the number of charging stations, and the range of EVs are high enough. Among these three conditions, the recharging speed is the most important and the number of charging stations is more important than the range of EVs. We also find that including EVs in the car sharing market may lead to a higher total emission when ignoring customers’ other transportation choices (due to a lower rental price that results in a higher usage rate). Moreover, we consider the problem with the objective of maximizing the social welfare and find that when considering the environmental impact, governments should tax the CSC to induce a higher rental price and when ignoring this impact, they should subsidize the CSC to reduce the rental price. We demonstrate our results with the case study of Car2go. These results are in line with that the slow recharging speed may have been one of the contributing factors to that Car2go replaced EVs with FVs in San Diego.

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We consider a state-dependent Mn/Gn/1 queueing system with both finite and infinite buffer sizes. We allow the arrival rate of customers to depend on the number of people in the system. Service times are also statedependent and service rates can be modified at both arrivals and departures of customers. We show that the steady-state solution of this system at arbitrary times can be derived using the supplementary variable method, and that the system's state at arrival epochs can be analyzed using an embedded Markov chain. For the system with infinite buffer size, we first obtain an expression for the steady-state distribution of the number of customers in the system at both arbitrary and arrival times. Then, we derive the average service time of a customer observed at both arbitrary times and arrival epochs. We show that our state-dependent queueing system is equivalent to a Markovian birth-and-death process. This equivalency demonstrates our main insight that the Mn/Gn/1 system can be decomposed at any given state as a Markovian queue. Thus, many of the existing results for systems modeled as M/M/1 queue can be carried through to the much more practical M/G/1 model with state-dependent arrival and service rates. Then, we extend the results to the Mn/Gn/1 queueing systems with finite buffer size.