This paper comprises a one warehouse multiple retailer (OWMR) inventory model operating under a continuous-review (R, Q) policy. Customer demand at each retailer is modeled as a compound Poisson process with stochastic lead times while the warehouse has a fixed lead time. Solution Procedure together with convexity analysis of the total cost function has been carried out. An algorithm is given to obtain optimal decision variables. Sensitivity analysis is performed to investigate the effects of key system parameters on the inventory policy and total system cost. The results demonstrate that the proposed policy is robust to variations in warehouse ordering, holding, and shortage costs, whereas the demand size distribution and retailer lead time have the greatest influence on the optimal inventory decisions and total system cost.

This paper investigates a centralized one-warehouse multiple-retailer (OWMR) distribution system with quantity-restricted deliveries from the warehouse to downstream retailers. Demand at each retailer follows a compound Poisson process, and inventory is managed through continuous-review (R,Q) policies. Shortages are completely backordered, with customer orders fulfilled according to a first-come-first-served (FCFS) rule. The model explicitly incorporates stochastic retailer lead times. To analyze the proposed system, several theoretical results are established regarding the convexity of the total cost function. An algorithm-based optimization procedure is developed to jointly determine base quantity, retailer, and warehouse reorder points that minimize the total cost. The numerical study reveals that the combined effect of stochastic retailer lead times and restricted deliveries substantially influences inventory decisions, which results in higher reorder points to maintain service levels. The results further reveal that retailer backordering costs are a key driver of the optimal policy, higher shortage penalties lead to increased reorder points across the supply chain as a precaution against stockouts under stochastic lead times and restricted delivery operations

In this paper, we study the cooperative games between companies that pool their spare part inventory to maintain their equipment. Due to the high cost of service disruptions, any stockout is assumed to be satisfied by an expedited delivery. We firstly derive the performance measures used to formulate the long run average cost of running these spare parts systems and show that, in the long run, these performance measures are equivalent to those in classical spare parts system with backlogs. Afterwards, we show that the core of these games are non-empty by showing that proportional allocation is a population monotonic allocation scheme.