Analysis of a queueing-inventory system with Client Choice Service under a modified (s, S) reorder policy

초록

This study investigates a novel queueing-inventory system governed by a newly proposed Client Choice Policy, which extends the modified (s, S) ordering policy. The system considers a maximum capacity of S units of raw material. Upon the arrival of a client, the raw material is processed into finished goods after some random time. Client arrivals follow a Markovian arrival process (MAP) and a finite waiting platform is available. A reorder point is fixed as s. At the time of replenishment, the inventory gets filled up to the level of S units. In addition to that, the clients in the waiting platform may choose to purchase the raw materials. Clients who accept this offer leave the system immediately with the raw material, while the others remain in the queue to receive the finished goods. The numerical cost analysis estimates the expected total cost using steady-state probabilities derived from the finite generator matrix. The total cost is computed as the weighted sum of holding, replenishment, processing, and waiting costs. By evaluating these costs over different parameter combinations, the optimal policy that minimizes the expected total cost is identified numerically.

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