Asian Research Journal of Mathematics

Shipbuilding involves highly complex multi-station assembly operations where the timely availability of materials is critical for maintaining production flow and preventing bottlenecks. Traditional inventory management in shipyards relies heavily on deterministic planning and static ordering policies, which often fail to capture system uncertainties associated with stochastic material demand and the sequential nature of multi-station operations. This paper develops a pure theoretical queueing-inventory model to optimize material allocation among assembly stations in a shipbuilding environment. Each workstation is modeled as an M/M/1 queue, and material inventory replenishment follows an (s, S) policy. The interaction between queueing dynamics (arrival and service rates) and inventory control (reorder point and replenishment level) is formulated using a continuous-time Markov chain. The state space is defined as a two-dimensional process based on inventory level and queue length at each station. The transition probability matrix (TPM) is derived to compute steady-state probabilities, enabling quantitative assessment of performance measures including stockout probability, average number of jobs in queue, expected inventory levels, and utilization rates of assembly stations. The model provides analytical insights into minimizing holding costs, reorder frequencies, and production delays. The contribution of this work lies in integrating queueing theory with stochastic inventory control specifically tailored for shipbuilding operations, providing a foundation for future simulation or optimization-based studies.