Equilibrium Joining Strategies and Optimal Control of a Make‐to‐Stock Queue
研究了具有设置成本和延迟敏感顾客的按订单生产系统，生产经理采用两临界数控制策略，顾客根据效用决定是否购买，通过Stackelberg博弈分析均衡策略并优化控制变量。
We consider a make‐to‐stock, finite‐capacity production system with setup cost and delay‐sensitive customers. To balance the setup and inventory related costs, the production manager adopts a two‐critical‐number control policy, where the production starts when the number of waiting customers reaches a certain level and shuts down when a certain quantity of inventory has accumulated. Once the production is set up, the unit production time follows an exponential distribution. Potential customers arrive according to a Poisson process. Customers are strategic, i.e., they make decisions on whether to stay for the product or to leave without purchase based on their utility values, which depend on the production manager's control decisions. We formulate the problem as a Stackelberg game between the production manager and the customers, where the former is the game leader. We first derive the equilibrium customer purchasing strategy and system performance. We then formulate the expected cost rate function for the production system and present a search algorithm for obtaining the optimal values of the two control variables. We further analyze the characteristics of the optimal solution numerically and compare them with the situation where the customers are non‐strategic.