Lead-time analysis and a control policy for production lines

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We address a control problem for a production line that produces one product to stock and faces random demand. During stockouts, the system quotes a fixed response time for each arriving order, and the customers place their orders only if the response time promised meets their deadlines. Customer orders are filled on a first come, first served basis. A penalty cost is incurred whenever a customer is served later than promised. A two-parameter admission/inventory control policy is implemented that maintains a bounded backlog and a constant inventory position (total inventory minus backlog) in the system. For production lines with exponential processing times and Poisson demand, the mean profit rate of the system is computed analytically using closed queueing network formulae. For systems with general processing or interarrival time distributions, the profit rate is estimated via simulation. Simple properties are established that ensure that the profit maximising control parameters can be determined in finite time using exhaustive search. Numerical results show that the proposed policy performs better than the make-to-order/zero-inventory and the lost-sales/make-to-stock policies.