Asymptotically Optimal Production Policies in Dynamic Stochastic Jobshops with Limited Buffers
Journal of Mathematical Analysis and Applications, Vol. 317, No. 2, pp. 398-428, 2006
31 Pages Posted: 4 Mar 2008 Last revised: 27 Apr 2008
We consider a production planning problem for a jobshop with unreliable machines producing a number of products. There are upper and lower bounds on intermediate parts and an upper bound on finished parts. The machine capacities are modelled as finite state Markov chains. The objective is to choose the rate of production so as to minimize the total discounted cost of inventory and production. Finding an optimal control policy for this problem is difficult. Instead, we derive an asymptotic approximation by letting the rates of change of the machine states approach infinity. The asymptotic analysis leads to a limiting problem in which the stochastic machine capacities are replaced by their equilibrium mean capacities. The value function for the original problem is shown to converge to the value function of the limiting problem. The convergence rate of the value function together with the error estimate for the constructed asymptotic optimal production policies are established.
Keywords: Optimal production policy, Stochastic manufacturing systems, Stochastic dynamic programming, Discounted cost, Asymptotic analysis
JEL Classification: M11, C61
Suggested Citation: Suggested Citation