A stochastic production planning model with a dynamic chance constraint

Abstract

This paper deals with the optimal production planning for a single product over a finite horizon. The holding and production costs are assumed quadratic as in Holt, Modigliani, Muth and Simon (HMMS) [7] model. The cumulative demand is compound Poisson and a chance constraint is included to guarantee that the inventory level is positive with a probability of at least α at each time point. The resulting stochastic optimization problem is transformed into a deterministic optimal control problem with control variable and of the optimal solution is presented. The form of state variable inequality constraints. A discussion the optimal control (production rate) is obtained as follows: if there exists a time t1 such that t1ϵ[O, T]where T is the end of the planning period, then (i) produce nothing until t1 and (ii) produce at a rate equal to the expected demand plus a ‘correction factor’ between t1 and T. If t1 is found to be greater than T, then the optimal decision is to produce nothing and always meet the demand from the inventory.