Optimal Strategies in a Production Inventory Control Model

We consider a production-inventory control model with finite capacity and two different production rates, assuming that the cumulative process of customer demand is given by compound Poisson process. It possible at any time to switch over from rates but it mandatory switch-off when inventory reaches storage maximum capacity. holding, production, shortage penalty switching costs. This was introduced Doshi, Van Der Duyn Schouten Talman in 1978. In their paper they found formula for long-run average expected cost per unit as function critical levels, this we discounted costs instead. seek minimize all admissible strategies. show optimal functions satisfy corresponding Hamilton-Jacobi-Bellman system equations viscosity sense prove verification theorem. The way which solve variational inequalities gives regions strategy, hence stationary depends only on current rate level. define notion band strategies derive, using scale functions, formulas one or bands. also there are examples where strategy levels not optimal.