Reduce shortage with self-reservation policy for a manufacturer paying both fixed and variable stockout expenditure

\u3cp\u3eThis study considers a single item make-to-stock system with continuous-time production and inventory controls to meet bulk demand with an exponential inter-arrival time. A key issue in this system is the non-convex shortage cost consisting of fixed and variable expenditures when the demand is not fully satisfied. We propose a self-reservation policy by building a Markov Decision Process to minimize the overall cost. We find that the optimal production control is still a base stock policy, but the structure of the optimal self-reservation policy is very complicated. However, if the effective outstanding variable shortage cost is sufficiently large, the optimal self-reservation policy has an easy form of “Reserve All or Nothing.” Our numerical examples indicate the optimal policy may reduce the total average cost by 47% on average.\u3c/p\u3

Recensione dell'articolo:(Huang, Boray; Wu, Andy - " Reduce shortage with self-reservation policy for a manufacturer paying both fixed and variable stockout expenditure. " - European J. Oper.Res. 262 (2017), no.3, 944-953.) MR3656877 MathSciNet ISSN 2167-5163

In this paper, the authors study a continuous-time make-to-stock (MTS) model for a manufacturer who needs to handle bulk demand with shortage expenditure including both fixed and variable costs. As stockout incurs additional fixed costs, the authors propose a self-reservation policy along with the production control: in the occurrence of stockout, the manufacturer can place an urgent order whose size is larger than the shortfall, and reserve some inventory for the future demand. The manufacturer can take this chance to quickly raise its inventory position and reduce the chance of stockout for future demand. The main contributions of this study are the investigation of the optimal production control and the introduction of the self-reservation policy to a manufacturer facing lot-size demand with a shortage cost including a fixed penalty. The authors model the production and reservation controls as a continuous-time Markov decision problem (CTMDP)