Real-time disruption management in a two-stage production and inventory system

This paper presents a general disruption management approach for a two-stage production and inventory control system. A penalty cost for deviations of the new plan from the original plan is incorporated and the concept of a disruption recovery time window is introduced. We define two classes of problems: one with fixed setup epochs and another with flexible setup epochs. With linear or quadratic penalty functions for production/ordering quantity change and fixed setup epochs, the best recovery plan is obtained by solving a quadratic mathematical programming problem. With convex penalty functions for quantity changes and flexible setup epochs, it is shown that the second stage orders have identical order quantities within each production cycle. Therefore, in a lot-for-lot system, the ordering and production quantities for both stages are the same. As a special case, we consider disruption recovery problems with short time windows spanning one or two production cycles. We also discuss solution procedures for both major and minor disruption problems and give an extension for the case of multiple retailers. Throughout the paper managerial insights are presented that indicate how a company should respond to various types of disruptions during its operations.