Multi - product Multi - route Production Planning Simultaneously Considering Partial Backlogs and Lost Sales

A production planning approach is addressed in this paper for multi-period, multi-product and multi-route production environment considering backlogs and lost sales. When the production capacity or order demand fluctuates, it could lead to a low utilization of the production resource if considering the production system as a whole. Hence, each production stage and inventory is depicted separately, for which fluctuations can be alleviated by utilizing the spare capacity or even overtime in advance. Order demand can be fulfilled from end item inventory, however, if insufficient, both backlogs and lost sales are allowed. Trade-off between these two scenarios is interposed by a policy that lost sales occur when orders are backlogged over a time-phased threshold. The proposed planning problem is exactly formulated by a mixed-integer nonlinear programming (MINLP) model that minimizes the corresponding cost, and then reformulated by a mixed-integer linear programming model (MILP) using linearization techniques. Consequently, a case study oriented from a steel rolling mill plant is introduced to illustrate the effectiveness of the proposed approaches.