Batch Production Plan for Periodic Demands with Uncertain Recycling Rate in a Closed-Loop Supply System

Optimal Process/Reprocess Production Mix for Multiple Orders in Multiple Periods

“…They introduced a capacity limitation into their model, characterized useful properties for the general concave cost functions, and discussed several simplified but useful specific cases of their problem. Most recently, Wang and Fu [6] proposed a batch production plan, in which the production quantity at each period is presented in batches and permitted a backlogging policy. Therefore, products can be supplied even after the product delivery period.…”

“…Constraint (5) calculates the number of products returned at the end of each period. Constraint (6) ensures that, once the order is accepted, the retailer has to be satisfied before the latest delay period or the end of the planning horizon. Constraint (7) refers to the capacity limitation of the factory, and each production activity consumes these resources.…”

“…After we replace the objective function (1) by (16); constraint (2) by (17); constraints (5-1) and (5-2) by (18-1) and (18-2), respectively; and constraint (6) by (19) and (20), we reduce the number of variables by…”

“…In recent years, numerous studies on production planning problem have been published. Most studies consider the case in which the producer receives one batch of orders for each period at the beginning of the planning horizon [3][4][5][6]. This assumption is contrary to actual practice where producers often receive multiple orders from retailers, which place their periodic orders at the beginning.…”