Replenishment-shipment decision for a multiproduct producer-client coordinated FPR model with postponement, rework and subcontracting

This research constructs a mathematical scheme to explore replenishment-shipment decisions for a multiproduct producer-client coordinated finite production rate (FPR) model with the postponement, rework, and subcontracting plan. The considered multiple goods have a common component, and a batch FPR fabrication with postponement is planned to meet the annual multiproduct requirements. The first fabricating phase makes only the standard components needed for a batch and subcontracts a proportion of them (with additional cost) to expedite the process. In contrast, the second fabricating phase produces the finished multiple merchandise in sequence. The in-house rework processes with extra expense help retain the desirable quality. Each merchandise’s finished batch is transported to the clients in equal-sized numerous shipments. This study derives the optimal batch cycle length and transporting frequency by minimizing the overall fabricating-shipment expenses (including clients’ holding costs). This work offers a numerical example demonstrating various crucial system features influenced by the factors of subcontracting, postponement, rework, and transportation policies to facilitate managerial decision making in industries.