Impacts of inspection rate on integrated inventory models with defective items considering capacity utilization: Rework-versus delivery-priority

In an integrated inventory system with an imperfect production process, the manufacturer usually devotes itself to inspecting and reworking defective items. However, inspecting and reworking processes consume additional time, thereby possibly delaying the manufacturer's timely delivery and further failing to satisfy the retailer's order requirement on time. Thus, this paper builds joint economic lot-size problem (JELP) models that consider defective items, where the manufacturer is responsible for production, inspection and reworking processes. Based on the relationship between the inspection rate and production rate, this paper incorporates both the inspection-rate-insufficient (IRI) and inspection-rate-sufficient (IRS) scenarios. Under each scenario, two rework policies are proposed based on the order of priority between reworking process and delivery process: rework-priority policy (RPP) and delivery-priority policy (DPP). In addition, by incorporating the inspection/production/rework rate, effective-capacity-utilization (ECU) is first defined to consider the feasibility of joint production-inventory solutions, thus resulting in the following several interesting findings. (1) The integrated inventory system under IRI (IRS) scenario is suggested to be based on the system's inspection rate (production rate) to quantify its ECU to ensure the feasibility of derived solutions. (2) Furthermore, ECU under RPP (DPP) is related (unrelated) to the number of shipments, thus implying that the corresponding integrated system can (cannot) initiatively manage its ECU by adjusting the number of shipments. (3) Additionally, the integrated system can be based on the defect rate to evaluate applications of RPP and DPP. That is, under the middle-defect-rate, RPP can be theoretically proven to be the preferred rework policy, while under the lower-defect-rate, the integrated system performs better under DPP via numerical results.