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A multi-item producer-retailer integrated system featuring overtime and random scrap is studied. The objectives are to jointly decide the most economic rotation fabrication cycle time and distribution of products. In order to meet the increasing demands of diversified end items, production managers today need to plan a multiproduct fabrication schedule and to expedite both manufacturing and transportation times so that they can meet product demands as quickly as possible. Also, due to potential uncontrollable reasons, scrap items are generated randomly in a real fabrication process. To address the aforementioned issues, this study examines a multi-item producer-retailer integrated system featuring overtime and random scrap. We build a mathematical model to interpret the proposed multi-item producer-retailer integrated system which incorporates shipping and retailer’s holding cost. The Hessian matrix equations are used for solving the optimality of the system. Diverse important system information can now be exposed to backing managerial decision makings, which includes individual and combined influences of variations in particular system factor(s) (such as scrap rate and overtime related parameters) on the specific system performance.
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