With the aim of increasing capacity to smooth production planning and coping with existence of random scrap in real fabrication processes, this paper explores an economic production quantity (EPQ)-based inventory system with random scrap and adjustable production rate. Mathematical modeling is used to carefully portray and analyze the problem, and the expected system cost function is derived and proved to be a convex function. Then, differential calculus is employed to help determine the optimal batch size for the proposed system. Numerical example along with sensitivity analysis is provided to demonstrate applicability of the obtained results. Analytical outcomes pointed out that this in-depth exploration to the problem reveals diverse important managerial decision-making required information.

In order to gain competitive advantages, managers of present-day supply chain systems need to achieve critical operation goals, such as keeping fl exible fabrication schedule, retaining product quality, maintaining timely delivery, and lowering overall operating costs. Inspired by these factors, this study developed a decision model for managers to investigate the joint impacts of quality-assured issues, overtime, and multi-shipment plan on optimal fabrication-shipment policy and on diverse system parameters of the economic production quantity (EPQ)-based supply chain system. An imperfect fabrication process producing perfect quality, repairable, and scrap items is assumed in the proposed system, along with assumptions of a fl exible overtime schedule to partially expedite fabrication rate and a discontinuous multi-delivery policy for distributing end products. With a help from mathematical modeling and optimization method, the closed-form optimal fabrication-shipment policy is derived. A numerical example was employed to demonstrate applicability of our result and to expose critical managerial information of the system for supporting decision-making.

This study investigates a multi-item fi nite production rate-(FPR-) based system incorporating a delayed product differentiation policy and common parts' outsourcing strategy. A two-stage fabrication scheme is proposed, wherein, in stage one, all common parts of the end products (assuming they have a known completion rate as compared with the fi nished products) are partially produced in-house and partially supplied by an outside contractor with an extra unit outsourcing; in stage two, all end products are fi nished in sequence, under a rotation fabrication cycle time discipline. An explicit model is developed to clearly represent the proposed problem. Through the optimization technique, the optimal rotation cycle decision is obtained. Thus, diverse characteristics of this particular multi-item, FPR-based system with postponement and outsourcing strategies can now be revealed. As demonstrated by numerical illustrations, these characteristics include the (i) convexity of the system cost function, (ii) impact of common parts' outsourcing strategy on the utilization, (iii) breakup of system cost components, (iv) combined impact of the outsourcing ratio and common parts' completion rate on the system cost function, and (v) effect of the outsourcing ratio on optimal rotation cycle decision. Our decision-support-type system can facilitate production managers in achieving their goals of reducing orders' response times and minimizing the overall system cost.

A manufacturing batch-size and end-product shipment problem with outsourcing, multi- shipment, and rework was investigated in a recent article [1] using the mathematical modeling and derivatives in their solution procedure. The present work employs an alternative method namely, a two-phase algebraic approach to resolve the problem in [1] and determine the optimal manufacturing batch-size and end-product shipment policies that keep total system cost at minimum. Such a straightforward solution process enables the practitioners in production planning and controlling filed, who may have inadequate knowledge of the differential calculus, to comprehend and easily solve the best replenishing batch-size and shipment policies of this realistic problem.