Huei-Hsin Chang

Mathematical modeling for determining the replenishment policy for EMQ model with rework and multiple shipments

Abstract This paper uses mathematical modeling to determine optimal inventory replenishment policy for the economic manufacturing quantity (EMQ) with rework and multiple shipments. The classic EMQ model considers a continuous inventory issuing policy for satisfying customer’s demands. It also assumes that all products produced are of perfect quality. However, in a real world vendor-buyer integrated environment, multi-shipment policy is practically used in lieu of the continuous issuing approach and generation of random defective items is inevitable. In this study, we assume the reworking of all defective items takes place when the regular production process ends in each cycle. Failure in repair exists; a portion of reworked items fails during the reworking and becomes scrap. The finished items can only be delivered to customers if the whole lot is quality assured at the end of rework. Fixed quantity multiple installments of the finished batch are delivered to customers at a fixed interval of time. Mathematical modeling and analysis are employed in this study for solving such a realistic EMQ model. The long-run average cost function is derived, its convexity is proved, and a closed-form optimal manufacturing lot size is obtained. Two special cases to the proposed model are examined.

Mathematical modeling for solving manufacturing run time problem with defective rate and random machine breakdown

This paper employs mathematical modeling for solving manufacturing run time problem with random defective rate and stochastic machine breakdown. In real life manufacturing systems, generation of nonconforming items and unexpected breakdown of production equipment are inevitable. For the purpose of addressing these practical issues, this paper studies a system that may produce defective items randomly and it is also subject to a random equipment failure. A no resumption inventory control policy is adopted when breakdown occurs. Under such a policy, the interrupted lot is aborted and malfunction machine is immediately under repair. A new lot will be started only when all on-hand inventory are depleted. Modeling and numerical analyses are used to establish the solution procedure for such a problem. As a result, the optimal manufacturing run time that minimizes the long-run average production-inventory cost is derived. A numerical example is provided to show how the solution procedure works as well as the usages of research results.

Remarks on the optimization process of a manufacturing system with stochastic breakdown and rework

Abstract This paper reexamines the optimization process of a manufacturing system with stochastic breakdown and rework proposed by Chiu [S.W. Chiu, An optimization problem of manufacturing systems with stochastic machine breakdown and rework process, Applied Stochastic Models in Business and Industry 24 (2008) 203–219]. The proof of convexity of the long-run average cost function for the aforementioned manufacturing system is provided in this note. It can be used to replace the conditional convexity given in Theorem 1 of Chiu (2008) [1] . Therefore, when determining the optimal solution for such a real-life system, computational efforts in verifying the conditional convexity can now be omitted, due to the improved quality of the optimization process.

Replenishment lot sizing with an improved issuing policy and imperfect rework derived without derivatives

This study uses an alternative approach to reexamine a replenishment lot size problem with discontinuous issuing policy and imperfect rework. A straightforward approach in terms of algebraic derivation is proposed instead of conventional method with the need of applying first-order and second-order differentiations to system cost function for proof of convexity before derivation of the optimal lot size. The research result obtained in this study is identical to that in Lee et al. (2011), where they adopted conventional method to solve the problem. The proposed algebraic approach is helpful for practitioners who may have insufficient knowledge of differential calculus to understand with ease such a real life vendor-buyer integrated problem.

Solving multi-customer FPR model with quality assurance and discontinuous deliveries using a two-phase algebraic approach.

A multi-customer finite production rate (FPR) model with quality assurance and discontinuous delivery policy was investigated in a recent paper (Chiu et al. in J Appl Res Technol 12(1):5–13, 2014) using differential calculus approach. This study employs mathematical modeling along with a two-phase algebraic method to resolve such a specific multi-customer FPR model. As a result, the optimal replenishment lot size and number of shipments can be derived without using the differential calculus. Such a straightforward method may assist practitioners who with insufficient knowledge of calculus in learning and managing the real multi-customer FPR systems more effectively.