Yuan-Shyi Peter Chiu

Optimization of the finite production rate model with scrap, rework and stochastic machine breakdown

This study employs mathematical modeling along with a recursive searching algorithm to determine the optimal run time for an imperfect finite production rate model with scrap, rework, and stochastic machine breakdown. In real-life manufacturing systems, generation of defective items and machine breakdown are inevitable. The objective of this paper is to address these issues and to be able to derive the optimal production run time. It is assumed that the proposed manufacturing system produces defective items randomly, a portion of them is considered to be scrap, and the other portion can be repaired through rework. Further, the proposed system is subject to random breakdown and when it occurs, the abort/resume (AR) policy is adopted. Under such an inventory control policy, the production of the interrupted lot will be resumed immediately when machine is fixed and restored. Mathematical modeling along with a recursive searching algorithm is used for deriving the replenishment policy for such a realistic production system.

Optimal production lot sizing with rework, scrap rate, and service level constraint

This paper studies the optimal lot-sizing decision for a production system with rework, a random scrap rate, and a service level constraint. In most real-life manufacturing settings, generation of defective items is inevitable. Reworking of defective items may significantly reduce overall costs. We derive an optimal operating policy and prove that the expected overall costs of such a production system with backlogging permitted is less than or equal to that of the same model without backlogging. Then the relationship between the imputed backorder cost and maximal permitted shortage level is derived for decision-making on whether the required service level is achievable. In the case that the required service level is not attainable, an equation for calculating the intangible backorder cost is proposed. This enables us to derive a new optimal lot-size policy that minimizes expected overall costs as well as satisfies the service level constraint. A numerical example is provided to demonstrate its practical usage.

Replenishment run time problem with machine breakdown and failure in rework

This paper studies the optimal replenishment run time for a production system with stochastic machine breakdown and failure in rework. In most real world manufacturing processes, generation of defective items and random breakdown of equipment are inevitable. This research addresses such reliability issues by examining a production system with a Poisson breakdown rate and an imperfect reworking process. When machine breaks down, no-resumption policy is adopted. Under such a policy, the present production run is aborted and will be restarted only when all on-hand inventories are depleted. Mathematical modeling is used. Derivations of production- inventory cost functions and proofs of theorems and proposition are presented, with the objective of determination of the optimal replenishment run time and lot size that minimize the expected costs per unit time. An illustrating example is provided to show its practical usage.

A note on optimal replenishment policy for imperfect quality EMQ model with rework and backlogging

A recent article on optimal replenishment policy of imperfect EMQ model by Chiu [S.W. Chiu, Optimal replenishment policy for imperfect quality EMQ model with rework and backlogging, Applied Stochastic Models in Business and Industry 23 (2007) 165-178], used mathematical modeling and differential calculus to derive the optimal ordering policy that minimizes overall costs. This paper presents a straightforward algebraic approach to replace the use of calculus on the cost function for determining the optimal replenishment solutions as well as the long-run average production-inventory costs for such an imperfect EMQ model. The algebraic method presented in this paper may enable students or practitioners with little or no knowledge of calculus to learn or to manage with ease the real-life manufacturing systems.

Combining an alternative multi-delivery policy into economic production lot size problem with partial rework

Highlights? This paper combines an alternative multi-delivery policy into an imperfect EPQ model with partial rework. ? It extends the work of Chiu et al. Journal of Scientific & Industrial Research, 2009; 68(6); 505-512]. ? It incorporates an n+1 delivery policy instead of n deliveries for the purpose of reducing vendors inventory holding cost. ? Mathematical modeling is used and as a result a closed-form optimal replenishment lot size solution to the problem is derived. ? A numerical example demonstrates that the research results serve the purpose of reducing vendors holding cost significantly. This paper combines an alternative multi-delivery policy into an imperfect economic production quantity (EPQ) model with partial rework, with the purpose of reducing suppliers stock holding cost. We extend the problem examined by Chiu et al. Chiu, Y.-S. P, Chiu, S. W., Li, C.-Y., & Ting, C.-K. (2009). Incorporating multi-delivery policy and quality assurance into economic production lot size problem. Journal of Scientific and Industrial Research, 68(6), 505-512] by considering an n+1 delivery policy in lieu of n multi-delivery plan for the specific EPQ model with partial rework. Under such a policy, an initial delivery of perfect (finished) items is distributed to customer for satisfying product demand during manufacturers regular production time and rework time. At the end of rework, fixed quantity n installments of the finished products are delivered to customer at a fixed interval of time. As a result, a closed-form optimal replenishment batch size solution to the problem is obtained. A numerical example with analysis and comparison is provided to show practical usage of the proposed model and demonstrate its significant savings in stock holding cost.

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.

Optimal production lot sizing with backlogging, random defective rate, and rework derived without derivatives

Abstract This paper is concerned with the algebraic derivation for the production lot size problem with backlogging, random defective rate, and rework. Conventional approaches for solving optimal production lot size are by using the differential calculus on the productioninventory cost function with the need to prove optimality first. Recent articles proposed the algebraic approach to the solution of the classic economic order quantity (EOQ) and economic production quantity (EPQ) models without reference to the use of derivatives. This paper extends it to an EPQ model taking backlogging, random defective rate, and rework into consideration. This note demonstrates that optimal lot size for such an imperfect quality EPQ model can be derived without derivatives. The expected production-inventory costs can also be obtained immediately.

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.

Intra-supply chain system with multiple sales locations and quality assurance

The emergence of the global economy has transformed the interdepartmental nature of a transnational enterprise into a highly collaborative oriented team. This transformation enables the enterprise to lower its transaction and coordination costs and increase its competitive advantage in the global market. This study investigates such a so-called intra-supply chain system that exists in present-day transnational firms, wherein a single production unit manufactures products to meet the demands of multiple regional sales offices and incorporates quality assurance in its production. The objective of the present study is to determine an optimal production quantity and shipment policy that minimizes the integrated production-inventory-delivery costs for the intra-supply chain system. In this study, considerations related to a products quality assurance include inspection for quality, rework of defective items and failure in rework. Delivery of the finished products starts when quality of the entire production lot is assured. Multi-shipment policy is used to synchronously transport finished items to multiple locations for satisfying customer demands in each cycle. Mathematical modeling along with Hessian matrix equations is employed to solve the proposed intra-supply chain system. A numerical example with a discussion and cost-benefit analysis of outsourcing work to an external distributor is presented to demonstrate the practical applicability of the obtained results.

Notes on the mathematical modeling approach used to determine the replenishment policy for the EMQ model with rework and multiple shipments

Abstract A recent article (Chiu etxa0al. (2011)xa0 [22] ) used mathematical modeling along with differential calculus to derive the optimal replenishment lot size for an economic manufacturing quantity (EMQ) model with rework and multiple shipments. Unlike the conventional method that uses differential calculus with the system cost function to solve the economic lot size problem, this paper proposes a straightforward algebraic approach. It is demonstrated that both the optimal replenishment lot size Q ∗ and a simplified form for the long-run average cost E[TCU( Q ∗ )] for such a specific lot size problem can be derived without using differential calculus. This approach enables practitioners or students who may not have sufficient knowledge of differential calculus to better understand such a practical vendor–buyer integrated system.