On Improving Replenishment Lot Size of an Integrated Manufacturing System with Discontinuous Issuing Policy and Imperfect Rework

Abstract

ABSTRACT

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

“…In this study, an alternative approach is adopted to reexamine Lee et al's model (2011) as stated earlier. To ease the readability, this study adopts the exact notation as used in Lee et al (2011). Description the model is as follows: consider a real life production system may produce x portion of random nonconforming items at a production rate d. Among nonconforming items, a θ portion is assumed to be scrap and the other (1 -θ) portion can be reworked at a rate P1, within the same cycle when regular production ends.…”

“…E[TCU(Q)] = the long-run average costs per unit time for the proposed model. Figure 1 depicts producer's on-hand inventory of perfect quality items (Lee et al, 2011). Again, for the purpose of easing readability, this paper adopted the same basic formulations as that in Lee et al (2011).…”

“…Figure 1 depicts producer's on-hand inventory of perfect quality items (Lee et al, 2011). Again, for the purpose of easing readability, this paper adopted the same basic formulations as that in Lee et al (2011). Total production-inventory-delivery cost per cycle TC(Q) consists of variable manufacturing cost, setup cost, variable rework and disposal cost, the fixed and variable (n + 1) shipping cost, holding cost for perfect quality and nonconforming items during t1 and t2, holding cost for reworked items during t2, and vendor's holding cost for finished goods during the delivery time t3.…”

“…Research has since been focused on addressing issues of various aspects of multi-deliveries in supply chain optimization (Goyal, 1977;Banerjee, 1986;Hahm and Yano, 1992;Viswanathan, 1998;Swenseth and Godfrey, 2002;Diponegoro and Sarker, 2006;Kim et al, 2008;Abolhasanpour et al, 2009;Chiu et al, 2009;Chen et al, 2010;Ye and Xu, 2010;Wong, 2010;Hsieh et al, 2010;Chiu et al, 2011b;Chen et al, 2011;Lee et al, 2011). Lee et al (2011) investigated the optimal replenishment lot size for a vendor-buyer integrated system with discontinuous issuing policy and imperfect rework. They employed the differential calculus to prove the convexity and derive the optimal production batch size for such a specific problem.…”

“…Other studies that have applied the same (or similar) method include Cheng and Ting (2010), Chiu et al (2010d). This paper applies the same algebraic approach to reexamine the problem studied by Lee et al (2011). As a result, the optimal replenishment lot size and the long-run average cost function can all be derived without using differential calculus.…”