Economic manufacturing quantity model with imperfect rework and random breakdown under abort/resume policy

Abstract

This paper studies the optimal production run time in an economic manufacturing quantity (EMQ) model with imperfect rework and Poisson machine breakdowns under abort/resume (A/R) control policy. In most realistic manufacturing processes, generation of defective items and random machine breakdowns are inevitable. In this study, a random defective rate is assumed and all defective items produced are reworked when regular production ends. The rework process is assumed to be imperfect. A proportion of reworked items fail during the reworking and become scrap. The system is subject to random breakdowns. The A/R inventory control policy is adopted when breakdowns occur, under such a policy, and the production of the interrupted lot will be immediately resumed when the machine is fixed and restored. Mathematical modelling is used and the integrated long-run average production-inventory cost per unit time is derived. Theorems on conditional convexity and on bounds of optimal production run times are proposed and proved. A recursive searching algorithm is developed for locating the optimal run time within the bounds, which minimizes the expected production-inventory costs. A numerical example with sensitivity analysis is provided to give insight into the operational planning and control of such a realistic production system.

Replenishment Lot Size and Number of Shipments for EPQ Model Derived Without Derivatives

“…The aforementioned results derived by algebraic approach, especially Equations (16) to (18) are verified in this section using the same numerical example [22]. Reconsider that customer demand of a product is 3,400 units per year and it can be produced at an annual rate of 60,000 units.…”

“…This paper also reveals a simpler form (i.e. Equation (18) for calculating the optimal cost function E[TCU(Q*,n*)]. The algebraic approach demonstrated in this paper, may enable practitioners or students who with little or no knowledge of calculus to learn or handle with ease the real-life EPQ model.…”

“…Studies have been carried out to enhance the classic EPQ model by addressing the issue of defective items produced [9][10][11][12][13]. The nonconforming items sometimes can be reworked and repaired hence the overall production costs can be significantly reduced [14][15][16][17][18][19][20][21][22]. Jamal et al [16] studied the optimal manufacturing batch size with rework process at a single-stage production system.…”

An Algebraic Approach for Determining the Optimal Lot Size for EPQ Model with Rework Process

“…For examples, the printed circuit board assembly (PCBA) in PCBA manufacturing, plastic goods in the plastic injection molding process, and production process in other industries, such as metal components, textiles, etc., sometimes employ rework as an acceptable process in terms of level of quality. Many studies were carried out to address imperfect quality issue of production systems [5][6][7][8][9][10][11][12][13][14]. Effect of random defective rate and the reworking of defective items on EPQ model were studied by Chiu and Chiu [15] using conventional methodology.…”

Reliability of a production system with intersectional lines

“…13 , a 14 , a 5 , a 15 , a 16 , a 17 , a 18 , a 19 g,16 , a 17 , a 18 , a 19 g. The following flow analysis of each workstation is based on the decomposed paths.…”