Heuristic Procedure for a Supply Chain DesiCombinatorial Optimization Problem gn Incorpor ting Cost of Quality in

ln this paper, M'e present a modelfor st{rzply chain clesig. n that consicters the Cost ofeuati4, as well as the traditional mantijbcluring and distribution e sts. 71he main contributions are; 1) our moclet internatly eomputes quality costsfor the whote siuzpCJ; chain eonsidering the interdependencies among business entities ivhereas previous works have assumed exogenously gii)en Cost of'euatityjunctions; and 2) our model can be used at a stratagic ptanning tevel to design a togistic route that achieves a mctxintum prqfit ",hile considering the overatt quatity level within a st{nply chain, PVe provicle a sotution method based on simutated annealiizg and discuss severat iUustrative xanrptes. Kqyivords: (ombinatoriatproblem, heuristic aigorithms, st{tzp4v ehain netivork design, Cost of9uality. 1.Introduction Cost ofQuality (COQ). or quality cost. represents a powerfu1 measurement system that translates the implications of poor quality, activities of a quaHty program, and quality improvement efforts into a monetary language for managers. COQ is a language that every stakeholder can understand and afTects operating costs. profitability, and consumer need[1]. Although COQ has been applied mostly within enterprises, it is crucial to extend COQ as an external measure and integrate hese costs into supply chain modeling. Srivastaya [1], who gives the first step towards estimating COQ in a supply chain, measured COQ in monetary terms at selected third-party contract manufacturing sites ofa pharmaceutical company located in India. Another work that focuses on integrating COQ in the supply chain is the work by Ramudhln et al. [2]. This seminat study presents a model that integrates COQ into the modeling ofa supply chain network for a sing]e product, three-echelon system (suppliers, manufacturing plants, and customer groups), The model seeks to minimize the overall operational and quality costs. Ramudhin et al. [2] found that adding a known COQ fi]nction nly for suppliers into the objective function results in a difference ofabout 16% in Quality and Manufacturing Centcr. '1'ecnol6gico de Monterrey. Carnpus Monterrey. Mexice. E. Garza Sada 2501 Sur, C,P. 64849. Monterrey. N.L. M6xico. '1'el. : +52 818 358 2000 ext. 5364 E-mail address: krystel.casti]]oet}'ttu.edu CCasti]lo-Vil]ar) costs and changes the network solution. When COQ is not included. the optimal solution includes the suppliers with the lowest operational costs, but there is ne infbrmation in regard to the quality non-confbrmance cost Thus, choices made solely on operational cost could sacrifice quality and lead to additional quality non-confbrrnance costs or corrective action costs in the subsequent stages of the supply chain. More recently, Alzaman et al. [3] established a mathematical model utilizing an exogenously given COQ quadratic function that considers a defect ratio at aLl supp]y chain nodes. In previous studies, the COQ function based on percent defective is assumed to be given. This paper deals with the development ofa mathematica] model that internally computes the COQ for a whole supply chain considering the interdependencies among the fraction defective at each stage of the supply chain. The model seeks to maximize the total profit by selecting the appropriate suppliers. ptants, and retailers, as well as by determining operating parameters (fraction defectiye and error rate at inspection) within the manufacturing plants. The resulting model is a constrained nonlinear O-1 integer problem. No previous work has addressed how the COQ arises for an entire supply chain by taking internal and operational decisions within the manufacturing plant. The proposed mode] aims to serve as a decision making tool for engineering managers by helping with the design and quaLity planning of logistic routes for manufacturing plants in the design phase, i.e. not yet oper-