Optimal locations of on-line and off-line rework stations in a serial production system

The production rate and product quality are two vital concerns for any manufacturing industry. Number of defective items reduces production rate and increases unit production cost. Moreover, if nonconforming items reach to the customers then manufacturer’s goodwill may drastically go down. Thus, quality inspection is treated as an inherent part of manufacturing. In this research, an N -stage serial production line with an inspection station at the end of it is considered to make decisions concerning this issue. On detecting a defective item at the end of the line it is scrapped or repaired at regular workstation or is sent to an off-line rework station for repair. Assuming each workstation produces a single type of defect a unit cost function is developed for alternative decisions on each type of defect. In order to minimise the unit cost of production and determine an appropriate decision for individual defect types, a fractional mixed integer nonlinear programming is formulated. After transformation to a mixed integer linear programming problem it is solved optimally. A small problem from garments industry is described in detail to show the solution procedure with a branch and bound method. Empirical tests with up to 40 workstations are permed to show the efficiency of the solution process.