An imperfect production process in a volume flexible inventory model

This paper hypothesizes an imperfect production/inventory system where the items produced are a mixture of perfect and imperfect quality. Some of the imperfect quality items can be sold at a reduced selling price. The unit production cost is taken to be a function of the finite production rate which is treated as a decision variable. The mathematical expression for the expected profit function is derived and it is maximized subject to different constraints of the system using Interior Penalty Function Method for Constrained Optimization, the algorithm of which is given. The solution procedure is illustrated with the help of numerical examples. The sensitivity of each variable to changes in the values of the parameters of the system is examined. Lastly, various issues conforming the system are discussed.