Optimal lot size with learning consideration on an imperfect production system with allowable shortages

This paper investigates the learning effect of the unit production time on optimal lot size for the imperfect production system with allowable shortages. We seek to minimize the total cost of the imperfect production system through optimal determinations of the production quantity and the shortage level of each cycle. From the optimality conditions of the proposed model, several interesting and useful properties are investigated and an efficient and effective algorithm is developed to search for the optimal solution. Also, the convergence of the iterative algorithm in this paper is shown. Finally, numerical examples are provided to illustrate the features of the model and sensitivity analyses are performed to discuss the impact of changes in parameter values on the decision variables and objective function.