Quality and pricing decisions for substitutable items under imperfect production process over a random planning horizon

The paper determines the optimum qualities and prices of two substitute products for a manufacturer cum retailer in an imperfect production process over a random planning horizon for maximum profit. In this Economic Production Lot-size (EPL) process, items are produced simultaneously, defective production commences during the out of-control state after the passage of some time from the commencement of production and the defective units are partially reworked. The items are substitutable to each other depending on their prices and qualities jointly or either of these two. Unit production cost depends directly on raw-material, labour and quality improvement costs and inversely on the production rate. A part of it is spent against environment protection. Here learning effect is introduced in the set-up and maintenance costs. For the whole process, the planning horizon is random with normal distribution, which is treated as a chance constraint. The models are formulated as profit maximization problems subject to a chance constraint and solved using Genetic Algorithm with Variable Populations (GAVP). The models are demonstrated numerically and the near-optimum results are presented graphically.