Decision process for multiobjective, multi-item production-inventory system via interactive fuzzy satisficing technique

Multiobjective and single-objective inventory models of stochastically deteriorating items are developed in which demand is a function of inventory level and selling price of the commodity. Production rate depends upon the quality level of the items produced and unit production cost is a function of production rate. Deterioration depends upon both the quality of the item and duration of time for storage. The time-related deterioration function follows a two-parameter Weibull distribution in time. In these models, results are derived for both without shortages and partially backlogged shortages. Here, objectives for profit maximization for each item are separately formulated with different goals and compromise solutions of the multiobjective production/inventory problems are obtained by goal programming method. The models are illustrated with numerical examples and results for different formulations are compared. The results for the models assuming them to be a single house integrated business are also obtained using a gradient-based optimization technique and compared with those obtained from the respective decentralized models. Taking man-machine interaction into consideration, interactive solutions are derived for one of the said models—multiobjective model with shortages using interactive fuzzy satisficing method. Pareto optimum and satisficing results are derived for some numerical data.