An imperfect fuzzy production-inventory model over a finite time horizon under the effect of learning

This article develops a production-inventory model for a deteriorating item under a defective production process over a finite time horizon. Here, demand varies with marketing cost and mark-up to the production cost. There is a learning effect on the set-up cost in each production cycle. The objective of this model is to maximise total profit (TPF) which includes sale proceed shortage cost, holding cost, deterioration cost, production cost, set-up cost and marketing cost. Considering the fuzzy nature in demand parameter, marketing cost and defective fraction of production rate, a fuzzy model is also developed. Here, fuzziness is introduced using triangular fuzzy numbers. Now using signed distance method and centroid method, respectively, the objective function is reduced to two different crisp models. For the crisp model, analytically it is shown that it possesses a global optimal solution. The models are solved using a gradient based non-linear optimisation technique – generalised reduced gradient method. Numerical illustrations have been made with the help of examples. Changes in TPF due to different deterioration rate, defective fraction of production rate and marketing costs are also presented graphically.