Title: A random fuzzy production inventory problem with backorder rate based on controllable preparation time and safety factor via genetic algorithm

Authors: Dipak Kumar Jana; Dipankar Chakraborty; Manoranjan Maiti

Addresses: Department of Applied Science, Haldia Institute of Technology, Haldia, Purba Midnapur-721657, West Bengal, India ' Department of Applied Science, Haldia Institute of Technology, Haldia, Purba Midnapur-721657, West Bengal, India ' Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapur-721102, West Bengal, India

Abstract: A random fuzzy (Ra-Fu) production inventory model with Ra-Fu backorder and lost sales in which the preparation time, cycle length and safety factor is formulated and solved. Instead of having stockout term in the objective function, a service level constraint is introduced to the model which implies that the stockout level per cycle is bounded. Also, a non-serviceable cost, unit production cost are included in the objective function due to the lost sale. We relax the assumption about the probability distribution of preparation time demand and apply the minimax distribution free procedure to solve the proposed problem. We have developed a computational algorithm to find the optimal values of preparation time, cycle length, safety factor and the decision reorder point. Finally, we have solved the proposed problem using three different soft computing techniques: 1) genetic algorithm (GA) technique; 2) generalised reduced gradient (GRG) technique; 3) Lagrange multiplier method via LIngo-11.0. In addition, the effects of the parameters are also incorporated. The above Ra-Fu model is illustrated graphically with a practical problem.

Keywords: random fuzzy production inventory; backorder rate; genetic algorithms; production-inventory systems; safety factor; preparation time; random-fuzzy demand; inventory modelling; lost sales; cycle length; service level constraints; stockout level; decision reorder point; generalised reduced gradient; GRG; Lagrange multiplier.

DOI: 10.1504/IJMOM.2014.067370

International Journal of Modelling in Operations Management, 2014 Vol.4 No.3/4, pp.170 - 192

Received: 17 May 2014
Accepted: 08 Aug 2014
Published online: 14 Feb 2015 *

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