A production-inventory model with permissible delay incorporating learning effect in random planning horizon using genetic algorithm

Subject Areas : Mathematical Optimization

Mohuya B. Kar ¹ , Shankar Bera ² , Debasis Das ³ , Samarjit Kar ⁴

1 - Department of Computer Science, Heritage Institute of Technology, Kolkata, WB, 700107, India
2 - Department of Mathematics, National Institute of Technology, Durgapur, WB, 713209, India
3 - Department of Mathematics, National Institute of Technology, Durgapur, WB, 713209, India
4 - Department of Mathematics, National Institute of Technology, Durgapur, WB, 713209, India

Received: 2020-10-02 Accepted : 2020-10-02 Published : 2015-12-01

Keywords: Inventory . Learning effect . Inflation . Random planning horizon . Permissible delay in payment,

Abstract :

This paper presents a production-inventory model for deteriorating items with stock-dependent demand under inflation in a random planning horizon. The supplier offers the retailer fully permissible delay in payment. It is assumed that the time horizon of the business period is random in nature and follows exponential distribution with a known mean. Here learning effect is also introduced for the production cost and setup cost. The model is formulated as profit maximization problem with respect to the retailer and solved with the help of genetic algorithm (GA) and PSO. Moreover, the convergence of two methods—GA and PSO—is studied against generation numbers and it is seen that GA converges rapidly than PSO. The optimum results from methods are compared both numerically and graphically. It is observed that the performance of GA is marginally better than PSO. We have provided some numerical examples and some sensitivity analyses to illustrate the model.