Bi-product inventory planning in a three-echelon supply chain with backordering, Poisson demand, and limited warehouse space

In this paper, we apply continuous review (S-1, S) policy for inventory control in a three-echelon supply chain (SC) including r identical retailers, a central warehouse with limited storage space, and two independent manufacturing plants which offer two kinds of product to the customer. The warehouse of the model follows (M/M/1) queue model where customer demands follow a Poisson probability distribution function, and customer serving time is exponential random variable. To evaluate the effect of considering bi-product developed model, solution of the developed model is compared with that of the two (M/M/1) queue models which are separately developed for each product. Moreover, and in order to cope with the computational complexity of the developed model, a particle swarm optimization algorithm is adopted. Through the conducted numerical experiments, it is shown that total profit of the SC is significantly enhanced using the developed model.