A Queuing Model for Stochastic Location‌-inventory Problem with Waiting Cost Considerations

This paper presents a three-level supply chain model which includes single supplier, several distribution centers and sets of retailers. For this purpose, by adopting the queuing approach, a mixed nonlinear integer programming model is formulated. The proposed model follows minimizing the total cost of the system by determining: 1) the number and location of distribution centers between candidated ones; 2) the possibility of allocating each of the retailers to the distribution centers; 3) the amount of retailers demand; and 4) the policy of distribution centers. In the proposed model, the cost of waiting in queue is also considered. In order to make the problem more realistic, we consider uncertain demand and lead-time, which follow Poisson and Exponential distributions, respectively. Hence, we apply continuous-time Markov process approach to obtain the amount of annual ordering, purchase and inventory. Then, the results are used to formulate the location-inventory problem. Finally, the proposed model is solved using GAMS software version 24.1.3.