Analysis of a production/inventory system with multiple retailers

We study a production/inventory system with one manufacturing plant and multiple retailers. Production lead times at the plant are stochastic and endogenously determined by the orders placed by the different retailers. Assuming stochastic (phase-type distributed) production and setup times, we make use of matrix analytic techniques to develop a queuing model that is capable to compute the distribution of the time orders spend in the production facility, depending on the retailer’s lot sizing decisions. The time orders spend in the production facility influences holding and backlogging costs at the retailers. Given the distribution of the time spent in the production facility, the distribution of inventory levels at each retailer can be computed. The goal is to compute total costs given the inventory parameters for every retailer, taking the endogeneity of their order policy on production lead times into account. Thanks to this procedure we will be able to analyse the interactions between the order policies of the retailers.status: publishe