A stochastic Petri net approach for inventory rationing in multi-echelon supply chains

Manufacturing supply chains are considered as discrete event dynamical systems (DEDS) where coordination of material and information flows is essential to satisfy customer orders and to improve the bottomline of the constituent organizations. A critical problem that is often faced by distribution centres that hold finished good inventory is that of inventory rationing. Inventory rationing is a useful strategy to tackle the problem of conflicting objectives i.e., minimizing inventory costs (holding and backorder) on the one hand and achieving the desired customer service levels (CSLs) on the other. The focus of this paper is to formulate Generalized Stochastic Petri net models to address the inventory rationing problem in the context of multi-echelon make-to-stock distribution chains, where the goods flow through multiple echelons, typically from product manufacturers all the way up-to the retail outlets. The statistical inventory control (SIC) policies modeled by the GSPN are (R, s, S) and a variant that we propose, (R*, s, S). We compare the performance of the model under two rationing settings. The first setting considers a case without cooperation, where the individual local stockpoints maximize their own performance. The second setting considers a case with cooperation, where the local stockpoints cooperate with each other to maximize the overall system performance. We provide a methodology to approximately determine the optimal rational fractions with different weights assigned to expected backorder and holding cost components (b/h). We present some interesting results obtained after rigorous numerical experimentation on the model.