Two-echelon fuzzy stochastic supply chain for the manufacturer–buyer integrated production–inventory system

This paper deals with two-echelon integrated procurement production model for the manufacturer and the buyer integrated inventory system. The manufacturer procures raw material from outside suppliers (not a part of supply chain) then proceed to convert it as finished product, and finally delivers to the buyer, who faces imprecise and uncertain, called fuzzy random demand of customers. The manufacturer and the buyer work under joint channel, in which a centralized decision maker makes all decisions to optimize the joint total relevant cost (JTRC) of entire supply chain. In this account, in one production cycle of the manufacturer we determine an optimal multi-ordering policy for the buyer. To be part of this, we first derive the JTRC in stochastic framework, and then extend it in fuzzy stochastic environment. In order to scalarize the fuzzy stochastic JTRC, we use an evaluation method wherein randomness is estimated by probabilistic expectation and fuzziness is estimated by possibilistic mean based on possibility evaluation measure. To derive the optimal policies for both parties, an algorithm is proposed. A numerical illustration addresses the situations of paddy procurement, conversion to rice and fulfillment of uncertain demand of rice. Furthermore, sensitivity of parameters is examined to illustrate the model and algorithm.