This inventory model is regarding the analysis of an efficient production plan with two stage supply chain consisting of customers, multiple retailers and one manufacturer. The demand from customers appears arbitrarily from more retailers at a time. The multiple retailers ’stock up inventory from the manufacturer when the customer's orders are obtained after the inventory exhausted to zero level. There is one assumption that the manufacturer's inventory is always constant. At the zero level or below the zero level inventories, the manufacturer starts the production and when there is optimal level of the inventory, he stops the production. The inventory system is being planned while orders arrived from the multi number of retailers are being discharged. The arrival times of the order from customers are independent and these orders are going to be distributed indistinguishably. Therefore, the inventory processes are be converted by the manufacturer and the retailer into renewal process that is complicated to solve analytically for a general distribution. The theoretical analysis is made to calculate the manufacturing-holding volume in period 1 and 2, production cycle length in long run average cost to solve the problem.
Production lot sizing, Inventory with stochastic demand, Renewal theory, Volterra equation of the second kind
