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The goal of this paper is to propose a Generalized EOQ inventory model, which combines Inventory replenishment and pricing decisions for perishable product in an Inventory model. The Stochastic Demandrequests for new and old items are derivedvia linear functions of their cost. The proposed solution obtains from the optimum system solution, such as food Procurement price, Shortage cost, Purchasing cost, Operational cost and Total costare reduced. A Mathematical model is introduced along with differential matrix to find optimal solutions for the Inventory method in food production planning. Numerical example and Sensitivity Analysis are explained in the proposed system. Brownian Motion are found from Cycle Length (L= 1.1 to 1.5). The Brownian Motionanalyses all the costs and plays a major part to reduce it further.

Generalized Economic Order Quantity Inventory Model using Brownian Motion in Food Production Planning