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The subject of this paper is the inventory-production problem, which is a oneof the optimization problems in a decision area in which inventory volumeand production volume are considered together. There are many approachesto this problem but for the first time, this problem is modelled by means ofa capacitated graph network and a solution to the problem is proposed onthe basis of this model which consists of finding the maximum flow with theminimum sum of production and inventory cost. In this article, only a solutionfor one kind of product for the deterministic inventory-production optimisationproblem is presented and for this one kind of product, a maximum flow witha minimum cost for each considered demand period is calculated. The maximumflow with minimum cost is a solution to the homogenous inventory-productionoptimisation problem. The solution to the one kind of product for the inventoryproductionproblem consist of maximum flow with minimum cost for a totaldemand from all periods, which has been taken into consideration.

A method for the solution of the homogeneous inventory-production optimisation problem