The cost of inventory management depends mainly on two basic units, the cost of keeping inventory and the cost of orders, as these two units, one complements the other. To show the total cost of inventory through laws, the authors suggested many techniques for this purpose. The cost of this operation gradually decreases with the use of its materials. In this work, the authors proposed some techniques in order to obtain the minimum cost by dividing the agreed period in three percentages after it was divided into two periods, meaning that the percentage of the costs paid by the company in the first part, middle part, and in last part of the period in order to reduce the cost as much as possible through several equations. That is we try to reduce the number of times that the goods are ordered to the minimum by increasing the number of units of goods in one order and to know the total inventory costs.

The ST ST is a sub-tree of the original network so that the network graph can contain more than one sub-tree that reaches all the vertices of the network and the minimum spanning tree MST is the smallest measure among all the weights of the sub-spanning trees. To get the MST in a simplified way the Kruskal algorithm and the prime algorithm have been applied to several examples. In this work, we applied the new technique to the same examples, and the results were equal or have less value comparing with the above algorithms. The main idea of this technique is to link between the subject of the MST and the subject of the minimum cutoff, so that all the paths of the original graph were extracted and we calculated the weight of each path and chose the path that carried the largest weight, then we can grade by taking the paths according to need from largest to smallest and we cut the edge with the largest weight from that path and continue this process until the conditions of the ST are met.

It's known that the network is a graph that connects activities to points, as in every project the representation of activities and points varies, where the researchers previously assumed a weighted estimate of the time through a law in which they put the optimistic time estimate with the pessimistic time estimate with a weight of 1 and decided to give a greater weight to the weighted time estimate of 4, while in our current research it was proposed to improve the time estimate more likely and make it closer to reality with the achievement of the required results without any negative impact on the project, where the cost and time are reduced while the results are satisfactory, as we can give less weight to the weighted time estimate of 3 instead of 4 to estimate the potential time for distributors, while the pessimistic and optimistic time estimates remain the same with a weight of 1 for each of them.