In many things have deterioration such as

In general, Inventory model refers to deal with items in stocks or materials detained by an organization for use sometimes in the future. Items carried inventory include raw materials, purchased parts, components sub-assemblies, work in process, finished goods, supplies. Some reasons organizations maintain inventory include the difficulties in precisely preceding sales levels production times, demand, usage needs. Thus, inventory serves as a buffer against uncertain and fluctuation usage and keeps a supply of items available in case the items are needed by the organization or its customers. Even though inventory servers an important and essential role the expenses associated with financing and maintaining inventories is a substantial part of the cost of doing business 1. In real life, there are many things have deterioration such as chemicals, volatile liquids, a bank of blood, medicines and some other goods during shortage period is non-negligible 2. Deterioration is defined as decay, damage and it decreases usefulness so, the management and holding of inventories of perishable items become an important problem for the inventory management. On the other hand, delayed payment is an important from financing for business in aboard range of industries and Economics that extremely well developed and is being used in financial markets. Furthermore, both inflation and time value of money issue will have the main effect on financial markets 3.The elements of study are mentioned as following: All of the above-mentioned issues are separately regarded in some inventory models. But there are a few types of research in which only the number of all considered topics are mentioned together. Yung 7 developed two warehouse inventory management problems for perishable products with constant demand rate and back ordering shortages under inflation. Y Jung’s research in constant to the traditional deterministic two warehouse inventory model with shortages at the end of each replenishment cycle, an alternative model in which cycle begins with shortages and ends without shortages is proposed by author. Hou 10 developed an EOQ model over a finite planning horizon for perishable products with stock-depend demand rate and fullback ordering under inflation and time value money. Ghosh and Chaudhuri 11 developed an EOQ model with quadratic demand, shortages and time proportional deterioration in all cycles while Mukhopadhyay et al.15 developed and EOQ model for perishable items in which demand is price dependent. Mohan and Gopala Krihnan 18 proposed a multi-products EOQ model with delayed payment and budget limitation. Jamal et. al. 17 developed the EOQ model for perishable products whereas partial back ordering, the linear trend in demand and inflation are an assumed. Chen and Kang 16 developed and integrated inventory control model with the permissible delay in payment for determining the optimal order quantity time and replenishment frequency. Cheng et. al. 13 developed an inventory control model for deteriorating item in which trapezoidal type-demand and partial backlogging are assumed. Urban 12 developed the work on an extension of inventory models incorporating financing agreement with both supplier and customers.

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