In real life literature review of inventory theory, it is assumed that the payment will be made to the vendor for the goods immediately after the receiving the consignment is relevant to economic policy for the companies of supplying. The several researchers have developed analytical inventory models with some considerations. Chang, et al (2010) presented the discount cash flows approach to the analysis of the optimal inventory policy in the presence of the trade credit Ghare, Schrader (1963), Goyal (1985). Since this literature reviews of study as Chung (1997), Goswami and Chaudhuri (1992), Covert, Philip (1973), Misra (1975), Elsayed and Teresi (1983), Donaldson (1977) used inventory replenishment policy for a linear trend in demand.
Buzacott (1975) developed economic order quantity model with the inflation rate. Pakkala, Achary (1992) developed deterministic -inventory model for deteriorating items with two warehouses and finite replenishment rate, Hwang, and Hahn (2000) proposed an optimal procurement policy for items with an inventory level-dependent demand rate and fixed lifetime. Teng and Chang (2005), Soni and Shah (2008), Stavrulaki (2011), Musa and Sani (2012), most of the researcher’s Authors formulated model with infinite horizon demand of the items exist over infinite time. According to this assumption, keep product specification remains unchanged forever. Mishra (1973) formulated an inventory model with a variable rate of deterioration, a finite rate of production and no shortage. Goswami and Chaudhuri (1992) represented inventory model the deterioration rate is assumed to be proportional with time, the finite production rate to be proportional to the demand rate, the demand rate to be time-dependent with a linear positive trend. Silver and Meal (1973) developed an approximate solution procedure referred to as Silver, Meal Heuristic for the general case of deterministic time-varying demand pattern.
Donaldson (1977) solve analytically the classical inventory policy for the case of the linear trend in demand. Cobber and Oudheusden (1996) developed Inventory models for fast moving spare parts subject to sudden death obsolescence. Break-ability is defined as broken items cannot use it under any circumstances to sell it directly to the buyers. Enter in this model there is case can add it as the items have break-ability rate especially tiles with ability to sell the breakable items as raw material for local industry used them as small pieces, in the local tiles production to increase the quality as strength that is decrease the total cost for the items ,because the cost of breakable items is not distributed to the cost of no breakable, Whatever if the break-ability rate occurs unintentionally or intentionally, so that is helpful to decrease the total cost . The management and holding inventories for breakable items become an important for inventory managers at the same time the minimization of total cost, there are many items having break-ability property as tiles with each types which are used for bathrooms, dining halls, kitchens, platforms of house and trains and many purposes, including Yemen as one world’s countries as produced in Yemen or imported others companies at neighboring counties as Saudi companies of production tiles, Emirates, European, Egypt.