Abstract
This paper presents an EOQ model with constant demand rate for non deteriorating items where shortages are allowed. In this paper shortages are considered as completely backlogged. The production rate is assumed to be proportional to demand rate and finite. The optimal solution of the model has been done for finding optimal time, optimal average cost by considering four different situations. Numerical example and sensitivity analysis is given to illustrate the proposed model.
Highlights
In last few decades, Mathematical ideas have been developed in different areas in real life problems, for controlling inventory
When items are kept in stock as an inventory for fulfilling the future demand, there may be deterioration of items in the inventory system, In inventory models generally four types of demand are assumed: (a) constant demand (b) time-dependent demand (c) probabilistic demand and (d) stock-dependent demand, inventory models dealing with constant demand have more relevance and common in the present situations
The production starts at t=T1 and backlog is cleared at t=T2
Summary
Mathematical ideas have been developed in different areas in real life problems, for controlling inventory. Chung et al [2], established the optimal inventory policies under permissible delay in payments depending on the order quantity and total minimum variable cost per unit of time is obtained. Tripathi and Mishra [9], established an inventory model with shortage, time-dependent demand rate and quantity dependent permissible delay in payment. In this paper [10] demand rae is considered as a function of selling price and order level inventory model for deteriorating items with single warehouse is developed where shortages are taken into consideration and it is completely backlogged. In paper [11] backlogging rate is considered as variable and dependent on the waiting time for the replenishment Research such as Park [12], Hollier and Mark [13], and Wee [14] considered the constant partial backlogging rate during the shortage period in their inventory models. The thime proportion partial backlogging rate was developed by Chang and Dye [16], Wang [17], Teng and Yang [18], Yang [19], Wu et al [20], Dye et al [21] and so on
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