An Ordering Policy for Deteriorating Items with Quadratic Demand, Permissible Delay, and Partial Backlogging
This paper develops an economic order quantity (EOQ) model for deteriorating items with time-dependent quadratic demand and permissible delay in payments. Shortages are allowed and are partially backlogged. The objective is to develop an optimal policy th
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globally challenging environment, customer satisfaction bounds to play a crucial role to enhance trade. Settlement of accounts is one of the factors which influence it. In traditional inventory models, either in deterministic or probabilistic, it is often assumed that payment will be made to the supplier for the goods, immediately after receiving them. But in reality this is not so. In order to promote demand and market share or decrease inventories of certain items, a supplier provides credit period to the customers. During that period, the customer earns interest on the payment received for the goods sold and thus enhances revenue. Therefore, customers prefer to delay payment until the deadline given by the supplier. Goyal [1] was the first to develop an inventory model with permissible delay in payments. A more general economic order quantity (EOQ) model with permissible delay in payments, price-discount effect, and different types of demand rate were developed by Sana and Chaudhury [2]. Recently, a permissible delay model for noninstantaneous deteriorating items with price and timedependent demand and partial backlogging has been developed by Reza and Isa [3]. In formulating inventory models, deterioration of items must be given due to consideration. During the storage period, items like foodstuff, pharmaceuticals, K. F. Mary Latha (*) Jayaraj Annapackiam College for Women, Periyakulam, Theni, Tamil Nadu, India e-mail: [email protected] R. Uthayakumar The Gandhigram Rural Institute-Deemed University, Gandhigram, Dindigul, Tamil Nadu, India
S. Sathiyamoorthy et al. (eds.), Emerging Trends in Science, Engineering and Technology, Lecture Notes in Mechanical Engineering, DOI: 10.1007/978-81-322-1007-8_63, © Springer India 2012
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chemicals, etc., deteriorate significantly with time which in turn decreases the amount or value of these products. Ghare and Schrader [4] developed a model for an exponentially decaying inventory. Researchers [4–6] relaxed the assumption of constant deterioration rate and developed models by considering the varying rate of deterioration. Deteriorating inventory models with trended demand were developed by researchers [7–15]. Inventory models with exponentially time-varying demand patterns were developed by Jalan and Chaudhuri [16]. Sometimes stock may be inadequate to fulfill the customer’s demand. In stock out period, if the customers prefer to wait for the items they can be backlogged; if they move to other suppliers the demand is lost. Several researchers have developed models under the assumption that stock out items are partially backordered. Many EOQ models were developed in the literature considering constant demand focusing on the control of inventories. Of late, many researchers [17–23] etc., have concentrated on realistic models with time-varying demand. The review of the literature shows that the researchers have focused only on linear and exponential time-dependent demand. A linearly time-varying demand indicates an unrealistic
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