Stochastic Inventory System with Compliment Item and Retrial Customers

Stochastic Inventory System with Compliment Item and Retrial Customers

N. Anbazhagan (Alagappa University, India)
Copyright: © 2016 |Pages: 17
DOI: 10.4018/978-1-5225-0044-5.ch009


In this chapter, the author consider a two commodity stochastic inventory system under continuous review with maximum capacity of i-th commodity is Si(i=1,2). In this two commodity one is main item and the other is compliment item. It is assumed that demand for the i-th commodity is of unit size and demand time points form a Poisson process. The compliment item is supplied as a gift whenever the demand occurs for the main item, but no main item is provided as a gift for demanding a compliment item. Reordering for supply is initiated as soon as the on-hand inventory level of the main item reaches a certain level s1, and there is a lead time until the reorder arrives but instantaneous replenishment for the compliment item. The arriving any primary demands enter into an orbit, when the inventory level of main item is zero. The limiting probability distribution for both commodities and the number of demands in the orbit, is computed and various operational characteristics are derived. The results are illustrated with numerical examples.
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The issue of maintaining a inventory system in the occurrence of random demand and lead time has motivated a considerable amount of research effort in recent years. Marketing of consumable goods have to be dealt carefully. Incentive for every purchase of one particular item is one strategy to boost its sale volume. This motivated the researchers to build an inventory models having two items in stock, and of which one is main item and the other one is a gift item. The gift item is supplied to a customer for every purchase of the main item. The significance of modeling such stochastic systems can be directly attributed to the severity of their potential negative effort on operating costs and customer service measures in modern manufacturing and business environments. Sivazlian and stanfel (1979) analysed a two commodity single period inventory system. Kalpakam and arivarigan (1993) analysed a multi-item inventory model with renewal demands under a joint replenishment policy. They assumed instantaneous supply of items and obtain various operational characteristics and also an expression for the long run total expected cost rate. Krishnamoorthy etal. (1994) analysed a two commodity continuous review inventory system with zero lead time. A two commodity problem with markov shift in demand for the type of commodity required, is considered by krishnamoorthy and varghese (1994). They obtain a characterization for limiting probability distribution to be uniform. Dhandra and prasad (1995) analysed a two commodity inventory model in which item 1 is substitutable for item 2 but not vice versa. Associated optimization problems were discussed in all these cases. However in all these cases zero lead time is assumed.

Anbazhagan and arivarignan [2000 , 2001, 2003, 2013] have analyzed two commodity inventory system under various ordering policies. Yadavalli et. al., (2004) have analyzed a model with joint ordering policy and varying order quantities. Yadavalli et. al., (2006) have considered a two commodity substitutable inventory system with poisson demands and arbitrarily distributed lead time. All the models considered in the two commodity inventory system assumed lost sales of demands occur during stock out periods.

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