Abstract
Article history: Received 1 June 2011 Received in revised form July, 29, 2011 Accepted 30 July 2011 Available online 3 August 2011 In this paper, a new multi-item inventory system is considered with random demand and random lead time including working capital and space constraints with three decision variables: order quantity, safety factor and backorder rate. The demand rate during lead time is stochastic with unknown distribution function and known mean and variance. Random constraints are transformed to crisp constraints with using the chance-constrained method. The Minimax distribution free procedure has been used to lead proposed model to the optimal solution. The shortage is allowed and the backlogging rate is dependent on the expected shortage quantity at the end of cycle. Two numerical examples are presented to illustrate the proposed solution method. © 2012 Growing Science Ltd. All rights reserved
Highlights
The shortage cost calculation is an important problem in estimating the inventory systems costs including purchasing, set up, holding, stock out costs and, etc
Many models for continuous inventory system with stochastic demand and allowable stock out such as Hadley and Whithin (1963), Parker (1964), Tinareli (1983) and Yano (1976) and some models in the stochastic demand and stochastic lead time environment such as Ord and Bagchi (2006), Burgin (2007) have been studied to find optimal solution on order quantity and backorder rate, which depends on expected shortage quantity and reorder point, which is replaced by safety factor
In our new suggested model, in the stochastic lead time and stochastic demand environment, we consider safety factor, order quantity and backorder rate as the decision variables and assume that the backorder rate is dependent on the expected shortage quantity at the end of cycle
Summary
The shortage cost calculation is an important problem in estimating the inventory systems costs including purchasing, set up, holding, stock out costs and, etc. Many models for continuous inventory system with stochastic demand and allowable stock out such as Hadley and Whithin (1963), Parker (1964), Tinareli (1983) and Yano (1976) and some models in the stochastic demand and stochastic lead time environment such as Ord and Bagchi (2006), Burgin (2007) have been studied to find optimal solution on order quantity and backorder rate, which depends on expected shortage quantity and reorder point, which is replaced by safety factor. In our new suggested model, in the stochastic lead time and stochastic demand environment, we consider safety factor, order quantity and backorder rate as the decision variables and assume that the backorder rate is dependent on the expected shortage quantity at the end of cycle. Gholami-Qadikolaei et al / International Journal of Industrial Engineering Computations 3 (2012)
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