Abstract
This paper proposed a general probabilistic continuous review multi-item, multi-source inventory model with constraint for crisp and fuzzy environment. This constraint on the expected varying holding cost. The demand is a continuous random variable, the distribution of the lead time demand is known and the holding cost is varying. This model is formulated to analyze how the firm can deduce the optimal order quantity and the optimal reorder point for the item and source to reach the main goal of minimizing the expected total cost using a Lagrange multiplier technique. The lead time demand is follow some continuous distributions. Also, an application with real data is analyzed and the goal of minimization the expected total cost is achieved.
Highlights
The multi-item, multi-source inventory system is the most general procurement system which may be described as follows; an inventory of i-items is maintained to meet the average demand rates designated,..., .Most of the probabilistic inventory models assume that the units of cost are constant or one of these units is varying
We investigate a probabilistic multi-item, multi-source (MIMS) continuous review inventory model with mixture shortage, varying holding unit cost, under the expected varying holding cost constraint for crisp and fuzzy environment
The expected total cost of inventory system is composed of three components
Summary
The multi-item, multi-source inventory system is the most general procurement system which may be described as follows; an inventory of i-items is maintained to meet the average demand rates designated , , ,..., .Most of the probabilistic inventory models assume that the units of cost are constant or one of these units is varying. [1] Studied the probabilistic multi-item single- source inventory model with varying order cost under two restrictions. Constrained periodic review probabilistic inventory model with continuous distributions and varying holding cost have been studied by [7]. [8] Examined Probabilistic multi-item inventory model with varying mixture shortage cost under restrictions. [3] Deduced a multi-item single-source mixture inventory model involving random lead time and demand with budget constraint and surprise function. [15] Presented deterministic inventory models with a mixture of backorders and lost sales under fuzzy cost. We investigate a probabilistic multi-item, multi-source (MIMS) continuous review inventory model with mixture shortage, varying holding unit cost, under the expected varying holding cost constraint for crisp and fuzzy environment. The model will be studied when the lead time demand follows Gamma, Weibull, Chi-square, Erlang and Exponential distributions and an application is added to illustrate the model for crisp and fuzzy environment
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