This paper proposed a new general probabilistic multi-item, single-source inventory model with varying mixture shortage cost under two restrictions. One of them is on the expected varying backorder cost and the other is on the expected varying lost sales cost. This model is formulated to analyze how the firm can deduce the optimal order quantity and the optimal reorder point for each item to reach the main goal of minimizing the expected total cost. The demand is a random variable and the lead time is a constant. The demand during the lead time is a random variable that follows any continuous distribution, for example; the normal distribution, the exponential distribution and the Chi square distribution. An application with real data is analyzed and the goal of minimization the expected total cost is achieved. Two special cases are deduced.
This study treats the probabilistic safety stock n-items inventory system having varying order cost and zero lead-time subject to two linear constraints. The expected total cost is composed of three components: the average purchase cost; the expected order cost and the expected holding cost. The policy variables in this model are the number of periods Nr* and the optimal maximum inventory level Qmr* and the minimum expected total cost. We can obtain the optimal values of these policy variables by using the geometric programming approach. A special case is deduced and an illustrative numerical example is added.
This study derives the probabilistic lost sales inventory system when the order cost is a function of the order quantity. Our objective is to minimize the expected annual total cost under a restriction on the expected annual holding cost when the lead-time demand follows the normal distribution by using the Lagrangian method. Then a published special case is deduced and an illustrative numerical example is added.
Although the deterioration is one of the main problems that have been investigated in the inventory systems science the last twenty years ago but Most deteriorating inventory studies focused on deterministic models. This paper presents a Constraint Deteriorating Probabilistic Periodic Review Inventory Model (CDPPRIM); a model is applicable when: (1) the demand is a random variable that follows Pareto distribution without lead-time, (2) some costs are varying, (3) shortages are permitted, and (4) the deterioration rate follows exponential distribution.The objective function under a constraint is imposed here in crisp and fuzzy environment. A numerical analysis method (Newton's method) is used to solve the model. The main objective is to find the optimal values of four decision variables (maximum inventory level, stock-out time, the deteriorating time and review time), which minimize the expected annual total cost under the assumptions. At the end, the paper explains the model through an application.
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