a b s t r a c tThis study deals with a multi-item mixture inventory model in which both demand and lead time are random. A budget constraint is also added to this model. The optimization problem with budget constraint is then transformed into a multi-objective optimization problem with the help of fuzzy chance-constrained programming technique and surprise function. In our studies, we relax the assumption about the demand, lead time and demand during lead time that follows a known distribution and then apply the minimax distribution free procedure to solve the problem. We develop an algorithm procedure to find the optimal order quantity and optimal value of the safety factor. Finally, the model is illustrated by a numerical example.
This paper develops a single wholesaler and multi retailers mixture inventory distribution model for a single item involving controllable lead-time with backorder and lost sales. The retailers purchase their items from the wholesaler in lots at some intervals throughout the year to meet the customers' demand. Not to loose the demands, the retailers offer a price discount to the customers on the stock-out items. Here, it is assumed that the lead-time demands of retailers are uncertain in both stochastic and fuzzy sense, i.e., these are simultaneously random and imprecise. To implement this behavior of the lead-time demands, at first, these demands are assumed to be random, say following a normal distribution. With these random demands, the expected total cost for each retailer is obtained. Now, the mean lead-time demands (which are crisp ones) of the retailers are fuzzified. This fuzzy nature of the lead-time demands implies that the annual average demands of the retailers must be fuzzy numbers, suppose these are triangular fuzzy numbers. Using signed distance technique for defuzzification, the estimate of total costs for each retailer is derived. Therefore, the problem is reduced to optimize the crisp annual costs of wholesaler and retailers separately. The multi-objective model is solved using Global Criteria method. Numerical illustrations have been made with the help of an example taking two retailers into consideration. Mathematical analyses have been made for global pareto-optimal solutions of the multi-objective optimization problem. Sensitivity analyses have been made on backorder ratio and pareto-optimal solutions for wholesaler and different retailers are compared graphically.
a b s t r a c tThis study deals with an EOQ inventory model with fuzzy stochastic demand and controllable lead-time by relaxing the assumption that demand during lead-time follows a specific probability distribution. Here considering the unsatisfied demands to be partially backordered, both lead-time and order quantity are considered as the decision variables. Instead of having a stockout term in the objective function, a service level constraint, which implies that the stockout level per cycle is bounded, is added to the model. This study, we provide an elegant methodology to determine the optimal order quantity and reorder point such that total expected annual cost in fuzzy sense has a minimum value. Finally the proposed model is illustrated by a numerical example.
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