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An EOQ model with shortages and selling price dependent time varying demand

TL;DR: In this paper, an EOQ type model for time and selling price dependent demand, decreasing selling price and partial backlogging is presented. But the model is not suitable for the case of high-quality products.
Abstract: Owing to intense technological growth and extreme global competition, demand of a newly launched hi-tech item may decrease over time because some better quality items may be available in the marketplace at the same or lower price. This situation pushes the manufacturers to reduce selling price so that demand of that item may increase. If a particular product is not available, competitive market motivates customers to switch to another organisation for similar type of products. Keeping all these things in mind, we have developed an EOQ type model for time and selling price dependent demand, decreasing selling price and partial backlogging. We have formulated the mathematical model, and the procedures to derive the optimal solution are discussed. The effectiveness of the proposed model is illustrated with the help of numerical examples. Sensitivity of the optimal order quantity and optimal cost for changes in various parameter values are also examined.
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TL;DR: This article presents one generalized order-level inventory system with fully permissible delay in payment in various trade-credit intervals and finds that when the trade- credit period is longer than the inventory depletion time to settle the account, the optimal Inventory depletion time is dependent of demand.
Abstract: This article presents one generalized order-level inventory system with fully permissible delay in payment in various trade-credit intervals. Review of existing literature finds few EOQ models under simultaneous considerations of time-dependent generalized demand rate, time-dependent generalized rate of deterioration and time-dependent generalized backordering under fully permissible delay in payment. In those existing studies, the optimal inventory depletion time is independent of demand over the entire cycle. Here, present article frames one generalized order-level inventory system with fully permissible delay in payment across various trade-credit intervals. This finds that when the trade-credit period is longer than the inventory depletion time to settle the account, the optimal inventory depletion time is dependent of demand. Under this ambiance, one particular case having time-dependent ramp type demand rate, two variables time-dependent Weibull distribution rate of deterioration and time-dependent backordering rate with fully permissible delay in payment, finds that the optimal inventory depletion time varies inversely over demand in that period. Moreover, the proposed model shrinks to obtain many well-established EOQ models as the special cases to it. Next, a general algorithm determines the various optimal solutions corresponding to seven cases. The managerial insights extracted from sensitivity analysis of parameters include the suggestion to halt the promotional activities so as to foreshorten the demand in shortage period. Also, this analysis attests that the longer waiting period of retailers should be counterbalanced with various promotional activities and anticipated benefits.

10 citations

Journal ArticleDOI
TL;DR: In this article, a wholesaler-retailer supply chain model is developed for a seasonal deteriorating item where demand of the item increases with time at the beginning of season, reaches a maximum level, and then decreases gradually to normal demand at the end of the season.
Abstract: SYNOPTIC ABSTRACTIn this research article, a wholesaler-retailer supply chain model is developed for a seasonal deteriorating item where demand of the item increases with time at the beginning of season, reaches a maximum level, and then decreases gradually to normal demand at the end of the season. A retailer introduces some promotional cost to boost the base demand of the item. The demand of the item also depends on the unit selling price. In the case of any shortages, the demand is partially backlogged. It is found that if a wholesaler contributes a portion of promotional cost, then joint profit, as well as individual profit, increases. The supply chain model is also analyzed in an imprecise environment when different inventory parameters are fuzzy in nature. In this case, individual and channel profits become fuzzy in nature. As optimization of a fuzzy objective is not well defined, following the credibility measure of the fuzzy event, an approach is proposed for a comparison of fuzzy objectives and a...

10 citations

Journal ArticleDOI
TL;DR: This research work provides a two-echelon supply chain model for short-lifetime deteriorating products involving a retailer and a manufacturer and suggests that shorter time spans of replenishment are more appropriate forshort-lifetimes deteriorating products.
Abstract: Food products’ wholesomeness is affected due to continuous degradative changes with time, resulting in reduced quality and lost sales. The degradation is caused by several factors, which have been frequently studied by the researchers. The modelling and optimization of such supply chain systems, involving real-time effects of deterioration and demand, has been a challenge always. In this context, this research work provides a two-echelon supply chain model for short-lifetime deteriorating products involving a retailer and a manufacturer. The rate of deterioration is considered as a dynamic parameter that increases with time. The rate of product’s demand is considered as a min–max function of its selling-price, which depicts the general behavior of customers. In view of the actual market trends for short-life products, their selling-price is considered as a function of its maximum lifetime. Profit of the supply chain is modelled as a nonlinear function, which is maximized on optimal values of selling-price and cycle-time through analytical optimization techniques. A computational algorithm is proposed to obtain optimal solutions and robustness of the model is verified through numerical experiments. A sensitivity analysis is provided to realize the effects of variation in several system parameters on its profit. Results of the experiments suggest that shorter time spans of replenishment are more appropriate for short-lifetime deteriorating products. Some important managerial insights are provided to support the decision makers while implementing the proposed models in real-world situations.

2 citations