Abstract
This model investigates the instantaneous fuzzy economic order quantity model by allocating the percentage of units lost dueto deterioration in an on-hand inventory by framing variable ordering cost. The objective is to maximize the fuzzy net profit so as to determine the order quantity, the cycle length and number of units lost due to deterioration in fuzzy decision space. For any given number of replenishment cycles the existence of aunique optimal replenishment schedule are proved and mathematical model is developed to find some important characteristics for the concavity of the fuzzy net profit function. Numerical examples are provided to illustrate the results of proposed model which benefit the retailer and this policy is important, especially for wasting of deteriorating items. Finally, sensitivity analyses of the fuzzy optimal solution with respect to the major parameters are also studied.
Highlights
Most of the literature on inventory control and production planning has dealt with the assumption that the demand for a product will continue infinitely in the future either in a deterministic or in a stochastic fashion
There is hidden cost not account for when modeling inventory cost. This model studies the problem of promotion for a deteriorating item subject to loss of these deteriorated units. This model postulates that measuring the behavior of production systems may be achievable by incorporating the idea of retailer in making optimum decision on replenishment with wasting the percentage of on-hand inventory due to deterioration and compares the optimal results with none wasting the percentage of on-hand inventory due to deterioration traditional model
Promotional effort and replenishment decision are adjusted arbitrarily upward or downward for profit maximization model in response to the change in market demand within the planning horizon. The objective of this model is to determine the optimal time length, optimal units lost due to deterioration, the promotional effort and the replenishment quantity with variable ordering cost so that the net profit is maximized in an instantaneous replenishment fuzzy economic order quantity (EOQ) model and the numerical analysis show that an appropriate promotion policy can benefit the retailer and that promotion policy is important in fuzzy space, especially for deteriorating items
Summary
Most of the literature on inventory control and production planning has dealt with the assumption that the demand for a product will continue infinitely in the future either in a deterministic or in a stochastic fashion. Promotional effort and replenishment decision are adjusted arbitrarily upward or downward for profit maximization model in response to the change in market demand within the planning horizon The objective of this model is to determine the optimal time length, optimal units lost due to deterioration, the promotional effort and the replenishment quantity with variable ordering cost so that the net profit is maximized in an instantaneous replenishment fuzzy EOQ model and the numerical analysis show that an appropriate promotion policy can benefit the retailer and that promotion policy is important in fuzzy space, especially for deteriorating items. Assumptions and Notations r : Consumption rate, tc : Cycle length, h : Holding cost of one unit for one unit of time, HC(q) : Holding cost per cycle, c : Purchasing cost per unit, Ps : Selling Price per unit, α : Percentage of on-hand inventory that is lost due to deterioration, q : Order quantity, K × (qγ−1) : Ordering cost per cycle where 0, q∗∗ : Modified fuzzy economic ordering / production quantity (FEOQ/FEPQ), q∗ : Traditional economic ordering quantity (EOQ), φ(t) : On-hand inventory level at time t, Π1(q) : Net profit per unit of producing q units per cycle in crisp strategy, Π(q) : Average profit per unit of producing q units per cycle in crisp strategy, Π1(q, ρ) : The net profit per unit per cycle in fuzzy decision space, Π(q, ρ) : The average profit per unit per cycle in fuzzy decision space, h : Fuzzy holding cost per unit, K × (qγ−1) : Fuzzy setup cost per cycle
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