Abstract:
This study considers an EOQ inventory model with advance payment policy in a fuzzy situation by employing two types of fuzzy numbers that are trapezoidal and triangular. Two fuzzy models are developed here. In the first model the cost parameters are fuzzified, but the demand rate is treated as crisp constant. In the second model, the demand rate is fuzzified but the cost parameters are treated as crisp constants. For each fuzzy model, we use signed distance method to defuzzify the fuzzy total cost and obtain an estimate of the total cost in the fuzzy sense. Numerical example is provided to ascertain the sensitiveness in the decision variables about fuzziness in the components. In practical situations, costs may be dependent on some foreign monetary unit. In such a case, due to a change in the exchange rates, the costs are often not known precisely. The first model can be used in this situation. In actual applications, demand is uncertain and must be predicted. Accordingly, the decision maker faces a fuzzy environment rather than a stochastic one in these cases. The second model can be used in this situation. Moreover, the proposed models can be expended for imperfect production process.
Machine summary:
"Uthayakumara a Department of Mathematics, The Gandhigram Rural Institute - Deemed University, Gandhigram, Dindigul, Tamil Nadu, India Abstract This study considers an EOQ inventory model with advance payment policy in a fuzzy situation by employing two types of fuzzy numbers that are trapezoidal and triangular.
In this paper, an EOQ inventory model with advance payment policy is described by establishing fuzziness in the cost and demand parameters.
The main contribution of this paper is to establish the mathematical model and propose a solving approach for the EOQ inventory problem with advance payment policy in fuzzy random environment.
A backorder inventory model which fuzzifies the order quantity as triangular and trapezoidal fuzzy numbers and keeps the shortage cost as a crisp parameter was developed by Yao and Lee (1999).
Recently, Mahata and Goswami (2013) developed inventory models for items with imperfect quality and shortage backordering in fuzzy environments by employing two types of fuzzy numbers such as trapezoidal and triangular.
From the authors’ literature, none of the authors developed EOQ inventory model with advance payment policy and fuzziness in the cost and demand parameters.
We set some trapezoidal and triangular fuzzy numbers of the input parameters ( p, D, h and A) in Tables 1(a, b) and 2(a, b), respectively, to represent the components of fuzzy models developed in Section 4.
Based on these values, the optimal replenishment cycle T * with the minimum total cost for the fuzzy model developed in Section 5 are computed for each set of trapezoidal and triangular fuzzy numbers."