Fuzzy opportunity cost for EOQ model with quality improvement investment

The cost of capital (i.e. opportunity cost) is one of the key factors that will influence the inventory and investment decisions. Previously, the classical EOQ model has been extended to include an imperfect production process and quality improvement investment, where the opportunity cost rate (interest rate or discounted rate) for evaluating the cost of capital investment is known with certainty. However, in some practical situations, the opportunity cost rate probably incurs disturbance due to the unstable environments. To capture this reality, this paper attempts to combine the statistical technique and fuzzy sets concept to deal with the unstable opportunity cost rate, so as to modify the aforementioned inventory/investment model. We derive the optimal lot size and the optimal process quality level in the fuzzy sense utilizing the logarithmic investment cost function. A numerical example is provided, and the results are compared with those obtained from a crisp opportunity cost rate model.