A Fuzzy EOQ Inventory Model with Learning Effects Incorporating Ramp-Type Demand, Partial Backlogging and Inflation under Trade Credit Financing
An EOQ Inventory model for a deteriorating item with ramp-type demand is developed in fuzzy stochastic environment under inflation and time value of money over a finite planning horizon, when delay in payment is allowed to the retailer to settle the accounts against the purchases made by him. In this paper we have considered two cases: (1) payment within the permissible time and (2) payment after the permissible time (i.e. time at which on hand inventory reaches to zero). Here, shortages are allowed and the deterioration follows random Weibull distribution. Under these assumptions, we propose a mathematical model and theorem to find minimum total relevant inventory cost and optimal order quantity. Firstly, we consider the demand and net inflation rate to be crisp in nature. The holding, purchasing, shortage, lost, selling, and ordering costs are represented by triangular fuzzy numbers which are then transformed to corresponding weighted interval numbers by using nearest interval approximation. Following interval mathematics, the single objective fuzzy problem is reduced to a crisp multi — objective decision making (MODM) problems. The MODM problem for optimizing the total relevant inventory cost is then again transformed to a crisp single objective problem with the help of weighted sum method. Next, the demand rate and the net inflation rate are taken as trapezoidal fuzzy numbers to make the problem much more realistic and then derive the expressions for the total inventory cost applying Function Principle. It is then defuzzified using graded mean integration representation method to get the total cost function. Numerical examples are cited to illustrate the developed model and the solution process. Some sensitivity analysis with respect to critical parameters is carried out to observe the changes in the total relevant inventory cost and optimal order quantity. Analyzing these changes, we have applied the learning effects to further improve the optimal order quantity. Finally the result of the objective for crisp demand and crisp net inflation rate with and without learning effects are compared to that for fuzzy demand and fuzzy net inflation rate in both case (1) and case (2).
Trade Credit Financing random Weibull distribution fuzzy ramp-type demand interval arithmetic function principle learning effects
Savita Pathak Seema Sarkar
Department of mathematics, National Institute of Technology Durgapur, West Bengal - 713209, India
国际会议
The Second International Conference on Uncertainty Theory(ICUT)(第二届不确定理论国际会议)
拉萨
英文
213-228
2011-08-06（万方平台首次上网日期，不代表论文的发表时间）