A New Mathematical Inventory Model with Stochastic and Fuzzy Deterioration Rate under Inflation

Abstract

This paper develops an inventory model for items with uncertain deterioration rate, time-dependent demand rate with nonincreasing function, and allowable shortage under fuzzy inflationary situation. The goods are not deteriorating upon reception, but the deteriorating starts after elapsing a specified time. The lead time and inflation rate are both uncertain in the model. The resultant effect of inflation and time value of money is assumed to be fuzzy in nature and also we consider lead time as a fuzzy function of order quantity. Furthermore the following different deterioration rates have been considered: for the first case we consider fuzzy deterioration rate and for the second case we assume that the deterioration rate is time dependent and follows Weibull distribution with three known parameters. Since the inflation rate, deterioration rate, and the lead time are fuzzy numbers, the objective function becomes fuzzy. Therefore the estimate of total costs for each case is derived using signed distance technique for defuzzification. The optimal replenishment policy for the model is to minimize the total present value of inventory system costs, derived for both the above mentioned policies. Numerical examples are then presented to illustrate how the proposed model is applied.

Optimizing a bi-objective location-allocation-inventory problem in a dual-channel supply chain network with stochastic demands

“…Jia and Li (2020) studied online and self-run sales policy in the closed-loop supply chain. Naserabadi et al (2014) examined the issue of inventory control under inflation and shortage conditions to minimizing the present value of total costs. Bhunia et al (2015) addressed an inventory model by proposing two different inventory policies under inflationary conditions and definite demand.…”

Money Leaks in Banking ATM’s Cash-Management Systems

“…Other papers of the existing literature focused on ATMs are (Van der Heide et al, 2020), (Ekinci et al, 2015), (Jadwal et al, 2018) or (Teddy and Ng, 2011) who optimize the ATM cash replenishment or develop different systems for predicting the daily amounts withdrawn from ATM´s. Under the Inventory management view, in (Naserabadi et al, 2014), an approach for an inventory system is developed. Other approaches on ATM forecasting techniques are in (Darwish, 2013), where a brief summary of the existing methods for cash forecasting are presented.…”

Fuzzy stochastic inventory model for deteriorating item

“…al [2014][2014] developed an inventory model by assuming time horizon as random variable with exponential distribution and deterioration rate, as well as available budget in fuzzy environment. Recently, Naserabadi [2014][2014] used triangular membership function to represent fuzzy parameters such as lead time and inflation rate where as weibull distribution is used to represent deterioration rate.…”