A Fuzzy Inventory Model having Exponential Demand with Weibull Distribution for Non-Instantaneous Deterioration, Shortages under Partially Backlogging and Time Dependent Holding Cost

Abstract

I. INTRODUCTIONThe inventory system takes an important part of cost controlling in business. The mathematical properties of inventory systems and details of different inventory models have been described in the well-known books ( Hardley and Whitin, 1958 [20], Naddor, 1963, [21] ). For the last few years, researchers in this area have extended investigation into various models with considerations of demand patterns, deterioration, shortage,payment option, order cycles and their combinations. Demand is different for different types of item, it also varies for different period of time. So demand cannot be taken constant for practical use. It can be linear or quadratic function of time. The deteriorating items with shortages have received much attention of several researchers in the recent years because most of the physical goods undergo decay or deterioration over time, example being fruits, vegetables, volatile goods and so on. In some inventory systems such as fashionable commodities, the length of the waiting time for the next replenishment would determine whether the backlogging will be accepted or not. Therefore, the backlogging rate should be variable and depends on the waiting time for the next replenishment. Most of models are based on the economic order quantity (E. O. Q. )/ economic production quantity (E. P. Q.) model developed by Harris [25]. The first attempt to describe the optimal ordering policies for such items was made by Ghare and Schrader [15]. Philip [11] developed an generalised inventory model with three parameter Weibull Distribution rate without considering shortages. Many researchers assume that the deterioration of the items in inventory starts from the instant of their arrival in stock. But in real-life most goods would have a span of maintaining quality or original condition, namely electronic goods, food grains etc., during that period, there is no deterioration occurring. K. S. Wu et. al [16]define the phenomenon as "non-instantaneous deterioration". In a classical inventory models, the demand rate and holding cost is assumed to be constant. In reality, the demand and holding cost for physical goods may be time dependent. In this connection, see the performed works by Mishra et. al [9] In the crisp inventory models, all the parameters in the total cost are known and have definite values.But in the practical situation it is not possible, these models provide some general understating of the behaviour of inventory under different assumptions, they are not capable of representing real-life situations. So, applying these models as they are, generally, leads to erroneous decisions. Further, using these models require inventory managers to have some flexibility when deciding on the sizes of the order quantities to reduce the cost of uncertainty.Hence fuzzy inventory models fulfil that gap. Using fuzzy set theory to solve inventory problems, instead of the traditional probability theory, produces more accurate results. Different fuzzy inventory models occur due to fuzzy various cost par...

A Fuzzy EPQ Model for Non-Instantaneous Deteriorating Items where Production Depends on Demand which is Proportional to Population, Selling Price as well as Advertisement

“…Maragatham et al (2014) researched on a fuzzy inventory model for deteriorating items with price-dependent demand. Islam and Biswas (2017) studied on a fuzzy inventory model having exponential demand with weibull distribution for non-instantaneous deterioration, shortages under partially backlogging and time dependent holding cost.…”