An Inventory Model for Deteriorating Items with Stochastic Demand, Variable Lead Time, Shortages Considering Inflation and Time Value of Money

Abstract

(ProQuest: ... denotes formulae omitted.)1. IntroductionMonk (1987) defined inventory as idle resources that possess economic value. In a broad sense, everyone keeps inventory such as food, clothes, domestic items, paper, pens and many other goods. Inventory applies to all types of work systems. Some types of inventory are raw materials inventory, in-process inventory, finished goods inventory, spare parts inventory, and so on.There are three basic reasons for keeping an inventory:a. Time - The time lags present in the supply chain, from supplier to user at every stage, requires that you maintain certain amounts of inventory to use during the lead time.b. Uncertainty - Inventories are maintained as buffers to address the problems of uncertainties in demand, supply and movements of goods.c. Economies of scale - Ideal condition of one unit at a time at a place where a user needs it, when he needs principle tends to incur lots of costs in terms of logistics. So bulk buying, movement and storing brings in economies of scale, thus inventory (Wikipedia, 2010).The total cost of inventory is calculated as the sum of the purchasing cost, setup cost, holding cost, and shortage cost (Taha, 2007).Economic order quantity is the level of inventory that minimizes the total inventory holding costs and ordering costs.Several models exist depending on the assumptions taken in efforts to describe real life situations. Some considerations used are:a. Demand: the classical inventory model assumed demand to be known with certainty (deterministic). Chaudhuri (2003) considered a scenario where the demand varies with time, while Teng et. al. (2005) considered demand as deterministic but as an exponential function. Kar et. al. (2001) also considered demand as stochastic and price-dependent.b. Shortages: The classical model assumes that shortages are not allowed. Many works have been carried out under this assumption in times past and even recent times (e.g. Covert & Phillip (1973), Teng. et. al. (2005)). However, some works have also been done in which shortage-costs component is added to the inventory model (e.g. Kar et. Al,.2001; Mirzazadeh, 2010).c. Ordering pattern: Sharma (1987) identified five ordering policies namely:i. (s ,Q) policy: Place order for a fixed quantity, Q whenever the inventory position drops to a given level s or below.ii. (s ,S) Policy: Place order for a quantity that would bring the inventory to a given maximum stock level, S whenever the inventory position drops to a given level s or below.iii. (T, S) Policy: Place order for a quantity that would bring the inventory to a given maximum stock level, S at regular interval of time T, spaced at time intervals of equal length.iv. (T, s, S) Policy: Place order for a quantity that would bring the inventory to a given maximum stock level, S at regular interval of time T, spaced at time intervals of equal length if the inventory level is at level s or below.v. (T, Q) Policy: Place order for quantity Q at every ordering interval, T.Researchers (Sivakumar, 2009; Kalpakam & Sapna, 1995; Kalpakam & Sapna, 1994) have considered ordering policy in their studies.d. Inflation: Inflation can simply be defined as an increase in the supply of currency or credit relative to the availability of goods and services, resulting in higher prices and a decrease in the purchasing power of money. Buzacott (1975) stated that while classical EOQ formula assumes all costs are constant, it would be unreasonable to use the EOQ formula without investigating how it is modified when inflation causes cost to increase with time. The Buzacott model (1975) led to the consideration of inflation as an important factor in the determination of economic order quantity by many researchers and thus led to the development of many other models with inflation considerations (Mirzazadeh, 2010; Mirzazadeh et al. …