# Economic Production Inventory Model

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An economic production quantity (EPQ) model is an inventory model that determines the quantity a retailer should order in order to minimize the total annual cost of setups and holding inventory with the assumption that daily demand is less than daily production. EPQ model for deteriorating items when the demand rate depends on certain criteria has been widely studied by researchers. Deterioration is a common factor in our daily life. Some items such as fruits, vegetables, milk and pharmaceutical have deterioration characteristic. Deterioration can be defined as decay, damage, spoilage, evaporation, loss of quality marginal value of a commodity that results in the decreasing usefulness from the original condition. Therefore, the loss due to…show more content…
Namhias, Goyal and Giri reviewed articles provide a complete and updated survey of published literature for the deteriorating inventory models. They reviewed literature which studied deteriorating inventory with deterministic demand such as uniform demand, time varying demand, stock- depended demand and price-dependent demand. Wee developed a model for joint pricing and replenishment policy for deteriorating inventory with price elastic demand rate that decline over time. Papachristos and Skouri studied a continuous review inventory model over a finite-planning horizon with deterministic varying demand and constant deterioration rate. Samanta and Roy developed a continuous production control inventory model for deteriorating items with shortages. It is assumed that the demand rate and production rate are constants and the distribution of the time to deterioration of an item follows the exponential distribution. Teng have established an economic production quantity (or EPQ) model for deteriorating items when the demand rate depends not only on the price but also the on-display stock…show more content…
However, this is not applicable in real life and in a competitive market demand cannot be constant but it is dependent on several factors. When the number of displayed goods increase, this will attract more buyers hence will increase the consumption rate and this phenomenon is termed as stock-dependent demand rate. In order to quantify this, Baker and Urban developed and EOQ model for a power form inventory level dependent demand where $D(t) = \alpha[I(t)]^\beta, (\alpha > 0, 0 < \beta < 1)$ followed by Mandal and Phaudjar, they established an EPQ model with linearly stock dependent demand where $D(t)=\alpha + \beta I(t), (\alpha,\beta > 0)$. Datta $\&$ Paul developed an EOQ model with demand rate dependent on the instantaneous stock amount displayed until the inventory level level, L is achieved. After that demand rate becomes constant (i.e.,$D(t) = \alpha[I(t)]^\beta if I(t)=L and D(t) = \alpha L^\beta if 0 \leq I(t) \leq L).$ Padmanabhan and Vrat studied an inventory model for perishable items with stock-dependent selling rate. Chung et. al studied the stock dependent inventory system where Newton-Raphson method was used in order to find the optimum solutions.However in previous study, the pricing strategy did not receive much attention in an EPQ model compare to an inventory-level-dependent demand rate. Since a pricing strategy is commonly used to spur demand for its