Simplification of EOQ Model for Planned Shortages by using Equivalent Holding Cost (original) (raw)
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Eoq Model for Deteriorating and Ameliorating Items Under Cubic Demand and Partial Backlogging
BAREKENG: Jurnal Ilmu Matematika dan Terapan
The inventory model aims to determine policies in inventory control. Therefore, the availability needs to be managed as well as possible to obtain optimal performance. This study aimed to produce EOQ models for deteriorating and ameliorating products with shortage and partial backlogging policies. The traditional Economic Order Quantity (EOQ) inventory model was used to develop the model. The search algorithm of the model solution was made to get a solution from the model. In the end, a case study of the model implementation at Minimarket SATUMART, Sidoarjo, is given
International Journal for Research in Applied Science & Engineering Technology, 2021
The effect of deterioration for items cannot be disregarded in many inventory system and it is a real phenomenon in our life. Along with, few papers considered inventory system under amelioration environment where amelioration occurs when the value or utility of a product increases over time. This paper discussed the development of an inventory model of deteriorating items in presence of ameliorating environment. Here the demand rate is considered as an exponentially increasing over a fixed time horizon and shortages which is partially backlogged. Finally the model is illustrated with the help of a numerical example and the sensitivity of the optimal solution towards the changes in the values of different parameters is also studied.
EOQ MODEL FOR PLANNED SHORTAGES BY USING EQUIVALENT HOLDING AND SHORTAGE COST
iaeme
In this manuscript, we propose the concept of Equivalent of Holding and shortage cost (EHSC). The EHSC is the effective holding cost due to holding the items in stock and also the cost of shortage when items are not in stock (back-ordered or planned shortages). We demonstrate Economic Order Quantity with Backordering (EOQB) model simplifies to the level of Economic Order Quantity (EOQ) model (in terms of formulae and difficulty-level) by use of new “Factor for Back-ordering” or “Factor for Planned Shortages”. We derive that the product of factor for backordering and holding cost is the Equivalent Holding and shortage cost for EOQB model. This factor magically simplifies EOQB model.
2019
This paper deals with development of deterministic inventory model with time and selling price dependent demand and time varying holding cost where as the time increases the deterioration is also increases. In this model the shortages are allowed and demand is partially backlogged. This model is solved mathematically by maximizing the total profit. Using numerical examples the sensitivity analysis is explained. This model has been applied to maximize the profit for the Economic enterprises where as the deterioration and holding cost are time dependent. The sensitivity analysis of this model shows that has more influence on the optimal times and pricing policies of the model.
INVENTORY MODEL THROUGH TIME DEPENDENT DEMAND AND DETERIORATION UNDER PARTIAL BACKLOGGING
ABSTARCT Deterioration of physical goods in stock is very realistic feature of inventory control because there are many goods that either deteriorate or obsolete in the course of time. Deterioration rate of any item is either constant or time dependent. When deterioration is time dependent, time is accompanied by proportional loss in the value of the product. Realization of this factor motivated modelers to consider the deterioration factor as one of the modeling aspects. In this paper we developed a general inventory model for deteriorating items with constant deterioration rate under the consideration of time dependent demand rate and partial backlogging. INTRODUCTION the recent years there is a state of interest of studying time dependent demand rate. It is observed that the demand rate of newly launched products such as electronics items, mobile phones and fashionable garments increases with time and later it becomes constant. Deterioration of items cannot be avoided in business scenarios. In most of the cases the demand for items increases with time and the items that are stored for future use always loose part of their value with passage of time. In inventory this phenomenon is known as deterioration of items. The rate of deterioration is very small in some items like hardware, glassware, toys and steel. The items such as medicine, vegetables, gasoline alcohol, radioactive chemicals and food grains deteriorate rapidly over time so the effect of deterioration of physical goods cannot be ignored in many inventory systems. The deterioration of goods is a realistic phenomenon in many inventory systems and controlling of deteriorating items becomes a measure problem in any inventory system. Due to deterioration the problem of shortages occurs in any inventory system and shortage is a fraction that is not available to satisfy the demand of the customers in a given period of time. Dye [2002] developed an inventory model with partial backlogging and stock dependent demand. Chakrabarty et al. [1998] extended the Philip's model [1974]. Skouri and Papachristors [2003] determine an optimal time of an EOQ model for deteriorating items with time dependent partial backlogging. Manjusri Basu and Sudipta Sinha [2007] extended the Yan and Cheng model [1998] for time dependent backlogging rate. Rau et al. [2004] considered an inventory model for determining an economic ordering policy of deteriorating items in a supply chain management system. Teng and Chang [2005] determined an economic production quantity in an inventory model for deteriorating items. Dave and Patel [1983] developed an inventory model together with an instantaneous replenishment policy for deteriorating items with time proportional demand and no shortage. Roy and Chaudhury [1983] considered an order level inventory model with finite rate of replenishment and allowing shortages.
International Transactions in Operational Research, 2019
All-units discount facilities are one of the attractive features in the competitive business situation. Due to the globalization of the marketing policy, all-units discount facilities play an important role in the competitive business. Typical economic order quantity (EOQ) models are cloistered by considering as constant not only the purchase cost (irrespective of the order size of the product) but also the carrying cost during the entire cycle period. However, the unit purchase cost has an antagonistic relationship with the order size, and the carrying cost has a commensurate relationship with the storage time-period of the product, that is, the higher the order size, the lower the unit purchase cost, and the longer the storage time-period, the greater carrying cost per unit. Also deterioration is another imperative issue in inventory analysis as it has a huge impact on profit or cost of the inventory system. Considering all of the above-mentioned factors, we study two different inventory models, namely (a) inventory model for zero-ending case and (b) inventory model for shortages case. The demand for both models is considered as price and stock dependent, whereas shortages are partially backlogged at a rate with the length of the waiting time to the arrivals of the next lot. The existence and uniqueness of the optimal solution for both models are examined theoretically and the solution procedures are discussed along with two proposed algorithms for minimizing the total cost. Finally, we perform sensitivity analyses for both models and make a fruitful conclusion regarding the proposed work.
Operations Research and Applications: An International Journal (ORAJ), 2015
This manuscript deals in developing an EOQ model for time deteriorating items and allowing shortages in the inventory. These shortages are considered to be completely backlogged. We have held that the production rate is finite and infinite. In this manuscript, we developed EOQ models for perishable products which consider continuous deterioration of a utility product and introduce an exponential penalty cost and linear penalty cost function. The theoretical expressions are obtained for optimum cycle time and optimum order quantity. The significant centre of our paper is to build up the EOQ model for time-deteriorating items utilizing penalty cost with finite and infinite production rate. The mathematical solution of the model has been done to obtain the optimal solution of the problem. The result is demonstrated with the help of mathematical example. To conclude, sensitivity study is carried out with respect to the key parameters and some managerial implications are also included. All the theoretical developments are numerically justified.