%0 Journal Article
%T An EOQ Model for Phase Inventory with Induced Demand and Periodic Cycle Time
%A Sujit Kumar De
%A Shib Sankar Sana
%A Adrijit Goswami
%J Journal of Industrial Engineering
%D 2014
%I Hindawi Publishing Corporation
%R 10.1155/2014/605178
%X This paper deals with a stock flow of an inventory problem over induced demand. The inventory is consumed through ¡°core customer¡± or chain marketing system in an induced environment (inductance) to exhaust all the items of the stock inventory in an indefinite time. The demand rate is depicted due to induced factor which is generated from the same inventory presented nearby. The inventory cycle time is split into several periodic times due to oscillatory feature of the inventory which is called phase inventory. Considering uniform demand, this cycle time splits into two basic parts, namely, ¡°first shift¡± (phase) and ¡°second shift¡± (phase). Since the process dampens over time, so the whole inventory will exhaust after few periods. A cost function consisted of inventory cost, setup cost, and loss for induced items is minimized to obtain optimal order quantity and replenishment time. The multivariate lagrange interpolation (MLI) over the average values of the postsensitivity analysis is developed here. Finally, graphical illustrations are made to justify the model. 1. Introduction Recently, a great evolution has been made in the traditional EOQ model. Through its process, a survey work of the industrial system over Harris¡¯s work [1] in the last century has been made by Andriolo et al. [2]. A capacitated lot sizing problem for coordination of transportation services is developed by Bruno et al. [3]. A review of consignment stocking policy under advertising, pricing, and bargaining strategies is also discussed by Sarker [4]. Moreover, several articles of the inventory in supply chain [5¨C11] have suggested that discounting on sales price is the emergent way to exhaust all items from the inventory in due course of time. Bozorgi et al. [12] develop a new model where the inventory moves with environmental temperature, controlled by emission function. Sodhi et al. [13] state the bullwhip effect on maintenance repair and overhaul (MRO) customers. Analysis of batch ordering inventory for infinite horizon with capacity constraints is studied by Yang et al. [14]. Coelho and Laporte [15] derive an inventory routing problem (IRP) for the inequalities, based on demand and available capacities. Also, Avinadav et al. [16] are able to develop a multiplicative demand function relating to age and price effect, whereas Chand and Sethi [17] made an analysis for dynamic and stationary demand in multiperiod lot sizing problem for both finite and infinite time horizons in the same time. Keskin and Capar [18] describe a decision support system model on the basis of the utility of
%U http://www.hindawi.com/journals/jie/2014/605178/