# American Institute of Mathematical Sciences

October  2014, 10(4): 989-1000. doi: 10.3934/jimo.2014.10.989

## A deteriorating inventory model for an intermediary firm under return on inventory investment maximization

 1 Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan, Taiwan

Received  April 2012 Revised  September 2013 Published  February 2014

This paper investigates how the intermediary firms can optimally determine the purchasing cycle length of a deteriorating product under return on inventory investment (ROII) maximization criterion. There are three key features differentiating this paper from the extant literature and being considered simultaneously in this paper, which are: 1) an alternative performance measurement (i.e., ROII) is proposed to formulate the inventory system; 2) the decision maker in this paper is an intermediary firm instead of a retailer; and 3) the deteriorating nature of products is considered. By incorporating the deteriorating nature of products and the special structure of the intermediary firm environments into the traditional economic order quantity model, the inventory problem encountered by the intermediary firm is mathematically formulated as a non-linear programming problem. Several interesting properties of the proposed inventory problem are developed and an efficient iterative algorithm is provided to search for the optimal solution. Also, the convergence of the iterative algorithm developed in this paper is proved. Finally, a numerical example is presented to illustrate the features of the proposed problem and the convergent search algorithm.
Citation: Cheng-Kang Chen, Yi-Xiang Liao. A deteriorating inventory model for an intermediary firm under return on inventory investment maximization. Journal of Industrial & Management Optimization, 2014, 10 (4) : 989-1000. doi: 10.3934/jimo.2014.10.989
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