Browse > Article
http://dx.doi.org/10.11627/jkise.2020.43.1.070

A Systematic Approach to the Purchase Dependence  

Park, Changkyu (College of Business, University of Ulsan)
Publication Information
Journal of Korean Society of Industrial and Systems Engineering / v.43, no.1, 2020 , pp. 70-78 More about this Journal
Abstract
Under the situation which customer orders are cancelled unless all products in the order are delivered all at once, this paper concentrates on the purchase dependent demands and explores the systematic approach to implant the purchase dependence into the multi-product inventory model. First, by acknowledging that it is a challenging task to formulate a suitable inventory model for the purchase dependence, we derive the optimal solution condition using an EOQ model and extend the optimal solution condition to periodic review models. Then, through the comparison simulation of four inventory policies regarding several degrees of purchase dependence, we demonstrate that the inventory models which consider the purchase dependence generate less total cost than the inventory models which ignore the purchase dependence. In general, the inventory models which consider the purchase dependence reduce the loss of sales by maintaining more inventories, which results in reducing the total cost. Consequently, the simulation result supports the effectiveness of this paper's approach. In addition, this paper uses the individual order period and joint order period obtained from the EOQ model for the multi-product inventory model. Through the in-depth analysis of comparing the two models, we observe that the model of using the joint order period produces less total cost when the degree of purchase dependence is high, but the model of using the individual order period produces less total cost when the degree of purchase dependence is low.
Keywords
Purchase Dependence; Periodic Review Model; Dependent Demand; EOQ;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Zhang, R., An extension of partial backordering EOQ with correlated demand caused by cross-selling considering multiple minor items, European Journal of Operational Research, 2012, Vol. 220, No. 3, pp. 876-881.   DOI
2 Zhang, R., Kaku, I., and Xiao, Y., Deterministic EOQ with partial backordering and correlated demand caused by cross-selling, European Journal of Operational Research, 2011, Vol. 210, No. 3, pp. 537-551.   DOI
3 Agrawal, N. and Cohen, M.A., Optimal material control in an assembly system with component commonality, Naval Research Logistics, 2001, Vol. 48, No. 5, pp. 409-429.   DOI
4 Larsen, C., The Q(s,S) control policy for the joint replenishment problem extended to the case of correlation among item-demands, International Journal of Production Economics, 2009, Vol. 118, No. 1, pp. 292-297.   DOI
5 Cohen, M.A., Kleindorfer, P.R., and Lee, H.L., Near-optimal service constrained stocking policies for spare parts, Operations Research, 1989, Vol. 37, No. 1, pp. 104-117.   DOI
6 Corbett, C.J. and Rajaram, K., A generalization of the inventory pooling effect to nonnormal dependent demand, Manufacturing and Service Operations Management, 2006, Vol. 8, No. 4, pp. 351-358.   DOI
7 Erkip, N., Hausman, W.H., and Nahmias, S., Optimal centralized ordering policies in multi-echelon inventory systems with correlated demands, Management Science, 1990, Vol. 36, No. 3, pp. 381-392.   DOI
8 Hadley, G. and Whitin, T.M., Analysis of Inventory Systems, Englewood Cliffs, N.J. : Prentice-Hall, 1963.
9 Hausman, W.H., Lee, H.L., and Zhang, A.X., Joint demand fulfillment probability in a multi-item inventory system with independent order-up-to policies, European Journal of Operational Research, 1998, Vol. 109, No. 3, pp. 646-659.   DOI
10 Lee, L.H. and Chew, E.P., A dynamic joint replenishment policy with auto-correlated demand, European Journal of Operational Research, 2005, Vol. 165, No. 3, pp. 729-747.   DOI
11 Liu, L. and Yuan, X.M., Coordinated replenishments in inventory systems with correlated demands, European Journal of Operational Research, 2000, Vol. 123, No. 3, pp. 490-503.   DOI
12 Nasr, W.W. and Maddah, B., Continuous (s, S) policy with MMPP correlated demand, European Journal of Operational Research, 2015, Vol. 246, No. 3, pp. 874-885.   DOI
13 Park, C., Partial backordering inventory model under purchase dependence, Industrial Engineering and Management Systems, 2015, Vol. 14, No. 3, pp. 275-288.   DOI
14 Shin, H., Park, S., Lee, E., and Bentond, W.C., A classification of the literature on the planning of substitutable products, European Journal of Operational Research, 2015, Vol. 246, No. 3, pp. 686-699.   DOI
15 Park, C., A partial backordering inventory model with a drop-shipping option under purchase dependence, Asia-Pacific Journal of Operational Research, 2017, Vol. 34, No. 4, pp. 1-20.   DOI
16 Park, C., Iterative approach to calculating the order fill rate under purchase dependence, Industrial Engineering and Management Systems, 2017, Vol. 16, No. 3, pp. 363-374.   DOI
17 Park, C. and Seo, J., Consideration of purchase dependence in inventory management, Computers and Industrial Engineering, 2013, Vol. 66, No. 2, pp. 274-285.   DOI
18 Song, J.S., On the order fill rate in a multi-item, basestock inventory system, Operations Research, 1998, Vol. 46, No. 6, pp. 831-845.   DOI
19 Urban, T.L., A periodic-review model with seriallycorrelated, inventory-level-dependent demand, International Journal of Production Economics, 2005, Vol. 95, No. 3, pp. 287-295.   DOI
20 Wong, R.C., Fu, A.W., and Wang, K., Data mining for inventory item selection with cross-selling considerations, Data Mining and Knowledge Discovery, 2005, Vol. 11, No. 1, pp. 81-112.   DOI
21 Yan, X.S., Robb, D.J., and Silver, E.A., Inventory performance under pack size constraints and spatiallycorrelated demand, International Journal of Production Economics, 2009, Vol. 117, No. 2, pp. 330-337.   DOI