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http://dx.doi.org/10.11627/jkise.2015.38.4.109

An Inventory Problem with Lead Time Proportional to Lot Size and Space Constraint  

Lee, Dongju (Dept. of Industrial & Systems Engineering, Kongju National University)
Publication Information
Journal of Korean Society of Industrial and Systems Engineering / v.38, no.4, 2015 , pp. 109-116 More about this Journal
Abstract
This paper is concerned with the single vendor single buyer integrated production inventory problem. To make this problem more practical, space restriction and lead time proportional to lot size are considered. Since the space for the inventory is limited in most practical inventory system, the space restriction for the inventory of a vendor and a buyer is considered. As product's quantity to be manufactured by the vendor is increased, the lead time for the order is usually increased. Therefore, lead time for the product is proportional to the order quantity by the buyer. Demand is assumed to be stochastic and the continuous review inventory policy is used by the buyer. If the buyer places an order, then the vendor will start to manufacture products and the products will be transferred to the buyer with equal shipments many times. The mathematical formulation with space restriction for the inventory of a vendor and a buyer is suggested in this paper. This problem is constrained nonlinear integer programming problem. Order quantity, reorder points for the buyer, and the number of shipments are required to be determined. A Lagrangian relaxation approach, a popular solution method for constrained problem, is developed to find lower bound of this problem. Since a Lagrangian relaxation approach cannot guarantee the feasible solution, the solution method based on the Lagrangian relaxation approach is proposed to provide with a good feasible solution. Total costs by the proposed method are pretty close to those by the Lagrangian relaxation approach. Sensitivity analysis for space restriction for the vendor and the buyer is done to figure out the relationships between parameters.
Keywords
Continuous Review Inventory System; Variable Lead Time; Space Restriction; Supply Chain Management;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
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1 Ben-Daya, M. and Hariga, M., Integrated single vendor single buyer model with stochastic demand and variable lead time. Int J Prod Eco, 2004, Vol. 92, pp. 75-80.   DOI
2 Ghalebsaz-Jeddi, B., Shultes, B.C., and Haji, R.A., multiproduct continuous review inventory system with stochastic demand, backorders, and a budget constraint. European Journal of Operational Research, 2004, Vol. 158, pp. 456-469.   DOI
3 Hadley, G. and Whitin, T.M., Analysis of Inventory Systems, Prentice Hall Inc., Englewood Cliffs, NJ, 1963.
4 Hariga, M., A single-item continuous review inventory problem with space restriction, Int J Prod Eco, 2010, Vol. 128, pp. 153-158.   DOI
5 Lee, D.J., A Study on Inventory Control Policy for Quantity-Discount and Budget Constraint. J Soc Korea Ind Syst Eng, 2015, Vol. 38, No. 2, pp. 145-151.   DOI
6 Lee, D.J., Quadratic Programming Approach to a VMI Problem. J of the Kor Ins of Plant Eng, 2007, Vol. 12, pp. 91-104.
7 Lee, D.J., Yoo, J.Y., and Lee, M.S., An Approximation Approach for A Multi-Product Continuous Review Inventory Problem with Budget Constraint. J Soc Korea Ind Syst Eng, 2008, Vol. 31, No. 4, pp. 134-139.
8 Tamjidzad, S. and Mirmohammadi, H., An optimal (r, Q) policy in a stochastic inventory system with all-units quantity discount and limited sharable resource. Eur J of Ope Res, 2015, Vol. 247, pp. 93-100.   DOI
9 Wang, T.Y. and Hu, J.M., An inventory control system for products with optional components under service level and budget constraints. Euro J of Oper Res, 2008, Vol. 189, pp. 41-58.   DOI
10 Wang, T.Y. and Hu, J.M., Heuristic method on solving an inventory model for products with optional components under stochastic payment and budget constraints. Exp sys with App, 2010, Vol. 37, pp. 2588-2598.   DOI
11 Zhao, X., Fan, F., Liu, X., and Xie, J., Storage-Space Capacitated Inventory System with (r, Q) Policies. Operations Research, 2007, Vol. 55, No. 5, pp. 854-865.   DOI