Genetic Algorithm-Based Coordinated Replenishment in Multi-Item Inventory Control

  • Nagasawa, Keisuke ;
  • Irohara, Takashi ;
  • Matoba, Yosuke ;
  • Liu, Shuling
  • Received : 2013.01.31
  • Accepted : 2013.08.28
  • Published : 2013.09.30


We herein consider a stochastic multi-item inventory management problem in which a warehouse sells multiple items with stochastic demand and periodic replenishment from a supplier. Inventory management requires the timing and amounts of orders to be determined. For inventory replenishment, trucks of finite capacity are available. Most inventory management models consider either a single item or assume that multiple items are ordered independently, and whether there is sufficient space in trucks. The order cost is commonly calculated based on the number of carriers and the usage fees of carriers. In this situation, we can reduce future shipments by supplementing items to an order, even if the item is not scheduled to be ordered. On the other hand, we can reduce the average number of items in storage by reducing the order volume and at the risk of running out of stock. The primary variables of interest in the present research are the average number of items in storage, the stock-out volume, and the number of carriers used. We formulate this problem as a multi-objective optimization problem. In a numerical experiment based on actual shipment data, we consider the item shipping characteristics and simulate the warehouse replenishing items coordinately. The results of the simulation indicate that applying a conventional ordering policy individually will not provide effective inventory management.


Inventory Management;Coordinated Replenishment;Ordering Policy;Genetic Algorithm


  1. Altiparmak, F., Gen, M., Lin, L., and Paksoy, T. (2006), A genetic algorithm approach for multi-objective optimization of supply chain networks, Computers & Industrial Engineering, 51(1), 196-215.
  2. Berling, P. and Marklund, J. (2006), Heuristic coordination of decentralized inventory systems using induced backorder costs, Production and Operations Management, 15(2), 294-310.
  3. Bijvank, M. and Vis, I. F. A. (2011), Lost-sales inventory theory: a review, European Journal of Operational Research, 215(1), 1-13.
  4. Brown, E. C. and Sumichrast, R. T. (2001), CF-GGA: a grouping genetic algorithm for the cell formation problem, International Journal of Production Research, 39(16), 3651-3669.
  5. Chan, L. M. A., Muriel, A., Shen, Z. J. M., Simchi-Levi, D., and Teo, C. P. (2002), Effective zero-inventoryordering policies for the single-warehouse multi retailer problem with piecewise linear cost structures, Management Science, 48(11), 1446-1460.
  6. Gruen, T. W., Corsten, D. S., and Bharadwaj, S. (2002), Retain out-of-stocks: a worldwide examination of extent, causes and consumer responses, Grocery Manu-facturers of American, Washington, DC.
  7. Huh, W. T., Janakiraman, G., Muckstadt, J. A., and Rusmevichientong, P. (2009), Asymptotic optimality of order-up-to policies in lost sales inventory systems, Management Science, 55(3), 404-420.
  8. Janakiraman, G., Seshadri, S., and Shanthikumar, J. G. (2007), A comparison of the optimal costs of two canonical inventory systems, Operations Research, 55(5), 866-875.
  9. Kiesmuller, G. P. (2009), A multi-item periodic replenishment policy with full truckloads, International Journal of Production Economics, 118(1), 275-281.
  10. Kiesmuller, G. P. (2010), Multi-item inventory control with full truckloads: a comparison of aggregate and individual order triggering, European Journal of Operational Research, 200(1), 54-62.
  11. Levi, R., Janakiraman, G., and Nagarajan, M. (2008), A 2- approximation algorithm for stochastic inventory control models with lost sales, Mathematics of Operations Research, 33(2), 351-374.
  12. Liao, T. W. and Chang, P. C. (2010), Impacts of forecast, inventory policy, and lead time on supply chain inventory: a numerical study, International Journal of Production Economics, 128(2), 527-537.
  13. Tiacci, L. and Saetta, S. (2009), An approach to evaluate the impact of interaction between demand forecast- ing method and stock control policy on the inventory system performances, International Journal of Production Economics, 118(1), 63-71.
  14. Van Donselaar, K. H. and Broekmeulen, R. A. C. M. (2013), Determination of safety stocks in a lost sales inventory system with periodic review, positive leadtime, lot-sizing and a target fill rate, International Journal of Production Economics, 143(2), 440-448.
  15. Watanabe, M., Ida, K., and Gen, M. (2005), A genetic algorithm with modified crossover operator and search area adaptation for the job-shop scheduling problem, Computers & Industrial Engineering, 48(4), 743-752.
  16. Xiao, Y., Zhang, R., and Kaku, I. (2011), A new approach of inventory classification based on loss profit, Expert Systems with Applications, 38(8), 9382-9391.
  17. Yang, W., Chan, F. T. S., and Kumar, V. (2012), Optimizing replenishment polices using genetic algorithm for single-warehouse multi-retailer system, Expert Systems with Applications, 39(3), 3081-3086.
  18. Zipkin, P. (2008), Old and new methods for lost-sales inventory systems, Operations Research, 56(5), 1256-1263.