Applying Genetic Algorithm for Can-Order Policies in the Joint Replenishment Problem

  • Nagasawa, Keisuke (Department of Information and Communication Sciences, Sophia University) ;
  • Irohara, Takashi (Department of Information and Communication Sciences, Sophia University) ;
  • Matoba, Yosuke (Fairway Solutions Inc.) ;
  • Liu, Shuling (Fairway Solutions Inc.)
  • Received : 2014.01.05
  • Accepted : 2015.03.09
  • Published : 2015.03.30


In this paper, we consider multi-item inventory management. When managing a multi-item inventory, we coordinate replenishment orders of items supplied by the same supplier. The associated problem is called the joint replenishment problem (JRP). One often-used approach to the JRP is to apply a can-order policy. Under a can-order policy, some items are re-ordered when their inventory level drops to or below their re-order level, and any other item with an inventory level at or below its can-order level can be included in this order. In the present paper, we propose a method for finding the optimal parameter of a can-order policy, the can-order level, for each item in a lost-sales model. The main objectives in our model are minimizing the number of ordering, inventory, and shortage (i.e., lost-sales) respectively, compared with the conventional JRP, in which the objective is to minimize total cost. In order to solve this multi-objective optimization problem, we apply a genetic algorithm. In a numerical experiment using actual shipment data, we simulate the proposed model and compare the results with those of other methods.


Inventory Modeling and Management;Logistics and Supply Chain Management(L/SCM);Supply Chain Management(SCM);Evolutionary Algorithms;Warehouse Operation and Management


  1. Amaya, C. A., Carvajal, J., and Castano, F. (2013), A heuristic framework based on linear programming to solve the constrained joint replenishment problem (C-JRP), International Journal of Production Economics, 144, 243-247.
  2. Andre, J., Siarry, P., and Dognon, T. (2001), An improvement of the standard genetic algorithm fighting premature convergence in continuous optimization, Advances in engineering software, 32, 49-60.
  3. Atkins, D. R. and Iyogun, P. O. (1988), Periodic versus 'can-order' policies for coordinated multi-item inventory systems, Management Science, 34, 791-796.
  4. Balintfy, J. L. (1964), On a basic class of multi-item inventory problems, Management Science, 10, 287-297.
  5. Chan, L. M. A., Muriel, A., and Shen, Z. J. M. (2002), Effective zero-inventory-ordering policies for the single-warehouse multi retailer problem with piecewise linear cost structures, Management Science, 48, 1446-1460.
  6. Dellaert, N. and Poel, E. (1996), Global inventory control in an academic hospital, International Journal of Production Economics, 46, 277-284.
  7. Federgruen, A., Groenevelt, H., and Tijms, H. C. (1984), Coordinated replenishments in a multi-item inventory system with compound Poisson demands, Management Science, 30, 344-357.
  8. Goyal, S. K. (1974), Determination of optimum packaging frequency of items jointly replenished, Management Science, 21, 436-443.
  9. Goyal, S. K. and Satir, A. T. (1989), Joint replenishment inventory control: Deterministic and stochastic models, European Journal of Operational Research, 38, 2-13.
  10. Gray, F. (1953), Pulse Code Communication, United States Patent Number 2621058.
  11. Johansen, S. G. and Melchiors, P. (2003), Can-order policy for the periodic review joint replenishment problem, Journal of the Operational Research Society, 54, 283-290.
  12. Kaspi, M. and Rosenblatt, M. J. (1991), On the economic ordering quantity for jointly replenishment items, International Journal of Production Research, 29, 107-114.
  13. Kayis, E., Bilgic, T., and Karabulut, D. (2008), A note on the can-order policy for the two-item stochastic joint-replenishment problem, IIE Transactions, 40, 84-92.
  14. Khouja, M., Michalewicz, M., and Satoskar, S. (2000), A comparison between genetic algorithms and the RAND method for solving the joint replenishment problem, Production Planning and Control, 11, 556-564.
  15. Liu, L. and Yuan, X. M. (2000), Coordinated replenishments in inventory systems with correlated demands, European Journal of Operational Research, 123, 490-503.
  16. Melchiors, P. (2002), Calculating can-order polices for the joint replenishment problem by the compensation approach, European Journal of Operational Research, 141, 587-595.
  17. Moon, I. K. and Cha, B. C. (2006), The joint replenishment problem with resource restriction, European Journal of Operational Research, 173(1), 190-198.
  18. Moutaz, K. and Goyal, S. (2008), A review of the joint replenishment problem literature: 1989-2005, European Journal of Operational Research, 186, 1-16.
  19. Pantumsinchai, P. (1992), A comparison of three joint ordering inventory policies, Decision Sciences, 23, 111-127.
  20. Silver, E. (1976), A simple method of determining order quantities in joint replenishments under deterministic demand, Management Science, 22, 1351-1361.
  21. Tsai, C. Y., Tsai, C. Y., and Huang, P. W. (2009), An association clustering algorithm for can-order policies in the joint replenishment problem, International Journal of Production Economics, 117, 30-41.
  22. van Eijs, M. J. (1994), On the determination of the control parameters of the optimal can-order policy, ZOR-Mathematical Models of Operations Research, 39, 289-304.
  23. Wang, L., Dun, C., Bi, W., and Zeng, Y. (2012a), An effective and efficient differential evolution algorithm for the integrated stochastic joint replenishment and delivery model, Knowledge-Based Systems, 36, 104-114.
  24. Wang, L., He, J., Wu, D., and Zeng Y. (2012b), A novel differential evolution algorithm for joint replenishment problem under interdependence and its application, International Journal of Production Economics, 135, 190-198.
  25. Yang, W., Chan, F. T., and Kumar, V. (2012), Optimizing replenishment polices using Genetic Algorithm for single-warehouse multi-retailer system, Expert Systems with Applications, 39, 3081-3086.
  26. Zhao, P., Zhang C., and Zhang X. (2011), A New Clustering Algorithm for Can-order Policies in Joint Replenishment Problem, Journal of Computational Information Systems, 7, 1943-1950.

Cited by

  1. A systematic literature review on the joint replenishment problem solutions: 2006-2015 vol.27, pp.0, 2017,
  2. Application of the joint replenishment problem in a collaborative Inventory approach to define resupply plans in urban goods distribution contexts vol.85, pp.207, 2018,