Reorder Point and Replenishment Point of Dynamic Inventory Model under Shortages

Öz

In this study, single item dynamic inventory control model is analyzed. In this model the decision maker counts the inventory periodically, calculates the reorder point and the replenishment point, and decides to replenish the stock according to the inventory position. This calculation is difficult and requires complex mathematical transactions when the demand and lead time are stochastic. For this reason, in this study, the simulation method and genetic algorithms method are used to calculate the reorder point and replenishment point by using total cost function per period. In this function, the ordering cost, the holding cost and the penalty cost are taken into account. The results of these two methods are compared with classic method based on real data where the demand distribution is normal, and the lead time distribution is uniform. Thereafter, three cost calculations and their effects on reorder point and replenishment point are analyzed at two different levels.

Anahtar Kelimeler

• .

Reorder Point and Replenishment Point of Dynamic Inventory Model under Shortages

Öz

In this study, single item dynamic inventory control model is analyzed. In this model the decision maker counts the inventory periodically, calculates the reorder point and the replenishment point, and decides to replenish the stock according to the inventory position. This calculation is difficult and requires complex mathematical transactions when the demand and lead time are stochastic. For this reason, in this study, the simulation method and genetic algorithms method are used to calculate the reorder point and replenishment point by using total cost function per period. In this function, the ordering cost, the holding cost and the penalty cost are taken into account. The results of these two methods are compared with classic method based on real data where the demand distribution is normal, and the lead time distribution is uniform. Thereafter, three cost calculations and their effects on reorder point and replenishment point are analyzed at two different levels

Anahtar Kelimeler

• Replenishment Point,Reorder Point,Inventory Control,Simulation

Kaynakça

1. Agrawal, P. M., & Sharda, R. (2012). Impact of frequency of alignment of physical and information system inventories on out of stocks: A simulation Economics,136(1), 45-55. Journal of Production
2. Allen, F., & Karjalainen, R. (1999). Using genetic algorithms to find technical trading rules. Journal of financial Economics, 51(2), 245- 271.
3. Arrow, K. J., Harris, T., & Marschak, J. (1951). Optimal inventory policy. Econometrica: Journal of the Econometric Society, 250-272.
4. Bollapragada, S., & Morton, T. E. (1999). A simple heuristic for computing nonstationary (s, S) policies. Operations Research, 47(4), 576-584
5. Buchan, J. A., & Koenıgsberg, E. A. (1966). Scientific inventory management. Prentice Hall.
6. DeYong, G. D., & Cattani, K. D. (2015). Fenced in? Stochastic and deterministic planning models in a time-fenced, rolling-horizon scheduling system.European Journal of Operational Research.
7. Diabat, A., & Deskoores, R. (2015). A hybrid genetic algorithm based heuristic for an integrated supply chain problem.Journal of Manufacturing Systems.
8. do Rego, J. R., & de Mesquita, M. A. (2015). Demand forecasting and inventory control: A simulation study on automotive spare parts.International Journal of Production Economics, 161, 1-16.

9. Duan, Q., & Liao, T. W. (2013). A new age-based replenishment policy for supply chain inventory optimization of highly perishable products. International Journal of Production Economics,145(2), 658-671.
10. Ehrhardt, R. (1979). The power approximation for computing (s, S) inventory policies. Management Science, 25(8), 777-786.
11. Ehrhardt, R. (1984). (s, S) policies for a dynamic inventory model with stochastic lead times. Operations Research, 32(1), 121-132.
12. Ehrhardt, R., & Mosier, C. (1984). A revision of the power approximation for computing (s, S) policies. Management Science, 30(5), 618-622.
13. Escuín, D., Polo, L., & Ciprés, D. (2016). On the comparison of inventory replenishment policies with time-varying stochastic demand for the paper industry.Journal of Computational and Applied Mathematics.
14. Freeland, J. R., & Porteus, E. L. (1980). Evaluating the effectiveness of a new method for computing approximately optimal (s, S) inventory policies. Operations Research, 28(2), 353-364.
15. García-Alvarado, M. S., Paquet, M., & Chaabane, A. (2015). On inventory control of product recovery systems subject to environmental mechanisms. International Journal of Production Economics,165, 132-144.
16. Glover, F., & Laguna, M. (1993). Modern heuristic techniques for combinatorial problems. Blackwell, London.
17. Goldberg, D. E. (1989). Genetic algorithms in search and machine learning. Reading, Addison Wesley.
18. Hillier, F. S. (1995).Introduction to operations research. Tata McGraw-Hill Education.
19. Hwang, H., Choi, B., & Lee, M. J. (2005). A model for shelf space allocation and inventory control considering location and inventory level effects on demand.International Journal of Production Economics,97(2), 185-195.
20. Iglehart, D. L. (1963). Optimality of (s, S) policies in the infinite horizon dynamic inventory problem. Management science, 9(2), 259-267.
21. Jana, D. K., Das, B., & Maiti, M. (2014). Multi-item partial backlogging inventory models over random planning horizon in random fuzzy environment. Applied Soft Computing,21, 12-27.
22. Karlin, S. (1958). The Application of Renewal Theory to the Study of Inventory Policies. Chap. 15 in Arrow, KJ, S. Karlin, and H. Scarf. Studies in the Mathematical Theory of Inventory and Production.
23. Kouki, C., & Jouini, O. (2015). On the effect of lifetime variability on the performance of inventory systems.International Journal of Production Economics,167, 23-34.
24. Köchel, Peter., & Nieländer, U. (2005). Simulation-based optimization of multi-echelon inventory systems. International journal of production economics, 93, 505-513.
25. Larson, C. E., Olson, L. J., & Sharma, S. (2001). Optimal inventory policies when the demand distribution is not known.Journal of economic Theory, 101(1), 281-300.
26. Lin, K. P., Chang, P. T., Hung, K. C., & Pai, P. F. (2010). A simulation of vendor managed inventory dynamics using fuzzy arithmetic operations Applications,37(3), 2571-2579. genetic
27. algorithms.Expert Systems with
28. Maiti, M. K., & Maiti, M. (2006). Fuzzy inventory model with two warehouses Systems,157(1), 52-73. possibility
29. constraints.Fuzzy Sets and
30. Naddor, E. (1975). Optimal and heuristic decisions in single-and multi-item inventory systems. Management Science, 21(11), 1234-1249.
31. Nia, A. R., Far, M. H., & Niaki, S. T. A. (2014). A fuzzy vendor managed inventory of multi-item economic order quantity model under shortage: An ant colony optimization algorithm.International Journal of Production Economics,155, 259-271.
32. Nielsen, C., & Larsen, C. (2005). An analytical study of the Q (s, S) policy applied to the joint replenishment problem. European Journal of Operational Research, 163(3), 721-732
33. Porteus, E. L. (1971). On the optimality of generalized (s, S) policies. Management Science, 17(7), 411-426.
34. Rabta, B., & Aïssani, D. (2005). Strong stability in an (R, s, S) inventory model.International Journal of Production Economics,97(2), 159- 171.
35. Rezaei, J., & Davoodi, M. (2011). Multi-objective models for lot-sizing with supplier Economics,130(1), 77-86. Journal of Production
36. Roberts, D. M. (1962). Approximations to optimal policies in a dynamic inventory model. Studies in applied probability and management science, (7), 207.
37. Scarf, H. (1960). The Optimality of (s, S) Policies in Dynamic Inventory Problems. K. Arrow, S. Karlin, P. Suppes, eds., Mathematical Models in the Social Sciences.
38. Schneider, H. (1978). Methods for determining the re-order point of an (s, S) ordering policy when a service level is specified. Journal of the Operational Research Society, 1181-1193.
39. Sezen, H. K., & Erdoğmuş, Ş. (2005). Envanter Politikası Belirlemede Benzetim Uygulaması. 7. Ulusal Ekonometri ve İstatistik Sempozyumu.
40. Silver, E. A., Pyke, D. F., & Peterson, R. (1998). Inventory management and production planning and scheduling (Vol. 3, p. 30). New York: Wiley.
41. Sivazlian, B. D. (1971). Dimensional and computational analysis in stationary (s, S) inventory problems with gamma distributed demand. Management Science, 17(6), B-307.
42. Stevenson, W. J., & Sum, C. C. (2009). Operations management (Vol. 8). Boston, MA: McGraw-Hill/Irwin.
43. Taleizadeh, A. A., Niaki, S. T. A., Aryanezhad, M. B., & Shafii, N. (2013). A hybrid method of fuzzy simulation and genetic algorithm to optimize constrained inventory control systems with stochastic replenishments and fuzzy demand. Information Sciences, 220, 425- 441.
44. Thiel, D., Hovelaque, V., & Le Hoa, V. T. (2010). Impact of inventory inaccuracy on service-level quality in (Q, R) continuous-review lost- sales inventory models.International Journal of Production Economics,123(2), 301-311.
45. Tijms, H. C., & Groenevelt, H. (1984). Simple approximations for the reorder point in periodic and continuous review (s, S) inventory systems with service level constraints. European journal of operational research, 17(2), 175-190.
46. Veinott, Jr, A. F. (1966). On the Optimality of (s,S) Inventory Policies: New Conditions and a New Proof. SIAM Journal on Applied Mathematics, 14(5), 1067-1083.
47. Wagner, H. M. (1975). Principle of Operations Research, Englewood Cliff.
48. White, A. S., & Censlive, M. (2015). Control system analysis of labor supply flows in production systems.Journal of Manufacturing Systems,37, 316-327.
49. Ye, W., & You, F. (2016). A computationally efficient simulation-based optimization method with region-wise surrogate modeling for stochastic inventory management of supply chains with general network structures. Computers & Chemical Engineering,87, 164- 179
50. Yin, K. K., L,iu H., & Johnson, N. E. (2002). Markovian inventory policy with application to the paper industry. Computers & chemical engineering, 26(10), 1399-1413.
51. Zheng, Y. S., & Federgruen, A. (1991). Finding optimal (s, S) policies is about as simple as evaluating a single policy.Operations research,39(4), 654-665.
52. Zhou, W. Q., Chen, L., & Ge, H. M. (2013). A multi-product multi-echelon inventory control model with joint replenishment strategy.Applied Mathematical Modelling,37(4), 2039-2050.