Applying Queuing Theory to Optimize Perishable Products Supply Chain with (S-1, S) Ordering Policy and Increasing Customers Satisfaction

Document Type: Research Paper

Authors

1 Faculty of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

2 دانشیار دانشکدة مهندسی صنایع، دانشگاه علم و صنعت ایران

Abstract

Applying queuing theory to optimize inventory control systems, is an important field in the literature of perishable inventory systems. However, a few studies have considered it with (S-1, S) ordering policy and customer satisfaction. In this paper, queuing theory was used to optimize inventory control system and to increase customer satisfaction in a two-stage supply chain of perishable products with exponential life time. The supply chain consists of a manufacturer and a supplier. Customers arrive at the manufacturer according to a Poisson process. Manufacturer uses (S-1, S) ordering policy for stock replenishment. Lead time and processing time are exponentially distributed. The aim is to determine the optimal values of manufacturer’s storage capacity and waiting room capacity. Therefore, the supply chain is modeled as a queuing system. After deriving steady state equations, system performance measures were calculated and a mathematical model was developed to minimize total cost. Optimal solutions were obtained by enumeration and direct search techniques. The sensitivity analysis of the model is performed by a numerical example.

Keywords

Main Subjects


1. Kalpakam, S. and Sapna, K. (1994). “Continuous review (s, S) inventory system with random lifetimes and positive leadtimes”, Operations Research letters, Vol.16, No.2, PP. 115– 119.

2. Sivakumar, B. and Arivarignan, G. (2005). "A perishable inventory system with service facilities and negative customers", Advanced Modeling and Optimization, Vol.7, No. 2,  PP. 193- 210.

3. Sivakumar, B., Elango, C. and Arivarignan, G. (2006). "A perishable inventory system with service facilities and batch markovian Demands", International Journal of pure and Applied Mathematics, Vol. 32, No.1, PP. 33- 40.

4. Yadavalli, V. S. S., Sivakumar, B. and Arivarignan, G. (2007). "Stochastic inventory management at a service facility with a set of reorder levels", ORION, Vol. 23, No. 2, PP. 137- 149.

5. Satheesh Kumar, R. and Elango, C. (2010). "Markov decision processes for service facility systems with perishable inventory", International Journal of Computer Applications, Vol. 9, Issue 4, PP. 14- 17.

6. Shophia Lawrence, A., Sivakumar, B. and Arivarignan, G. (2013). “A perishable inventory system with service facility and finite source”, Applied MathematicalModelling, Vol. 37, Issue 7, PP. 4771– 4786.

7. Jeganathan, K. (2014). “A Perishable Inventory Model with Bonus Service for Certain Customers, Balking and N + 1 Policy”, Mathematical Economics Letters, Vol. 2, No. 3– 4, PP. 83– 104.

8. Jeganathan, K. and Periyasamy, C. (2014). “A perishable inventory system with repeated customers and server interruptions”, Applied Mathematics & Information Sciences Letters, Vol. 2, No. 2, PP. 1- 11.

9. Al Hamadi, H. M., Sangeetha, N. and Sivakumar, B. (2015). “Optimal control of service parameter for a perishable inventory system maintained at service facility with impatient customers”, Annals of Operations Research, Vol. 233, Issue 1, PP. 3– 23.

10. Laxmi, V. P. and Soujanya, M. L. (2015). “Perishable inventory system with service interruptions, retrial demands and negative customers”, Applied Mathematics and Computation, Vol. 262, No. 1, PP. 102–110.

11. Jeganathan, K. (2015). “A single server perishable inventory system with N additional options for service”, Journal of Mathematical Modeling, Vol. 2, No. 2, PP. 187- 216.

12. Amirthakodi, M., Radhamani, V. and Sivakumar, B. (2015). “A perishable inventory system with service facility and feedback customers”, Annals of Operations Research, Vol. 233, Issue. 1, PP. 25-55.

13. Jeganathan, K., Sumathi, J. and Makalakshmi, G. (2016). “Markovian inventory model with two parallel queues, jockeying and impatient customers”, Yugoslav Journal of Operations Research, Vol. 26, No. 4, PP. 467– 506.

14. Mahmoodi, A., Haji, A., and Haji, R. (2014). “One for one period policy for perishable inventory”, Computers & Industrial Engineering, Vol. 79, No. 1, PP. 10-17.

15. Kouki, C. and Jouini, O. (2015). “On the effect of lifetime variability on the performance of inventory systems”, Int. J. Production Economics,  Vol. 167, No. ???, PP. 23– 34.

16. Kalpakam, S. and Sapna, K. (1995).“(S-1,S) perishable systems with stochastic leadtimes”, Mathematical and Computer Modeling, Vol. 21, No. 6, PP. 95– 104.

17. Kalpakam, S. and Shanthi, S. (2001). “A perishable inventory system with modified (S-1, S) policy and arbitrary processing times”, Computers and Operations Research, Vol. 28, Issue. 5, PP. 453– 471.

18. Ioannidis, S., Jouini, O. and Economopoulos, A. A. (2012). "Control policies for single stage production systems with perishable inventory and customer impatience", Operations Research, Vol. 209, Issue.1, PP. 115- 138.

19. Mahmoodi, A., Haji, A. and Haji, R. (2016). “A two-echelon inventory model with perishable items and lost sales”, Scientia Iranica E, Vol. 23, No. 5, PP. 2277- 2286.

20. Jewkes, E. M. and Alfa, A. S. (2009). “A queueing model of delayed product differentiation”, European Journal of Operational Research, Vol. 199, No. 3, PP. 734- 743.