Developing location-routing-inventory model under uncertainty: A queuing-based approach

Document Type : Research Paper

Authors

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

2 Faculty of Management, University of Tehran, Tehran, Iran

Abstract

This study develops a mathematical model for the designing of a supply chain network. The uncertain nature of demand and lead time is incorporated into the concerned model. This motivates us to deploy the queuing concept to deal with uncertainties and analysing the number of orders, number of shortages and average of on-hand inventory. Then, in accordance with the outputs of the queuing analysis, a mixed integer nonlinear programming model is devised to design the distribution network of a supply chain. The decisions to be made are facility locations, demand allocations along with inventory management decisions. The objective function of the model aims at minimising the total supply chain costs encompassing location, transportation and inventory costs. Notably, we assume that each facility manages its inventory policy based on a  policy and stock outs result in lost sales. Inasmuch as the developed problem is difficult to solve by means of exact methods, tailored hybrid solution algorithms based on simulated annealing and genetic algorithm are employed to overcome the computational complexity of the developed model. Finally, using the real information of the Telecommunication infrastructure company, we evaluate the proposed model and the management insights are reported.

Keywords

Main Subjects

References

Anđelić, Nikola et al. (2021). “Estimation of COVID-19 Epidemic Curves Using Genetic Programming Algorithm.” Health informatics journal 27(1): 1460458220976728.
Badri Ahmadi, Hadi, Seyed Hashemi Petrudi, and Xuping Wang. (2017). “Integrating Sustainability into Supplier Selection with Analytical Hierarchy Process and Improved Grey Relational Analysis: A Case of Telecom Industry.” International Journal of Advanced Manufacturing Technology 90.
Bashiri, Mahdi, and Hamid Hasanzadeh. (2016). “Modeling of Location-Distribution Considering Customers with Different Priorities by a Lexicographic Approach.” Scientia Iranica 23(2): 701–10.
Baumol, William J, and Philip Wolfe. (1958). “A Warehouse-Location Problem.” Operations research 6(2): 252–63.
Ben-Daya, Mohamed, Elkafi Hassini, and Zied Bahroun. (2019). “Internet of Things and Supply Chain Management: A Literature Review.” International Journal of Production Research 57(15–16): 4719–42.
Berman, Oded, and Eungab Kim. (1999). “Stochastic Models for Inventory Management at Service Facilities.” Stochastic Models 15(4): 695–718.
Berman, Oded, Dmitry Krass, and M Mahdi Tajbakhsh. (2012). “A Coordinated Location-Inventory Model.” European Journal of Operational Research 217(3): 500–508.
Büyüközkan, Gülçin, and Mehmet şakir Ersoy. (2009). “Applying Fuzzy Decision Making Approach to IT Outsourcing Supplier Selection.” system 2: 2.
Cárdenas-Barrón, L. E., & Sana, S. S. (2015). Multi-item EOQ inventory model in a two-layer supply chain while demand varies with promotional effort. Applied Mathematical Modelling, 39(21), 6725-6737.
Cárdenas-Barrón, Leopoldo Eduardo, and Shib Sankar Sana. (2014). “A Production-Inventory Model for a Two-Echelon Supply Chain When Demand Is Dependent on Sales Teams׳ Initiatives.” International Journal of Production Economics 155: 249–58.
Chew, Ek Peng, Loo Hay Lee, and Kanshukan Rajaratnam. (2007). “Evolutionary Algorithm for an Inventory Location Problem.” In Evolutionary Scheduling, Springer, 613–28.
Cochran, William G, and Gertrude M Cox. (1957). “Experimental Designs. John Willey and Sons.” Inc., New York: 546–68.
Dalfard, Vahid Majazi, Mojtaba Kaveh, and Nassim Ekram Nosratian. (2013). “Two Meta-Heuristic Algorithms for Two-Echelon Location-Routing Problem with Vehicle Fleet Capacity and Maximum Route Length Constraints.” Neural Computing and Applications 23(7): 2341–49.
Daskin, Mark S, Collette R Coullard, and Zuo-Jun Max Shen. (2002). “An Inventory-Location Model: Formulation, Solution Algorithm and Computational Results.” Annals of operations research 110(1): 83–106.
Diabat, Ali, Ehsan Dehghani, and Armin Jabbarzadeh. (2017). “Incorporating Location and Inventory Decisions into a Supply Chain Design Problem with Uncertain Demands and Lead Times.” Journal of Manufacturing Systems 43: 139–49. http://dx.doi.org/10.1016/j.jmsy.2017.02.010.
Eiben, Agoston E, James E Smith, and others. (2003). 53 Introduction to Evolutionary Computing. Springer.
Forouzanfar, F, Reza Tavakkoli-Moghaddam, Mahdi Bashiri, and Armand Baboli. (2016). “A New Bi-Objective Model for a Closed-Loop Supply Chain Problem with Inventory and Transportation Times.” Scientia Iranica 23(3): 1441–58.
Gebennini, Elisa, Rita Gamberini, and Riccardo Manzini. (2009). “An Integrated Production--Distribution Model for the Dynamic Location and Allocation Problem with Safety Stock Optimization.” International Journal of Production Economics 122(1): 286–304.
González-R, Pedro L, Jose M Framinan, and Rafael Ruiz-Usano. (2013). “A Methodology for the Design and Operation of Pull-Based Supply Chains.” Journal of Manufacturing Technology Management.
Holland, John Henry, and others. (1992). Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. MIT press.
Jain, Apurva. (2006). “Priority and Dynamic Scheduling in a Make-to-Stock Queue with Hyperexponential Demand.” Naval Research Logistics (NRL) 53(5): 363–82.
Javid, Amir Ahmadi, and Nader Azad. (2010). “Incorporating Location, Routing and Inventory Decisions in Supply Chain Network Design.” Transportation Research Part E: Logistics and Transportation Review 46(5): 582–97.
Kim, Eungab. (2005). “Optimal Inventory Replenishment Policy for a Queueing System with Finite Waiting Room Capacity.” European journal of operational research 161(1): 256–74.
Kumar, Vijay, and Dinesh Kumar. (2021). “A Systematic Review on Firefly Algorithm: Past, Present, and Future.” Archives of Computational Methods in Engineering 28(4): 3269–91.
Liao, Shu-Hsien, Chia-Lin Hsieh, and Peng-Jen Lai. (2011). “An Evolutionary Approach for Multi-Objective Optimization of the Integrated Location--Inventory Distribution Network Problem in Vendor-Managed Inventory.” Expert Systems with Applications 38(6): 6768–76.
Mak, Ho-Yin, and Zuo-Jun Max Shen. (2009). “A Two-Echelon Inventory-Location Problem with Service Considerations.” Naval Research Logistics (NRL) 56(8): 730–44.
Maleki, Leila, Seyed Hamid Reza Pasandideh, Seyed Taghi Akhavan Niaki, and Leopoldo Eduardo Cárdenas-Barrón. (2017). “Determining the Prices of Remanufactured Products, Capacity of Internal Workstations and the Contracting Strategy within Queuing Framework.” Applied Soft Computing 54: 313–21.
Manatkar, R P, Kondapaneni Karthik, Sri Krishna Kumar, and Manoj Kumar Tiwari. (2016). “An Integrated Inventory Optimization Model for Facility Location-Allocation Problem.” International Journal of Production Research 54(12): 3640–58.
Memari, Ashkan, Abd Rahman Abdul Rahim, Adnan Hassan, and Robiah Ahmad. (2017). “A Tuned NSGA-II to Optimize the Total Cost and Service Level for a Just-in-Time Distribution Network.” Neural Computing and Applications 28(11): 3413–27.
Metropolis, Nicholas et al. (1953). “Equation of State Calculations by Fast Computing Machines.” The journal of chemical physics 21(6): 1087–92.
Mirchandani, Pitu B, and Richard L Francis. (1990). Discrete Location Theory.
Nekooghadirli, N et al. (2014). “Solving a New Bi-Objective Location-Routing-Inventory Problem in a Distribution Network by Meta-Heuristics.” Computers \& Industrial Engineering 76: 204–21.
Otten, S, R Krenzler, and H Daduna. (2016). “Models for Integrated Production-Inventory Systems: Steady State and Cost Analysis.” International Journal of Production Research 54(20): 6174–91.
Ozsen, Leyla, Collette R Coullard, and Mark S Daskin. (2008). “Capacitated Warehouse Location Model with Risk Pooling.” Naval Research Logistics (NRL) 55(4): 295–312.
Park, Sukun, Tae-Eog Lee, and Chang Sup Sung. (2010). “A Three-Level Supply Chain Network Design Model with Risk-Pooling and Lead Times.” Transportation Research Part E: Logistics and Transportation Review 46(5): 563–81.
Puga, Mat\’\ias Schuster, and Jean-Sébastien Tancrez. (2017). “A Heuristic Algorithm for Solving Large Location--Inventory Problems with Demand Uncertainty.” European Journal of Operational Research 259(2): 413–23.
Ramirez-Nafarrate, Adrian, Ozgur M Araz, and John W Fowler. (2021). “Decision Assessment Algorithms for Location and Capacity Optimization under Resource Shortages.” Decision Sciences 52(1): 142–81.
Rayat, Farnaz, MirMohammad Musavi, and Ali Bozorgi-Amiri. (2017). “Bi-Objective Reliable Location-Inventory-Routing Problem with Partial Backordering under Disruption Risks: A Modified AMOSA Approach.” Applied Soft Computing 59: 622–43.
Ross, David Frederick, Frederick S Weston, and W Stephen. (2010). Introduction to Supply Chain Management Technologies. Crc Press.
Roy, R. (1990). “A Primer on the Taguchi Method, Society Of‎ Manufacturing Engineers. Ann Arbor, Mich, USA‎‏.‏.”
Sadjadi, Seyed Jafar, Ahmad Makui, Ehsan Dehghani, and Magsoud Pourmohammad. (2016). “Applying Queuing Approach for a Stochastic Location-Inventory Problem with Two Different Mean Inventory Considerations.” Applied Mathematical Modelling 40(1): 578–96.
Saffari, Mohammad, Søren Asmussen, and Rasosul Haji. (2013). “The M/M/1 Queue with Inventory, Lost Sale, and General Lead Times.” Queueing Systems 75(1): 65–77.
Schmidt, Charles P, and Steven Nahmias. (1985). “(S- 1, S) Policies for Perishable Inventory.” Management Science 31(6): 719–28.
Schwarz, Maike, and Hans Daduna. (2006). “Queueing Systems with Inventory Management with Random Lead Times and with Backordering.” Mathematical Methods of Operations Research 64(3): 383–414.
Shahabi, Mehrdad, Avinash Unnikrishnan, Ehsan Jafari-Shirazi, and Stephen D Boyles. (2014). “A Three Level Location-Inventory Problem with Correlated Demand.” Transportation Research Part B: Methodological 69: 1–18.
Shen, Zuo-Jun Max, Collette Coullard, and Mark S Daskin. (2003). “A Joint Location-Inventory Model.” Transportation science 37(1): 40–55.
Shu, Jia, Chung-Piaw Teo, and Zuo-Jun Max Shen. (2005). “Stochastic Transportation-Inventory Network Design Problem.” Operations Research 53(1): 48–60.
Simchi-Levi, David, Philip Kaminsky, and Edith Simchi-Levi. (2004). Managing the Supply Chain: Definitive Guide. Tata McGraw-Hill Education.
Simić, Dragan, Vasa Svirčević, and Svetlana Simić. (2015). “A Hybrid Evolutionary Model for Supplier Assessment and Selection in Inbound Logistics.” Journal of Applied Logic 13(2): 138–47.
Snyder, Lawrence V, Mark S Daskin, and Chung-Piaw Teo. (2007). “The Stochastic Location Model with Risk Pooling.” European Journal of Operational Research 179(3): 1221–38.
Teimoury, E, M Modarres, F Ghasemzadeh, and M Fathi. (2010). “A Queueing Approach to Production-Inventory Planning for Supply Chain with Uncertain Demands: Case Study of PAKSHOO Chemicals Company.” Journal of Manufacturing Systems 29(2–3): 55–62.
Tiwari, Manoj Kumar, N Raghavendra, Shubham Agrawal, and S K Goyal. (2010). “A Hybrid Taguchi--Immune Approach to Optimize an Integrated Supply Chain Design Problem with Multiple Shipping.” European Journal of Operational Research 203(1): 95–106.
Tsao, Yu-Chung. (2013). “Distribution Center Network Design under Trade Credits.” Applied Mathematics and Computation 222: 356–64.
Vahdani, Behnam, Donya Veysmoradi, N Shekari, and S Meysam Mousavi. (2018). “Multi-Objective, Multi-Period Location-Routing Model to Distribute Relief after Earthquake by Considering Emergency Roadway Repair.” Neural Computing and Applications 30(3): 835–54.
Wright, Margaret H. (1996). “Direct Search Methods: Once Scorned, Now Respectable.” Pitman Research Notes in Mathematics Series: 191–208.  
Journal of Industrial and Systems Engineering
Volume 13, Issue 4
November 2021
Pages 199-225

Files

History

  • Receive Date: 28 December 2020
  • Revise Date: 08 August 2021
  • Accept Date: 09 August 2021

Share

How to cite

Statistics