Optimizing Queuing-Inventory Problems under Uncertainty: A Fuzzy Mathematical Programming
Subject Areas :
Industrial Management
Alireza Alinezhad
1
,
Vahid Hajipour
2
,
Amin Mahmoudi
3
1 - Assistant Professor, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
2 - Young Researchers and Elite Club, Qazvin Branch, Islamic Azad University, Qazvin, Iran
3 - Department of Industrial Engineering, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran
Received: 2014-10-07
Accepted : 2015-02-11
Published : 2015-04-09
Keywords:
Abstract :
In this paper, a queuing-inventory system with continuous review inventory control policy and batch arrival queuing approach is proposed. To best of our knowledge, (I) demand function is stochastic and price dependent; (II) due to the uncertainty in real-world situations, a fuzzy programming approach is applied. Therefore, the presented model with the goal of maximizing total profit of system analyzes the price and order quantity decision variables. Since the proposed model belongs to NP-hard problems, two Pareto-based approaches based on genetic algorithm is applied to solve the model. At the end, several numerical illustrations are generated to demonstrate the model validity and algorithms performance.
References:
Alaghebandha. M , Hajipour. V. (2013). A soft computing-based approach to optimize queuing inventory control problem, International Journal of Systems Science, http://www. dx.doi.org/10.1080/00207721.2013.809614.
Al Jadaan. O, C.R. Rao, & L. Rajamani. (2008). Non-Dominated ranked genetic algorithm for solving Multi-Objective optimization problems: NRGA. Journal of Theoretical and Applied Information Technology, 60-67.
Berman, O., Kim, E. (1999). Stochastic models for inventory management at service facilities. Stochastic Models 15 (4), 695–718.
Berman, O., Sapna, K.P. (2000). Inventory management at service facilities for systems with arbitrarily distributed service times. Communications in Statistics. Stochastic Models 16 (3–4), 343–360.
Berman, O., Sapna, K.P. (2001). Optimal control of service for facilities holding inventory. Computers & Operations Research 28 (5), 429–441.
Berman, O., Kim, E. (2001). Dynamic order replenishment policy in internet-based supply chains. Mathematical Methods of Operations Research 53 (3), 371–390.
Berman, O., Kim, E. (2004). Dynamic inventory strategies for profit maximization in a service facility with stochastic service, demand and lead time. Mathematical Methods of Operations Research 60 (3), 497–521.
Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. Wiley, Chichester, UK.
Dong. M, Chen. F, (2005). Performance modeling and analysis of integrated logistic chains: An analytic framework. European Journal of Operational Research 162, 83–98.
Haji. R, A. Haji, Saffari. M. (2011). Queueing Inventory System in a Two-level Supply Chain with One-for-One Ordering Policy, Journal of Industrial and Systems Engineering, 5, 52-62.
Haupt. R.L., S.E. Haupt. (2004). Practical genetic algorithms. 2nd Ed, John Wiley & Sons.
Hill. R, 2007, Continuous-review, lost-sales inventory models with Poisson demand, a fixed lead time and no fixed order cost, European Journal of Operational Research, 176, 956–963.
Isotupa. K. (2006). An (s,Q) Markovian inventory system with lost sales and two demand classes”, Mathematical and Computer Modeling, 43, 687–694.
Krishnamoorthy, A., Deepak, T.G., Narayanan, V.C., Vineetha, K. (2006). Effective utilization of idle time in an (s, S) inventory with positive service time. Journal of Applied Mathematics and Stochastic Analysis, 1–13.
Krishnamoorthy, A.,Narayanan, V.C.,Deepak,T.G., Vineetha,P. (2006). Control policies for inventory with service time. Stochastic Analysis and Applications, 24 (4), 889–899.
Krishnamoorthy. A, R. Manikandan, B. Lakshmy. (2013). A revisit to queueing-inventory system with positive service time, Ann Oper Res, DOI 10.1007/s10479-013-1437-x.
Lai. Y.J, Hwang. C.-L. (1992). Fuzzy Mathematical Programming Methods and Applications, Springer–Verlag, Berlin, 203–213.
Manuel, P., Sivakumar, B., Arivarignan, G. (2007). A perishable inventory system with service facilities, MAP arrivals and PH-service times. Journal of Systems Science and Systems Engineering 16 (1), 62–73.
Manuel, P., Sivakumar, B., Arivarignan, G. (2008). A perishable inventory system with service facilities and retrial customers. Computers & Industrial Engineering 54 (3), 484–501.
Saffari. M , S. Asmussen, Rasoul Haji. (2013). The M/M/1 queue with inventory, lost sale, and general lead times, Queueing System 75:65–77.
Schwarz, M., Sauer,C., Daduna,H., Kulik,R. ,Szekli,R. (2006). M/M/1 queueing systems with inventory. Queueing Systems. Theory and Applications, 54(1), 55–78.
Schwarz, M., Daduna, H. (2006).Queueing systems with inventory management with random lead times and with back ordering. Mathematical Methods of Operations Research 64(3), 383–414.
Teimoury. E & M. Modarres & I. G. Khondabi & M. Fathi. (2012). A queuing approach for making decisions about order penetration point in multiechelon supply chains, Int J Adv Manuf Technol.
Zhao. N, Lian. Z. (2011). A queueing-inventory system with two classes of customers, Int. J. Production Economics, 129, 225–231.
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Alaghebandha. M , Hajipour. V. (2013). A soft computing-based approach to optimize queuing inventory control problem, International Journal of Systems Science, http://www. dx.doi.org/10.1080/00207721.2013.809614.
Al Jadaan. O, C.R. Rao, & L. Rajamani. (2008). Non-Dominated ranked genetic algorithm for solving Multi-Objective optimization problems: NRGA. Journal of Theoretical and Applied Information Technology, 60-67.
Berman, O., Kim, E. (1999). Stochastic models for inventory management at service facilities. Stochastic Models 15 (4), 695–718.
Berman, O., Sapna, K.P. (2000). Inventory management at service facilities for systems with arbitrarily distributed service times. Communications in Statistics. Stochastic Models 16 (3–4), 343–360.
Berman, O., Sapna, K.P. (2001). Optimal control of service for facilities holding inventory. Computers & Operations Research 28 (5), 429–441.
Berman, O., Kim, E. (2001). Dynamic order replenishment policy in internet-based supply chains. Mathematical Methods of Operations Research 53 (3), 371–390.
Berman, O., Kim, E. (2004). Dynamic inventory strategies for profit maximization in a service facility with stochastic service, demand and lead time. Mathematical Methods of Operations Research 60 (3), 497–521.
Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. Wiley, Chichester, UK.
Dong. M, Chen. F, (2005). Performance modeling and analysis of integrated logistic chains: An analytic framework. European Journal of Operational Research 162, 83–98.
Haji. R, A. Haji, Saffari. M. (2011). Queueing Inventory System in a Two-level Supply Chain with One-for-One Ordering Policy, Journal of Industrial and Systems Engineering, 5, 52-62.
Haupt. R.L., S.E. Haupt. (2004). Practical genetic algorithms. 2nd Ed, John Wiley & Sons.
Hill. R, 2007, Continuous-review, lost-sales inventory models with Poisson demand, a fixed lead time and no fixed order cost, European Journal of Operational Research, 176, 956–963.
Isotupa. K. (2006). An (s,Q) Markovian inventory system with lost sales and two demand classes”, Mathematical and Computer Modeling, 43, 687–694.
Krishnamoorthy, A., Deepak, T.G., Narayanan, V.C., Vineetha, K. (2006). Effective utilization of idle time in an (s, S) inventory with positive service time. Journal of Applied Mathematics and Stochastic Analysis, 1–13.
Krishnamoorthy, A.,Narayanan, V.C.,Deepak,T.G., Vineetha,P. (2006). Control policies for inventory with service time. Stochastic Analysis and Applications, 24 (4), 889–899.
Krishnamoorthy. A, R. Manikandan, B. Lakshmy. (2013). A revisit to queueing-inventory system with positive service time, Ann Oper Res, DOI 10.1007/s10479-013-1437-x.
Lai. Y.J, Hwang. C.-L. (1992). Fuzzy Mathematical Programming Methods and Applications, Springer–Verlag, Berlin, 203–213.
Manuel, P., Sivakumar, B., Arivarignan, G. (2007). A perishable inventory system with service facilities, MAP arrivals and PH-service times. Journal of Systems Science and Systems Engineering 16 (1), 62–73.
Manuel, P., Sivakumar, B., Arivarignan, G. (2008). A perishable inventory system with service facilities and retrial customers. Computers & Industrial Engineering 54 (3), 484–501.
Saffari. M , S. Asmussen, Rasoul Haji. (2013). The M/M/1 queue with inventory, lost sale, and general lead times, Queueing System 75:65–77.
Schwarz, M., Sauer,C., Daduna,H., Kulik,R. ,Szekli,R. (2006). M/M/1 queueing systems with inventory. Queueing Systems. Theory and Applications, 54(1), 55–78.
Schwarz, M., Daduna, H. (2006).Queueing systems with inventory management with random lead times and with back ordering. Mathematical Methods of Operations Research 64(3), 383–414.
Teimoury. E & M. Modarres & I. G. Khondabi & M. Fathi. (2012). A queuing approach for making decisions about order penetration point in multiechelon supply chains, Int J Adv Manuf Technol.
Zhao. N, Lian. Z. (2011). A queueing-inventory system with two classes of customers, Int. J. Production Economics, 129, 225–231.
