Vehicle Routing and Scheduling Problem for a multi-period, multi-perishable product system with time window: A Case study

[EN] The well-known Vehicle Routing Problem (VRP) is to find proper sequence of routes in order to minimize transportation costs. In this paper, a mixed-integer programming model is presented for a food distributer company and the model outputs are to determine the optimal routes and amount of pickup and delivery. In the objective function, the costs of transportation, holding, tardiness and earliness are considered simultaneously. The proposed model with respect to real conditions is multi-period and has two different time periods: one for dispatching vehicles to customers and suppliers and the other for receiving customers’ orders. Time window and split pickup and delivery are considered for perishable products. The proposed model is nonlinear and will be linearized using exact techniques. At the end, model is solved using GAMS and the sensitivity analysis is performed. The results indicate that the trend of changes in holding and transportation costs in compared to tardiness and earliness costs are closed together and are not so sensitive to demand changes.Rashidi Komijan, A.; Delavari, D. (2017). Vehicle Routing and Scheduling Problem for a multi-period, multi-perishable product system with time window: A Case study. International Journal of Production Management and Engineering. 5(2):45-53. doi:10.4995/ijpme.2017.5960SWORD455352DENG, A., MAO, C., & ZHOU, Y. (2009). Optimizing Research of an Improved Simulated Annealing Algorithm to Soft Time Windows Vehicle Routing Problem with Pick-up and Delivery. Systems Engineering - Theory & Practice, 29(5), 186-192. doi:10.1016/s1874-8651(10)60049-xAndersson, H., Hoff, A., Christiansen, M., Hasle, G., & Løkketangen, A. (2010). Industrial aspects and literature survey: Combined inventory management and routing. Computers & Operations Research, 37(9), 1515-1536. doi:10.1016/j.cor.2009.11.009Baldacci, R., Mingozzi, A., & Roberti, R. (2012). Recent exact algorithms for solving the vehicle routing problem under capacity and time window constraints. European Journal of Operational Research, 218(1), 1-6. doi:10.1016/j.ejor.2011.07.037Belfiore, P., & Yoshizaki, H. T. Y. (2013). Heuristic methods for the fleet size and mix vehicle routing problem with time windows and split deliveries. Computers & Industrial Engineering, 64(2), 589-601. doi:10.1016/j.cie.2012.11.007Cacchiani, V., Hemmelmayr, V.C., Tricoire, F., (2012). A set-covering based heuristic algorithm for the periodic vehicle routing problem. Discrete Applied Mathematics, 163(1), 53-64. https://doi.org/10.1016/j.dam.2012.08.032Cattaruzza, D., Absi, N., Feillet, D., & Vidal, T. (2014). A memetic algorithm for the Multi Trip Vehicle Routing Problem. European Journal of Operational Research, 236(3), 833-848. doi:10.1016/j.ejor.2013.06.012Çetinkaya, C., Karaoglan, I., & Gökçen, H. (2013). Two-stage vehicle routing problem with arc time windows: A mixed integer programming formulation and a heuristic approach. European Journal of Operational Research, 230(3), 539-550. doi:10.1016/j.ejor.2013.05.001Eksioglu, B., Vural, A. V., & Reisman, A. (2009). The vehicle routing problem: A taxonomic review. Computers & Industrial Engineering, 57(4), 1472-1483. doi:10.1016/j.cie.2009.05.009Hasani-Goodarzi, A., & Tavakkoli-Moghaddam, R. (2012). Capacitated Vehicle Routing Problem for Multi-Product Cross- Docking with Split Deliveries and Pickups. Procedia - Social and Behavioral Sciences, 62, 1360-1365. doi:10.1016/j.sbspro.2012.09.232Rahimi-Vahed, A., Gabriel Crainic, T., Gendreau, M., & Rei, W. (2015). Fleet-sizing for multi-depot and periodic vehicle routing problems using a modular heuristic algorithm. Computers & Operations Research, 53, 9-23. doi:10.1016/j.cor.2014.07.004Shahin Moghadam, S., Fatemi Ghomi, S. M. T., & Karimi, B. (2014). Vehicle routing scheduling problem with cross docking and split deliveries. Computers & Chemical Engineering, 69, 98-107. doi:10.1016/j.compchemeng.2014.06.015Silva, M. M., Subramanian, A., & Ochi, L. S. (2015). An iterated local search heuristic for the split delivery vehicle routing problem. Computers & Operations Research, 53, 234-249. doi:10.1016/j.cor.2014.08.005Taş, D., Jabali, O., & Van Woensel, T. (2014). A Vehicle Routing Problem with Flexible Time Windows. Computers & Operations Research, 52, 39-54. doi:10.1016/j.cor.2014.07.005Yu, B., & Yang, Z. Z. (2011). An ant colony optimization model: The period vehicle routing problem with time windows. Transportation Research Part E: Logistics and Transportation Review, 47(2), 166-181. doi:10.1016/j.tre.2010.09.010Zhang, S., Lee, C. K. M., Choy, K. L., Ho, W., & Ip, W. H. (2014). Design and development of a hybrid artificial bee colony algorithm for the environmental vehicle routing problem. Transportation Research Part D: Transport and Environment, 31, 85-99. doi:10.1016/j.trd.2014.05.01

Un modelo integrado para el enrutamiento de aeronaves y la programación de la tripulación: Relajación lagrangiana y algoritmo metaheurístico

[EN] Airline optimization is a significant problem in recent researches and airline industryl as it can determine the level of service, profit and competition status of the airline. Aircraft and crew are expensive resources that need efficient utilization. This paper focuses simultaneously on two major issues including aircraft maintenance routing and crew scheduling. Several key issues such as aircraft replacement, fairly night flights assignment and long-life aircrafts are considered in this model. We used the flight hours as a new framework to control aircraft maintenance. At first, an integrated mathematical model for aircraft routing and crew scheduling problems is developed with the aim of cost minimization. Then, Lagrangian relaxation and Particle Swarm Optimization algorithm (PSO) are used as the solution techniques. To evaluate the efficiency of solution approaches, model is solved with different numerical examples in small, medium and large sizes and compared with GAMS output. The results show that Lagrangian relaxation method provides better solutions comparing to PSO and also has a very small gap to optimum solution.[ES] La optimización de aerolíneas es un problema importante en investigaciones recientes e industria de aerolíneas, ya que puede determinar el nivel de servicio, el beneficio y el estado de competencia de la aerolínea. Las aeronaves y la tripulación son recursos costosos que necesitan una utilización eficiente. Este artículo se centra simultáneamente en dos cuestiones principales, incluyendo el enrutamiento de mantenimiento de aeronaves y la programación de la tripulación. En este modelo se consideran varios temas clave, como el reemplazo de aeronaves, la asignación de vuelos nocturnos y los aviones envejecidos. Usamos las horas de vuelo como un nuevo marco para controlar el mantenimiento de las aeronaves. Al principio, se desarrolla un modelo matemático integrado para el enrutamiento de aeronaves y los problemas de programación de la tripulación con el objetivo de la minimización de costos. A continuación, se utilizan como técnicas de solución la relajación lagran-giana y el algoritmo “Particle Swarm Optimization” (PSO). Para evaluar la eficiencia de los en-foques de la solución, el modelo se resuelve con diferentes ejemplos numéricos en tamaños pequeños, medianos y grandes y se compara con la salida GAMS. Los resultados muestran que el método de relajación lagrangiana proporciona mejores soluciones en comparación con PSO y también tiene una pequeña diferencia para una solución óptimaMirjafari, M.; Rashidi Komijan, A.; Shoja, A. (2020). An integrated model for aircraft routing and crew scheduling: Lagrangian Relaxation and metaheuristic algorithm. WPOM-Working Papers on Operations Management. 11(1):25-38. https://doi.org/10.4995/wpom.v11i1.12891OJS2538111Al-Thani, Nayla Ahmad, Ben Ahmed, Mohamed and Haouari, Mohamed (2016). A model and optimization-based heuristic for the operational aircraft maintenance routing problem, Transportation Research Part C: Emerging Technologies, Volume 72, Pages 29-44. https://doi.org/10.1016/j.trc.2016.09.004Azadeh, A., HosseinabadiFarahani, M., Eivazy, H., Nazari-Shirkouhi, S., &Asadipour, G. (2013). A hybrid meta-heuristic algorithm for optimization of crew scheduling, Applied Soft Computing, Volume 13, Pages 158-164. https://doi.org/10.1016/j.asoc.2012.08.012Barnhart C. and Cohn, A. (2004). Airline schedule planning: Accomplishments and opportunities, Manufacturing & Service Operations Management, 6(1):3-22, 47, 69, 141, 144. https://doi.org/10.1287/msom.1030.0018Basdere, Mehmet and Bilge, Umit (2014). Operational aircraft maintenance routing problem with remaining time consideration, European Journal of Operational Research, Volume 235, Pages 315-328. https://doi.org/10.1016/j.ejor.2013.10.066Bazargan, Massoud (2010). Airline Operations and scheduling second edition, Embry-Riddle Aeronautical University, USA, Ashgate publishing limite.Belien, Jeroen, Demeulemeester, Eric and Brecht (2010). Integrated staffing and scheduling for an aircraft line maintenance problem, HUB RESEARCH PAPER Economics & Management.Ben Ahmed, M., Zeghal Mansour, Farah and Haouari, Mohamed (2018). Robust integrated maintenance aircraft routing and crew pairing, Journal of Air Transport Management, Volume 73, Pages 15-31. https://doi.org/10.1016/j.jairtraman.2018.07.007Ben Ahmed, M., Zeghal Mansour, F., Haouari, M. (2017). A two-level optimization approach for robust aircraft routing and retiming, Computers and Industrial Engineering, Volume 112, Pages 586-594. https://doi.org/10.1016/j.cie.2016.09.021Borndorfer, R., Schelten, U., Schlechte, T., Weider, S. (2006). A column generation approach to airline crew scheduling, Springer Berlin Heidelberg, Pages 343-348. https://doi.org/10.1007/3-540-32539-5_54Clarke, L., E. Johnson, G. Nemhauser, Z. Zhu. (1997). The Aircraft Rotation Problem. Annals of Operations Research, 69, Pages 33-46. https://doi.org/10.1023/A:1018945415148Deveci, Muhammet and ÇetinDemirel, Nihan (2018). Evolutionary algorithms for solving the airline crew pairing problem, Computers & Industrial Engineering, Volume 115, Pages 389-406. https://doi.org/10.1016/j.cie.2017.11.022Dozic, S., Kalic, M. (2015). Three-stage airline fleet planning model, J. Air Transport. Manag, 43, Pages 30-39. https://doi.org/10.1016/j.jairtraman.2015.03.011Eltoukhy, A.E., Chan, F.T., Chung, S. (2017). Airline schedule planning: a review and future directions, Ind. Manag. Data Syst, 117(6), Pages 1201-1243. https://doi.org/10.1108/IMDS-09-2016-0358Feo, T. A., J. F. Bard. (1989). Flight Scheduling and Maintenance Base Planning. Management Science, 35(12), Pages 1415-1432. https://doi.org/10.1287/mnsc.35.12.1415Goffin, J. L. (1977). On the convergence rates of subgradient optimization methods. Math. Programming, 13, Pages 329-347. https://doi.org/10.1007/BF01584346Gopalakrishnan, B., Johnson, E. L (2005). Airline crew scheduling, State-of-the-art. Ann. Oper. Res, 140(1), Pages 305-337. https://doi.org/10.1007/s10479-005-3975-3Held, M. and Karp, R.M. (1970). The Traveling-Salesman Problem and Minimum SpanningTrees. Operations Research, 18, 1138-1162. https://doi.org/10.1287/opre.18.6.1138Held, M. Wolfe, P., Crowder, H. D. (1974). Validation of subgradient optimization, Math. Programming, 6, 62-88. https://doi.org/10.1007/BF01580223Jamili, Amin (2017). A robust mathematical model and heuristic algorithms for integrated aircraft routing and scheduling, with consideration of fleet assignment problem, Journal of Air Transport Management, Volume 58, Pages 21-30. https://doi.org/10.1016/j.jairtraman.2016.08.008Jiang, H., Barnhart, C. (2009) Dynamic airline scheduling, Transport. Sci, 43(3), Pages 336-354. https://doi.org/10.1287/trsc.1090.0269Kasirzadeh, A., Saddoune, M., Soumis, F. (2015). Airline crew scheduling: models, algorhitms and data sets, Euro Journal on Transportation and Logistics, 6(2), Pages 111-137. https://doi.org/10.1007/s13676-015-0080-xLacasse-Guay, E., Desaulniers, G., Soumis, F. (2010). Aircraft routing under different business processes, J. Air Transport. Manag, 16(5), Pages 258-263. https://doi.org/10.1016/j.jairtraman.2010.02.001Muter, İbrahim, Birbil, Ş. İlker, Bülbül, Kerem, Şahin, Güvenç,Yenigün, Hüsnü, Taş,Duygu andTüzün, Dilek (2013). Solving a robust airline crew pairing problem with column generation, Computers & Operations Research, Volume 40, Issue 3, Pages 815-830. https://doi.org/10.1016/j.cor.2010.11.005Saddoune, Mohammed, Desaulniers, Guy, Elhallaoui, Issmail and François Soumis (2011). Integrated airline crew scheduling: A bi-dynamic constraint aggregation method using neighborhoods, European Journal of Operational Research, Volume 212, Pages 445-454. https://doi.org/10.1016/j.ejor.2011.02.009Safaei, Nima and K.S.Jardine, Andrew (2018). Aircraft routing with generalized maintenance constraints, Omega, Volume 80, Pages 111-122. https://doi.org/10.1016/j.omega.2017.08.013Shao Shengzhi (2012). Integrated Aircraft Fleeting, Routing, and Crew Pairing Models and Algorithms for the Airline Industry, Faculty of the Virginia Polytechnic Institute and State University In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Industrial and Systems Engineering.Shao, S., Sherali, H.D., Haouari, M. (2017). A novel model and decomposition approach for the integrated airline fleet assignment, aircraft routing, crew pairing problem, Transport. Sci, 51(1), Pages 233-249. https://doi.org/10.1287/trsc.2015.0623Sherali, H.D., Bish, E.K., Zhu, X. (2006). Airline fleet assignment concepts, models and algorithms, Eur. J. Oper. Res, 172(1), Pages 1-30. https://doi.org/10.1016/j.ejor.2005.01.056Warburg, V., Hansen, T.G., Larsen, A., Norman, H., Andersson, E. (2008). Dynamic airline scheduling: an analysis of potentials of refleeting and retiming, J. Air Transport. Manag. 14(4), Pages 163-167. https://doi.org/10.1016/j.jairtraman.2008.03.004Yan, C. and Kung, J. (2018). 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An integrated mathematical model for aircraft routing and crew scheduling for airlines with multi fleet and multi maintenance hub

The problem of Airline planning has totally been divided into four sub-problems.These problems include Flight Scheduling, Fleet Assignment, Aircraft Routing, Maintenance, and Crew Scheduling. In this research, firstly, we defined basic concepts and common terminology about Airline Planning then early models and previous researchers were presenting investigated articles. Moreover, by identifying existing research gaps, an Integrated Mathematical model presented for Aircraft Routing and Crew Scheduling for Airlines with Multi Fleet and Multi Maintenance hub with considering the rules of the Airlines. The main purpose of the proposed model is to determine the flight chains for each aircraft and crew assignments to all aircrafts with the attention to the airlines rules and regulations for aircrafts and crew. In the integrated models by previous researcher in this field, usually the type of fleet is considered the same while in the model presented in this research, the type of fleet is considered different. Other innovations of this research consider several maintenance units for an airline. In addition, the minimizations of deadheading flights for crew and aircraft that can impose heavy costs to the airline is presented as a part of the objective function in the model presented. Finally, the problem has been solved into small dimensions by GAMS software and in order to solve it in the larger dimensions a meta-heuristic method is being used, such as genetics algorithm. At the end, we have presented the results, which came from meta-heuristic Algorithm and GAMS Software

Food production in batch manufacturing systems with multiple shared-common resources: A scheduling model and its application in the yoghurt industry

The industry-specific characteristics of food-processing make production scheduling a hard and complex issue. Food processing has involved relatively minor concerns in several scheduling researches. In this paper, the authors address the integrated lot sizing and scheduling problem in batch production systems and propose a new mixed integer linear programming (MILP) formulation with multiple objective functions. The considered production system contains semi-continues flow lines with series-parallel machines fed by parallel shared common resources. The model has been numerically and empirically validated using six weekly demand plan of a dairy company. The results demonstrate that both the operational cost and total completion time has been optimised