The Dispatch Problems in Power Distribution Systems

  • M. Schmitz
  • C. H. Barriquello
  • Vinícius Jacques Garcia


Planning the dispatch of distribution systems involves a variety of decision-making problems relating to the service crews and several equipment operations. These problems include the maintenance and repair of a service, through the routing, scheduling and assignment of vehicles and service orders. Also, in addition to the traditional offline dispatch, several technological advances have led to a renewed interest in online dispatch problems. This increases the opportunities for more optimized dispatch, but also raises the complexity of the problem. With a glance toward the power grid, the electric power distribution systems are being hugely transformed toward smart power distribution systems, integrating old and new energy players. In these systems, new energy transactions will become possible, bringing challenging problems to the system operators, in order to balance supply-demand-storage with the coordination among several players, such as smart controllable loads, distributed storage systems, intermittent power generators, reconfigurable networks, communication networks, and so on. Clearly, facing those problems will require a solid mathematical foundation for the understanding and solving of the problems at hand. Therefore, in this chapter, our goal is to introduce the reader to the study of an interesting problem that one could expect to face in the operation of a smart distribution system: the dispatch problem. To this end, along this chapter, we analyze the anatomy of the dispatch problem and study two instances which may be faced in the operation of the power distribution systems: (1) the economic dispatch problem, which deals with the (economic) dispatching of power generators and (2) the service dispatch problem, which deals with the dispatching of working personnel for attending customer, maintenance and emergency orders in the distribution system.


Dispatch Power system Economic Service Generators Assignment Scheduling Routing Operations 


  1. 1.
    Dantzig GB, Ramser JH (1959) The truck dispatching problem. Manag Sci 6:80–91. Scholar
  2. 2.
    Lamorgese L, Mannino C (2013) The track formulation for the train dispatching problem. Electron Notes Discrete Math 41:559–566CrossRefGoogle Scholar
  3. 3.
    Ruokokoski M, Sorsa J, Siikonen M-L, Ehtamo H (2016) Assignment formulation for the elevator dispatching problem with destination control and its performance analysis. Eur J Oper Res 252(2):397–406CrossRefGoogle Scholar
  4. 4.
    Jagtenberg CJ, van den Berg PL, van der Mei RD (2017) Benchmarking online dispatch algorithms for emergency medical services. Eur J Oper Res 258(2):715–725MathSciNetCrossRefGoogle Scholar
  5. 5.
    Burkard RE, Çela E (1999) Linear assignment problems and extensions. Handbook of combinatorial optimization, supplement, vol A. Kluwer, Dordrecht, pp 75–149. Scholar
  6. 6.
    Toth P, Vigo D (2014) Vehicle routing: problems, methods, and applications. Vehicle routing. Second. [S.l.]: MOS-SIAM Series on Optimization.Google Scholar
  7. 7.
    Braekers K, Ramaekers K, Nieuwenhuyse IV (2016) The vehicle routing problem: state of the art classification and review. Comput Ind Eng 99:300–313. Scholar
  8. 8.
    Lawler EL, Lenstra JK, Kan AHGR, Shmoys DB (1993) Chapter 9. Sequencing and scheduling: algorithms and complexity. In: Logistics of production and inventory. [S.l.]: Handbooks in operations research and management science, supplement C. Elsevier, New York, pp 445–522. Scholar
  9. 9.
    Blazewicz J, Schmidt G, Shaw M (2007) Chapter 2. Basics. In: Logistics of production and inventory. [S.l.]. Handbook on scheduling: from theory to applications. Springer, Berlin/Heidelberg, pp 9–56Google Scholar
  10. 10.
    Blazewicz J, Schmidt G, Shaw M (2007) Chapter 3. Definition, analysis and classification of scheduling problems. In: Logistics of production and inventory. [S.l.]. Handbook on scheduling: from theory to applications. Springer, Berlin/Heidelberg, pp 9–56Google Scholar
  11. 11.
    Spliet R, Desaulniers G (2015) The discrete time window assignment vehicle routing problem. Eur J Oper Res 244(2):379–391. Scholar
  12. 12.
    Boonsam P, Suthikarnnarunai N, Chitphaiboon W (2011) Assignment problem and vehicle routing problem for an improvement of cash distribution. Proc World Congr Eng Comput Sci 2:1160–1164Google Scholar
  13. 13.
    Chen H-K, Hsueh C-F, Chang M-S (2009) Production scheduling and vehicle routing with time windows for perishable food products. Comput Oper Res 36(7):2311–2319. Scholar
  14. 14.
    Ullrich CA (2013) Integrated machine scheduling and vehicle routing with time windows. Eur J Oper Res 227(1):152–165. Scholar
  15. 15.
    Desrosiers J, Dumas Y, Solomon MM, Soumis F (1995) Network routing. Handbook in operations research and management science. Chapter time constrained routing and scheduling, 8:35–139. North-Holland, doi: Scholar
  16. 16.
    Chen Z-L, Pundoor G (2006) Order assignment and scheduling in a supply chain. Oper Res 54:555–572. Scholar
  17. 17.
    Mosheiov G, Oron D (2006) Due-date assignment and maintenance activity scheduling problem. Math Comput Model 44:1053–1057. Scholar
  18. 18.
    Hervert-Escobar L, López-Ramos F, Esquivel-Flores OA (2016) Integrated approach to assignment, scheduling and routing problems in a sales territory business plan. Procedia Comput Sci 80:1887–1896, International Conference on Computational Science 2016, ICCS 2016, 6–8, San Diego, CA. Scholar
  19. 19.
    Happ HH (1977) Optimal power dispatch – a comprehensive survey. IEEE Trans Power Apparatus Syst PAS-96(3):841–854CrossRefGoogle Scholar
  20. 20.
    Chowdhury BH, Rahman S A review of recent advances in economic dispatch. IEEE Trans Power Syst 5(4):1248–1259MathSciNetCrossRefGoogle Scholar
  21. 21.
    Ipakchi A, Albuyeh F (2009) Grid of the future. Power Energy Mag 7:52–62CrossRefGoogle Scholar
  22. 22.
    Cheung K, Wang X, Chiu B-C, Xiao Y, Rios-Zalapa R (2010) Generation dispatch in a smart grid environment. Innovative Smart Grid Technologies (ISGT), Gaithersburg, MD, pp 1–6Google Scholar
  23. 23.
    Basu M (2011) Economic environmental dispatch using multi-objective differential evolution. Appl Soft Comput 2(11):2845–2853CrossRefGoogle Scholar
  24. 24.
    Varaiya PP, Wu FF, Bialek JW (2011) Smart operation of smart grid: risk-limiting dispatch. Proc IEEE 99(1):40–57. Scholar
  25. 25.
    Li Q, Gao DW, Zhang H, Wu Z, Wang F-Y (2017) Consensus-based distributed economic dispatch control method in power systems. IEEE Trans Smart Grid PP(99):1. Scholar
  26. 26.
    Liang Y, Liu F, Mei S (2017) Distributed real-time economic dispatch in smart grids: a state-based potential game approach. IEEE Trans Smart Grid PP(99):1. Scholar
  27. 27.
    Ng SKK, Zhong J (2012) Smart dispatch of controllable loads with high penetration of renewables, PES T&D 2012, Orlando, FL, pp. 1–6, doi:
  28. 28.
    Xia X, Elaiw AM (2010) Optimal dynamic economic dispatch of generation: a review. Electr Power Syst Res 80(8):975–986. Scholar
  29. 29.
    Reddy SS, Bijwe PR, Abhyankar AR (2015) Real-time economic dispatch considering renewable power generation variability and uncertainty over scheduling period. IEEE Syst J 9(4):1440–1451. Scholar
  30. 30.
    Zhang Y, Rahbari-Asr N, Chow M-Y (2016) A robust distributed system incremental cost estimation algorithm for smart grid economic dispatch with communications information losses. J Netw Comput Appl 59:315–324. Scholar
  31. 31.
    Kar S, Hug G (2012) Distributed robust economic dispatch in power systems: A consensus + innovations approach. 2012 I.E. Power and Energy Society General Meeting, San Diego, CA, pp. 1–8. doi:
  32. 32.
    Li N, Marden JR (2013) Designing games for distributed optimization. IEEE J Sel Top Signal Process 7(2):230–242. Scholar
  33. 33.
    Schäfer A, Moser A (2012) Dispatch optimization and economic evaluation of distributed generation in a virtual power plant, 2012 I.E. Energytech, Cleveland, OH, pp. 1–6. doi:
  34. 34.
    Li P, Liu Y, Xin H, Jiang X (2017) A robust distributed economic dispatch strategy of virtual power plant under cyber-attacks. IEEE Trans Ind Inf PP(99):1. Scholar
  35. 35.
    Graham RL, Lawler EL, Lenstra JK, Kan AHGR (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. In: Hammer PL, Johnson EL, Korte BH (eds) Discrete optimization II. [S.l.]: Annals of discrete mathematics, supplement C. Elsevier, New York, pp 287–326. Scholar
  36. 36.
    Perrier N et al (2013) A survey of models and algorithms for emergency response logistics in electric distribution systems. Part II: contingency planning level. Comput Oper Res 40(7):1907–1922. Scholar
  37. 37.
    Guha S, Moss A, Naor JS, Schieber B (1999) Efficient recovery from power outage. In: Conference proceedings of the annual ACM symposium on theory of computing. Atlanta. New York, NY: GA: ACM; pp. 574–578. doi:
  38. 38.
    Yao MJ, Min KJ (1998) Repair-unit location models for power failures. IEEE Trans Eng Manag 45:57–65. Scholar
  39. 39.
    Gillett BE, Miller LR (1974) A heuristic algorithm for the vehicle-dispatch problem. Oper Res 21:340–349. Scholar
  40. 40.
    Raff S (1983) Routing and scheduling of vehicles and crews: the state of the art. Comput Oper Res 10(2):63–212. Scholar
  41. 41.
    Miller CE, Tucker AW, Zemlin RA (1960) Integer programming formulations and travelling salesman problems. J Ass Comp Mach 7:326–329. Scholar
  42. 42.
    Bektas T, Gouveia L (2014) Requiem for the Miller–Tucker–Zemlin subtour elimination constraints? Eur J Oper Res 236(3):820–832. Scholar
  43. 43.
    Blazewicz J, Schmidt G, Shaw M (2007) Chapter 7. Scheduling in hard real-time systems. In: Logistics of production and inventory. Handbook on scheduling: from theory to applications. Springer, Berlin/Heidelberg, pp 243–269Google Scholar
  44. 44.
    Zografos KG, Douligeris C, Tsoumpas P (1998) An integrated framework for managing emergency-response logistics: the case of the electric utility companies. IEEE Trans Eng Manag 45(2):115–126. Scholar
  45. 45.
    Garcia VJ et al (2014) Reliability assessment by coordinating maintenance vehicles in electric power distribution systems. Procedia Soc Behav Sci 111:1045–1053. Scholar
  46. 46.
    Psaraftis HN, Wen M, Kontovas CA (2016) Dynamic vehicle routing problems: three decades and counting. Networks 67(1):3–31. Scholar
  47. 47.
    Ichoua S, Gendreau M, Potvin J-Y (2006) Exploiting knowledge about future demands for real-time vehicle dispatching. Transp Sci 40(2):211–225. Scholar
  48. 48.
    Larsen A, Madsen OBG, Solomon MM (2007) Chapter 2. Classification of dynamic vehicle routing systems. In: Zeimpekis V, Tarantilis CD, Giaglis GM, Minis I (eds) Dynamic fleet management, Operations Research/Computer Science Interfaces Series, vol 38. Springer, New York, pp 19–40. Scholar
  49. 49.
    Pillac V, Gendreau M, Guéret C, Medaglia AL (2013) A review of dynamic vehicle routing problems. Eur J Oper Res 225:1–11. Scholar
  50. 50.
    Psaraftis HN (1988) Dynamic vehicle routing. In: Golden BL, Assad AA (eds) Vehicle routing: methods and studies. North-Holland, Amsterdam, pp 223–248. Scholar
  51. 51.
    Bertsekas DP (2012) Dynamic programming and optimal control: approximate dynamic programming, vol II, 4th edn. Athena Scientific, Belmont, MAzbMATHGoogle Scholar
  52. 52.
    Ichoua S, Gendreau M, Potvin J-Y (2007) Chapter 1. Planned route approaches for real-time vehicle routing. In: Zeimpekis V, Tarantilis CD, Giaglis GM, Minis I (eds) Dynamic fleet management: concepts, systems, algorithms and case studies, Operations Research/Computer Science Interfaces Series, vol 38. Springer, New York, pp 1–18. Scholar
  53. 53.
    Larsen A (2001) The dynamic vehicle routing problem, PhD thesis, Technical University of Denmark (DTU)Google Scholar
  54. 54.
    Larsen A, Madsen OBG, Solomon MM (2002) Partially dynamic vehicle routing models and algorithms. J Oper Res Soc 53(6):637–646. Scholar
  55. 55.
    Laporte G (2009) Fifty years of vehicle routing. Transp Sci 43(4):408–416. Scholar
  56. 56.
    Bertsimas D, Simchi-Levi D (1996) A new generation of vehicle routing research: robust algorithms, addressing uncertainty. Oper Res 44:286–304. Scholar
  57. 57.
    Gendreau M, Laporte G, Séguin R (1996) Stochastic vehicle routing. Eur J Oper Res 88:3–12. Scholar
  58. 58.
    Psaraftis HN (1980) A dynamic-programming solution to the single vehicle many-to-many immediate request dial-a-ride problem. Transp Sci 14:130–154. Scholar
  59. 59.
    Ichoua S, Gendreau M, Potvin J-Y (2003) Vehicle dispatching with time-dependent travel times. Eur J Oper Res 144(2):379–396. Scholar
  60. 60.
    Gendreau M, Guertin F, Potvin J-Y, Séguin E (2006) Neighborhood search heuristics for a dynamic vehicle dispatching problem with pick-ups and deliveries. Transport Res Part C: Emerg Technol 14:157–174. Scholar
  61. 61.
    Ferrucci F, Block S, Gendreau M (2013) A pro-active real- time control approach for dynamic vehicle routing problems dealing with the delivery of urgent goods. Eur J Oper Res 225:130–141. Scholar
  62. 62.
    Goodson JC, Jeffrey WO, Thomas BW (2013) Rollout policies for dynamic solutions to the multivehicle routing problem with stochastic demand and duration limits. Oper Res 61:138–154. Scholar
  63. 63.
    Thomas BW, White CCI (2004) Anticipatory route selection. Transp Sci 38:473–487. Scholar
  64. 64.
    Jaillet P, Wagner MR (2008) Generalized online routing: new competitive ratios, resource augmentation, and asymptotic analyses. Oper Res 56(3):745–757. Scholar
  65. 65.
    Arab A, Khodaei A, Khator SK, Han Z (2016) Electric power grid restoration considering disaster economics. IEEE Access 4:639–649. Scholar
  66. 66.
    Nurre SG et al (2012) Restoring infrastructure systems: an integrated network design and scheduling (INDS) problem. Eur J Oper Res 223(3):794–806. Scholar
  67. 67.
    Hentenryck PV, Coffrin C, Bent R (2011) Vehicle Routing for the Last Mile of Power System Restoration. 17th Power Systems Computation Conference, v. 836Google Scholar
  68. 68.
    Simon B, Coffrin C, Hentenryck PV (2012) Chapter 25. Randomized adaptive vehicle decomposition for large-scale power restoration, computer science. In: Integration of AI and OR techniques in contraint programming for combinatorial optimzation problems. Springer, Berlin/Heidelberg, pp 379–394. Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • M. Schmitz
    • 1
  • C. H. Barriquello
    • 1
  • Vinícius Jacques Garcia
    • 1
  1. 1.Technology CenterFederal University of Santa MariaSanta MariaBrazil

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