We suppose that a vehicle visits N ordered customers in order to collect from them two similar but not identical materials. The actual quantity and the actual type of material that each customer possesses become known only when the vehicle arrives at the customer’s location. It is assumed that the vehicle has two compartments. We name these compartments, Compartment 1 and Compartment 2. It is assumed that Compartment 1 is suitable for loading Material 1 and Compartment 2 is suitable for loading Material 2. However it is permitted to load items of Material 1 into Compartment 2 and items of Material 2 into Compartment 1. These actions cause extra costs that are due to extra labor. It is permissible for the vehicle to interrupt its route and go to the depot to unload the items of both materials. The costs for travelling from each customer to the next one and the costs for travelling from each customer to the depot are known. The objective is to find the routing strategy that minimizes the total expected cost among all possible strategies for servicing all customers. A dynamic programming algorithm is designed for the determination of the routing strategy that minimizes the total expected cost among all possible strategies. The structure of optimal routing strategy is characterized by a set of critical numbers for each customer.
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Clarke G, Wright JR (1964) Scheduling of vehicle routing problem from a central depot to a number of delivery points. Oper Res 12:568–581
Dantzig G, Ramser R (1959) The truck dispatching problem. Manage Sci 6:80–91
Dimitrakos TD, Kyriakidis EG (2015) A single vehicle routing problem with pickups and deliveries, continuous random demands and predefined customer order. Eur J Oper Res 244:990–993
Elgesem AS, Skogen ES, Wang X, Fagerholt K (2018) A traveling salesman problem with pickups and deliveries and stochastic travel times: An application from chemical shipping. Eur J Oper Res 269:844–859
Gendreau M, Laporte G, Seguin R (1996) Stochastic vehicle routing. Eur J Oper Res 88:3–12
Haugland D, Ho SC, Laporte G (2007) Designing delivery districts for the vehicle routing problem with stochastic demands. Eur J Oper Res 180:997–1010
Kyriakidis EG, Dimitrakos TD (2008) Single vehicle routing problem with a predefined customer sequence and stochastic continuous demands. Math Sci 33:148–152
Kyriakidis EG, Dimitrakos TD (2013) A vehicle routing problem with a predefined customer sequence, stochastic demands and penalties for unsatisfied demands. Proceedings of 5th International Conference on Applied Operational Research Lect Notes Manage Sci 5:10–17
Kyriakidis EG, Dimitrakos TD, Karamatsoukis CC (2019) Optimal delivery of two similar products to N ordered customers with product preferences. Int J Prod Econ 209:194–204
Markov I, Bierlaire M, Cordeau JF, Maknoon Y, Varone S (2020) Waste collection inventory routing with non-stationary stochastic demands. Comput Oper Res 113:Article number 104798
Minis I, Tatarakis A (2011) Stochastic single vehicle routing problem with delivery and pickup and a predefined customer sequence. Eur J Oper Res 213:37–51
Nguyen VA, Jiang J, Ng KM, Teo KM (2016) Satisfying measure approach for vehicle routing problem with time windows under uncertainty. Eur J Oper Res 248:404–414
Pandelis DG, Kyriakidis EG, Dimitrakos TD (2012) Single vehicle routing problems with a predefined customer sequence, compartmentalized load and stochastic demands. Eur J Oper Res 217:324–332
Pandelis DG, Karamatsoukis CC, Kyriakidis EG (2013a) Single vehicle routing problems with a predefined customer order, unified load and stochastic discrete demands. Probab Eng Inf Sci 27(1):1–23
Pandelis DG, Karamatsoukis CC, Kyriakidis EG (2013b) Finite and infinite-horizon single vehicle routing problems with a predefined customer sequence and pickup and delivery. Eur J Oper Res 231:577–586
Pillac V, Gendreau M, Gueret C, Megaglia A (2013) A review of dynamic vehicle routing problems. Eur J Oper Res 225:1–11
Psaraftis HN, Wen M, Kontovas CA (2016) Dynamic vehicle routing problems: Three decades and counting. Networks 67:3–31
Ritzinger U, Puchinger J, Richard HF (2016) A survey on dynamic and stochastic vehicle routing problems. Int J Prod Res 54(1):215–231
Sipser M (2013) Introduction to the theory of computation, 3rd edn. Cengage Learning, Boston
Tatarakis A, Minis I (2009) Stochastic single vehicle routing with a predefined customer sequence and multiple depot returns. Eur J Oper Res 197:557–571
Toth P, Vigo D (eds) (2014) The vehicle routing problem. Problems, methods and applications, 2nd edn. MOS-SIAM, Philadelphia
Tsirimpas P, Tatarakis A, Minis I, Kyriakidis EG (2008) Single vehicle routing with a predefined customer sequence and multiple depot returns. Eur J Oper Res 187:483–495
Yang W-H, Mathur K, Ballou RH (2000) Stochastic vehicle routing problem with restocking. Transport Sci 34:99–112
Zhang J, Lam WHK, Chen BY (2016) On-time delivery probabilistic models for the vehicle routing problem with stochastic demands and time windows. Eur J Oper Res 249:144–154
The authors would like to thank a reviewer for useful suggestions that improved the presentation of the paper. The author Epaminondas G. Kyriakidis has been financed by the research program EP-3042-01 (RC/AUEB).
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Kyriakidis, E.G., Dimitrakos, T.D. & Karamatsoukis, C.C. A Stochastic Single Vehicle Routing Problem with a Predefined Sequence of Customers and Collection of Two Similar Materials. Methodol Comput Appl Probab (2020). https://doi.org/10.1007/s11009-019-09759-9
- Stochastic dynamic programming
- Vehicle routing problem
Mathematics Subject Classification (2010)
- Primary 90C39
- Secondary 90B06