Abstract
Online restaurants, which receive online orders and deliver food directly to the customer’s residence, are becoming increasingly popular. To be successful, online restaurants need to provide reliable and prompt deliveries. Careful design of the meal preparation and order delivery systems is needed to avoid excessive customer waiting time between ordering and delivery. This paper considers the meal preparation and delivery processes simultaneously to approximate average customer waiting time for deliveries. The authors first discuss the system performance with one cook and unit-capacity delivery vehicles, using an M/G/1 queue and a GI/G/1 queue. Numerical experiments show that our approximation can adequately describe real waiting times. Then, series queues with multiple cooks and multi-capacity delivery vehicles, e.g., an M/G/n queue and a GI/Gn/1 queue, are examined. Results show that except for situations with a large meal preparation time and a small vehicle capacity, compared with the result of simulation, the approximation in this paper is acceptable with a deviation of less than 20%. The marginal decrease in waiting time associated with hiring more vehicles is estimated under different meal preparation speeds, sizes of service area and vehicle capacities.
Similar content being viewed by others
References
iiMedia Research China. Online restaurant research report for China in 2017 Q1, 2017, https://doi.org/http://www.iimedia.cn/51210.html.
Yeo V C S, Goh S K, and Rezaei S, Consumer experiences, attitude and behavioral intention toward online food delivery (OFD) services, Journal of Retailing and Consumer Services, 2017, 35, 150–162.
Fancello G, Paddeu D, and Fadda P, Investigating last food mile deliveries: A case study approach to identify needs of food delivery demand, Research in Transportation Economics, 2017, 65: 56–66.
Giannikas E, Using customer-related data to enhance e-grocery home delivery, Industrial Management and Data Systems, 2017, 117(9), 1917–1933.
Siregar B, Gunawan D, Andayani U, et al., Food delivery system with the utilization of vehicle using geographical information system (GIS) and a star algorithm, Journal of Physics Conference Series, 2017, 801, 012038.
Dayama N R and Krishnamoorthy M, Facility location and routing decisions for a food delivery network, IEEE International Conference on Industrial Engineering and Engineering Management, 2016, 94–98.
Jayakumar Nair D, Grzybowska H, Rey D, et al., Food rescue and delivery: Heuristic algorithm for periodic unpaired pickup and delivery vehicle routing problem, Trasportation Research Board, 2016, DOI: 10.3141/2548-10.
Song B D and Ko Y D, A vehicle routing problem of both refrigerated- and general-type vehicles for perishable food products delivery, Journal of Food Engineering, 2016, 169, 61–71.
Deng N and Zhang J, Study on assign mode of O2O takeaway order delivery tasks, Shanghai Management Science, 2018, 40(1): 63–66.
Wang S, Zhao L, and Hu Q, Vehicle routing problem with O2O takeout delivery based on stochastic travel times, Logistics Sci-Tech, 2017, 1: 93–101.
Croes G A, A method for solving traveling-salesman problems, Operations Research, 1958, 6(6): 791–812.
Golden B, Raghavan S, and Wasil E, The Vehicle Routing Problem: Latest Advances and New Challenges, Springer, US, 2008.
Bertsimas D J and Garrett V R, A stochastic and dynamic vehicle routing problem in the Euclidean plane, Operations Research, 1991, 39(4): 603–615.
Bertsimas D J and Ryzin G V, Stochastic and dynamic vehicle routing in the Euclidean plane with multiple capacitated vehicles, Operations Research, 1993, 41(1): 60–76.
Du T C, Li E Y, and Chou D, Dynamic vehicle routing for online B2C delivery, Omega, 2005, 33(1): 33–45.
Molenbruch Y, Braekers K, and Caris A, Typology and literature review for dial-a-ride problems, Annals of Operations Research, 2017, 259(1–2): 295–325.
Santos D O and Xavier E C, Taxi and ride sharing: A dynamic dial-a-ride problem with money as an incentive, Expert Systems with Applications, 2015, 42(19): 6728–6737.
Muelas S, LaTorre A, and Pena J M,. A variable neighborhood search algorithm for the optimization of a dial-a-ride problem in a large city, Expert Systems with Applications, 2013, 40(14): 5516–5531.
Baldacci R, Maniezzo V, and Mingozzi A, An exact method for the car pooling problem based on lagrangean column generation, Operations Research, 2004, 52(3): 422–439.
Teal R F, Carpooling: Who, how and why, Transportation Research Part A: General, 1987, 21(3), 203–214.
Anderson J E, A review of the state of the art of personal rapid transit, Journal of Advanced Transportation, 2000, 34(1): 3–29.
Wang H, Routing and scheduling for a last-mile transportation system, Transportation Science, 2017, DOI: 10.1287/trsc.2017.0753.
Punakivi M, YrjoÉlaÉ H, and HolmstroÉm J, Solving the last mile issue: Reception box or delivery box?, International Journal of Physical Distribution & Logistics Management, 2001, 31(6): 427–439.
Lee H L and Whang S, Winning the last mile of e-commerce, MIT Sloan Management Review, 2001, 42(4): 54–62.
Esper T L, Jensen T D, Turnipseed F L, et al., The last mile: An examination of effects of online retail delivery strategies on consumers, Journal of Business Logistics, 2003, 24(2): 177–203.
Boyer K K, Prud’homme A M, and Chung W, The last mile challenge: Evaluating the effects of customer density and delivery window patterns, Journal of Business Logistics, 2009, 30(1): 185–201.
Song L, Cherrett T, McLeod F, et al., Addressing the last mile problem: Transport impacts of collection and delivery points, Transportation Research Record: Journal of the Transportation Research Board, 2009, 45(2097): 9–18.
Gross D, Fundamentals of Queueing Theory, 4th Ed., John Wiley & Sons, New Jersey, 2008.
Afeche P and Pavlin M, Optimal price-lead time menus for queues with customer choice: Priorities, pooling & strategic delay, Management Science, 2016, 62(1): 2412–2436.
Hayel Y, Quadri D, Jiménez T, et al., Decentralized optimization of last-mile delivery services with non-cooperative bounded rational customers, Annals of Operations Research, 2016, 239(2): 451–469.
Zhou L, Wang X, Ni L, et al., Location-routing problem with simultaneous home delivery and customer’s pickup for city distribution of online shopping purchases, Sustainability, 2016, 8(8): 828–847.
Olbert H, Protopappa-Sieke M, and Thonemann U W, Analyzing the effect of express orders on supply chain costs and delivery times. Production & Operations Management, 2016, 25(12): 2035–2050.
Swihart M R and Papastavrou J D, A stochastic and dynamic model for the single-vehicle pick-up and delivery problem, European Journal of Operational Research, 1999, 114(3): 447–464.
Wang H and Odoni A, Approximating the performance of a “last mile” transportation system, Transportation Science, 2014, 50(2): 659–675.
Alfa A S, Applied Discrete-Time Queues, Springer, New York, 2016.
Whitt W, Approximations for departure processes and queues in series, Naval Research Logistics (NRL), 1984, 31(4): 499–521.
Daley D J, The correlation structure of the output process of some single server queueing systems, The Annals of Mathematical Statistics, 1968, 39(3): 1007–1019.
Makino T, On a study of output distribution, Journal of the Operational Research Society, 1966, 8: 109–133.
Raghavendran C H V, Satish G N, Sundari M R, et al., Tandem communication network model with DBA having non homogeneous Poisson arrivals and feedback for first node, International Journal of Computers and Technology, 2014, 13(9): 621–625.
Wu K and Zhao N, Analysis of dual tandem queues with a finite buffer capacity and nonoverlapping service times and subject to breakdowns, IIE Transactions, 2015, 47(12): 1329–1341.
Wu K, Zhao N, and Lee C K M, Queue time approximations for a cluster tool with job cascading, IEEE Transactions on Automation Science and Engineering, 2016, 13(2): 1200–1206.
Zhou W, Zhang R, and Zhou Y, A queuing model on supply chain with the form postponement strategy, Computers & Industrial Engineering, 2013, 66(4): 643–652.
Lee Y J and Zipkin P, Tandem queues with planned inventories, Operations Research, 1992, 40(5): 936–947.
Kraemer W and Langenbach-Belz M, Approximate formulae for the delay in the queueing system GI/G/1, Proceedings of the 8th International Teletraffic Congress, 1976, 2(3): 2351–2358.
Whitt W, Approximations for the GI/G/m queue, Production & Operations Management, 1993, 2(2): 114–161.
Halfin S and Whitt W, Heavy-Traffic Limits for Queues with Many Exponential Servers, Informs, 1981.
Johnson D S, McGeoch L A, and Rothberg E E, Asymptotic experimental analysis for the Held-CKarp traveling salesman bound, Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, 1996, 341–350.
Beardwood J, Halton J H, and Hammersley J M, The shortest path through many points, Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, 1959, 55(4): 299–327.
Gremlich R, Hamfelt A, and Valkovsky V, Prediction of the optimal decision distribution for the traveling salesman problem, Proceedings of IPSI International Conf., 2004.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by the National Natural Science Foundation of China under Grant No. 71661167009, the Fundamental Research Funds for the Central Universities under Grant No. B17JB00280.
This paper was recommended for publication by Editor WANG Shouyang.
Rights and permissions
About this article
Cite this article
Zhang, T., Zhao, F., Zhang, J. et al. An Approximation of the Customer Waiting Time for Online Restaurants Owning Delivery System. J Syst Sci Complex 32, 907–931 (2019). https://doi.org/10.1007/s11424-018-7316-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-018-7316-4