Using regression models to understand the impact of route-length variability in practical vehicle routing

Roy, Debdatta Sinha; Golden, Bruce L.; Masone, Adriano; Wasil, Edward

doi:10.1007/s11590-022-01883-9

Cited by 5 publications

(4 citation statements)

References 19 publications

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“…Lastly, it would be interesting to incorporate the schedule disruption possibilities in the planning phase to make it more robust. As shown in the context of vehicle routing problem by Sinha Roy et al [48], the optimal solution of 'planning' may not necessarily be best under the real-life disruptions. Similarly, in the context of our problem while the via-routing of aircraft has an important revenue impact in the objective function, a practical limitation of having via-passengers is that it hampers the flexibility of the airline operations control center to dynamically change aircraft routing if the first flight of a via-itinerary is delayed or disrupted.…”

Section: Discussionmentioning

confidence: 99%

Integrated commercial and operations planning model for schedule design, aircraft rotation and crew scheduling in airlines

Garg,

Agarwal,

Srivastava

et al. 2024

Networks

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The commercial and operations planning in airlines has traditionally been a hierarchical process starting with flight schedule design, followed by fleet assignment, aircraft rotation planning and finally the crew scheduling. The hierarchical planning approach has a drawback that the optimal solution for a planning phase higher in hierarchy may either be infeasible for the subsequent phase or may lead to a sub‐optimal overall solution. In this paper, we solve a profit‐maximizing integrated planning model for clean‐sheet “rotated” schedule design with flight re‐time option and crew scheduling for a low‐cost carrier (LCC) in an emerging market. While the aircraft rotation problem has been traditionally modeled in the literature as a daily routing of individual aircraft for maintenance requirement, in this work we address the requirement of planned aircraft rotations as part of schedule design for LCCs. The planned aircraft routing is important in our case to create as many via‐flights as possible due to the underserved nature of the emerging market. We solve this large‐scale integer‐programming problem using two approaches – Benders Decomposition and Lagrangian Relaxation. For Lagrangian Relaxation, we exploit the special structure of our problem and intuitive understanding behind the Lagrangian duals to develop a multiplier adjustment approach to find an improved lower bound of integrated model solution. The crew‐pairing sub‐problem is solved using column generation through multi‐label shortest path algorithm followed by branch‐and‐price for integer solution. We test our solution methodology on a flight universe of 378 unique flights for different problem sizes by varying the number of aircraft available for operations. Our computational results show that within a reasonable run time of few hours both the approaches, Benders Decomposition and Lagrangian Relaxation, are successful in finding lower bounds of the integrated model solution, which are higher than the solution of traditional hierarchical approach by 0.5%–2.5%. We find Lagrangian Relaxation methodology to usually attain an improved solution faster than the Benders Decomposition approach, particularly for large‐scale problems.

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Section: Discussionmentioning

confidence: 99%

Integrated commercial and operations planning model for schedule design, aircraft rotation and crew scheduling in airlines

Garg,

Agarwal,

Srivastava

et al. 2024

Networks

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show abstract

“…Instead of strictly considering the three best savings probabilistically as in Sinha Roy et al. (2022), we consider either the three, four, or five best savings with equal probability when generating feasible VRP solutions using the modified Clarke and Wright algorithm. In addition and as in Sinha Roy et al.…”

Section: Mean and Standard Deviation For The Vrpmentioning

confidence: 99%

“…In addition and as in Sinha Roy et al. (2022), we apply Yellow's parameter in the calculation of savings. Let

mean_{CWi}

and

std_{CWi}

represent the mean and standard deviation in 1000 distances output by the modified Clarke and Wright algorithm when considering the best

i

savings, and then we can see how the mean and standard deviation work in predicting the optimal distance for the VRP, which is denoted by

D

.…”

Section: Mean and Standard Deviation For The Vrpmentioning

confidence: 99%

See 1 more Smart Citation

Estimating optimal objective values for the TSP, VRP, and other combinatorial problems using randomization

Kou

Golden

Poikonen

2023

Int Trans Operational Res

Self Cite

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Approximation of the optimal tour length in a Euclidean traveling salesman problem (TSP) has been studied by many researchers. In a previous study, we used the standard deviation in random tour lengths to approximate the optimal tour length in both Euclidean and non‐Euclidean TSPs and we obtained good estimates. In this paper, we show that the strong power‐law relationship between the standard deviation in random feasible solution values and the optimal solution value also holds for other Euclidean and near‐Euclidean combinatorial optimization problems like the minimum spanning tree (MST) and maximum weight matching (MWM) problems. We then enhance the estimation ability of the model by considering a second predictor: the mean in random feasible solution values. Experimental results show that by using the mean, standard deviation, and randomization, we can accurately predict the optimal solution values for the TSP, MST, MWM, and the capacitated vehicle routing problem (VRP).

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An improved model for estimating optimal VRP solution values

Kou,

Golden,

Bertazzi

2023

Optim Lett

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Using regression models to understand the impact of route-length variability in practical vehicle routing

Cited by 5 publications

References 19 publications

Integrated commercial and operations planning model for schedule design, aircraft rotation and crew scheduling in airlines

Integrated commercial and operations planning model for schedule design, aircraft rotation and crew scheduling in airlines

Estimating optimal objective values for the TSP, VRP, and other combinatorial problems using randomization

An improved model for estimating optimal VRP solution values

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