Integrated Vehicle Routing and Service Scheduling Under Time and Cancellation Uncertainties with Application in Nonemergency Medical Transportation

2021 ◽  
Author(s):  
Xian Yu ◽  
Siqian Shen ◽  
Huizhu Wang
Keyword(s):  
Vehicle Routing ◽  
Census Data ◽  
Integer Program ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Penalty Cost ◽  
Service Scheduling ◽  
Trip Time ◽  
Out Of Sample ◽  
Delivery Services

In this paper, we consider an integrated vehicle routing and service scheduling problem for serving customers in distributed locations who need pick-up, drop-off, or delivery services. We take into account the random trip time, nonnegligible service time, and possible customer cancellations, under which an ill-designed schedule may lead to undesirable vehicle idleness and customer waiting. We build a stochastic mixed-integer program to minimize the operational cost plus expected penalty cost of customers’ waiting time, vehicles’ idleness, and overtime. Furthermore, to handle real-time arrived service requests, we develop K-means clustering-based algorithms to dynamically update planned routes and schedules. The algorithms assign customers to vehicles based on similarities and then plan schedules on each vehicle separately. We conduct numerical experiments based on diverse instances generated from census data and data from the Ford Motor Company’s GoRide service, to evaluate result sensitivity and to compare the in-sample and out-of-sample performance of different approaches. Managerial insights are provided using numerical results based on different parameter choices and uncertainty settings.

scholarly journals Coordination and Optimization: The Integrated Supply Chain Analysis with Non-Linear Price-Sensitive Demand

2011 ◽  
Vol 2 (1) ◽  
pp. 83-94
Author(s):  
Mohammed Forhad UDDIN ◽  
Kazushi SANO
Keyword(s):  
Supply Chain ◽  
Demand Function ◽  
Integer Program ◽  
Coordination Mechanism ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Selling Price ◽  
Penalty Cost ◽  
Non Linear ◽  
Integrated Supply Chain

In this work, a supply chain with coordination mechanism consisting single vendor and buyer is considered. Further, instead of price sensitive linear or deterministic demand function, a price-sensitive non-linear demand function is introduced in this paper. To find the inventory cost, penalty cost and transportation cost, it is considered that the production and shipping functions of vendor are continuously harmonized and occur at the same rate. In this integrated supply chain, the Buyer’s Linear Program (LP), vendor’s Integer Program (IP) and coordinated Mixed Integer Program (MIP) models are formulated. Numerical examples presented in this research, which include the sensitivity of the key parameters to illustrate the models.  The solution procedures demonstrate that the individual profit as well as joint profit could be increased by coordination mechanism even though the demand function is non-linear. In addition, the results illustrate that Buyer’s selling price with consumers purchasing price could be decreased which may increase the demand of the end market. Finally, a conclusion is drawn in favor of the coordinated supply chain with non-linear price sensitive demand function.  

Intraroute Resource Replenishment with Mobile Depots

2021 ◽  
Author(s):  
Julian Hof ◽  
Michael Schneider
Keyword(s):  
Vehicle Routing ◽  
Distribution Systems ◽  
Time Windows ◽  
Computation Time ◽  
Integer Program ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Mixed Integer Program ◽  
Routing Problem ◽  
Commercial Solver

In numerous practical vehicle-routing applications, larger vehicles are employed as mobile depots to support a fleet of smaller vehicles that perform certain tasks. The mobile depots offer the possibility of keeping the task vehicles operational by supplying them en route with certain resources. For example, in two-echelon distribution systems, small task vehicles are used to navigate narrow streets and to deliver/collect goods or to collect waste, and larger vehicles serve as mobile depots to replenish the goods to be delivered or to receive collected goods or waste at the outskirts of the urban area. Accessibility constraints may also be imposed by regulations on emissions, which make some areas only accessible for environmentally friendly vehicles such as, for example, battery-powered electric vehicles. Especially if the respective refueling infrastructure is sparse, mobile refueling stations seem to be an interesting alternative. In this paper, we introduce the vehicle-routing problem with time windows and mobile depots (VRPTWMD) to capture the routing decisions of the described applications in a generalized fashion. The VRPTWMD is characterized by fleets of task vehicles (TVs) and support vehicles (SVs). The SVs may serve as mobile depots to restore either the load or the fuel capacity of the TVs that are used to fulfill the customer requests. We present a mixed-integer program for the VRPTWMD with which small instances can be solved using a commercial solver. Moreover, we develop a high-quality hybrid heuristic composed of an adaptive large neighborhood search and a path relinking approach to provide solutions on larger problem instances. We use a newly generated set of large VRPTWMD instances to analyze the effect of different problem characteristics on the structure of the identified solutions. In addition, our approach shows very convincing performance on benchmark instances for the related two-echelon multiple-trip VRP with satellite synchronization, which can be viewed as a special case of the VRPTWMD. Our heuristic is able to significantly improve a large part of the previous best-known solutions while spending notably less computation time than the comparison algorithm from the literature.

A stochastic mixed integer program to model spatial wildfire behavior and suppression placement decisions with uncertain weather

2016 ◽  
Vol 46 (2) ◽  
pp. 234-248 ◽  
Author(s):  
Erin J. Belval ◽  
Yu Wei ◽  
Michael Bevers
Keyword(s):  
Wildland Fire ◽  
Fire Behavior ◽  
Integer Program ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Weather Forecasts ◽  
Placement Decisions ◽  
Weather Events ◽  
Weather Changes ◽  
Nonanticipativity Constraints

Wildfire behavior is a complex and stochastic phenomenon that can present unique tactical management challenges. This paper investigates a multistage stochastic mixed integer program with full recourse to model spatially explicit fire behavior and to select suppression locations for a wildland fire. Simplified suppression decisions take the form of “suppression nodes”, which are placed on a raster landscape for multiple decision stages. Weather scenarios are used to represent a distribution of probable changes in fire behavior in response to random weather changes, modeled using probabilistic weather trees. Multistage suppression decisions and fire behavior respond to these weather events and to each other. Nonanticipativity constraints ensure that suppression decisions account for uncertainty in weather forecasts. Test cases for this model provide examples of fire behavior interacting with suppression to achieve a minimum expected area impacted by fire and suppression.

A Note on a Conceptual Framework for Dynamic Location—Allocation Analysis

1976 ◽  
Vol 8 (4) ◽  
pp. 443-446
Author(s):  
W G Truscott
Keyword(s):  
Conceptual Framework ◽  
Integer Program ◽  
Original Version ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Location Allocation ◽  
Dynamic Location

This note examines a previously published model for dynamic location—allocation analysis. The usefulness of this model is enhanced by reformulating the problem as an operational zero-one, mixed-integer program while retaining the intent of the original version.

scholarly journals A GRASP Approach for Solving Large-Scale Electric Bus Scheduling Problems

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6610
Author(s):  
Raka Jovanovic ◽  
Islam Safak Bayram ◽  
Sertac Bayhan ◽  
Stefan Voß
Keyword(s):  
Public Transport ◽  
High Speed ◽  
Large Scale ◽  
Integer Program ◽  
Mixed Integer ◽  
Transport Systems ◽  
Mixed Integer Program ◽  
Scheduling Problems ◽  
Electric Bus ◽  
Battery Capacity

Electrifying public bus transportation is a critical step in reaching net-zero goals. In this paper, the focus is on the problem of optimal scheduling of an electric bus (EB) fleet to cover a public transport timetable. The problem is modelled using a mixed integer program (MIP) in which the charging time of an EB is pertinent to the battery’s state-of-charge level. To be able to solve large problem instances corresponding to real-world applications of the model, a metaheuristic approach is investigated. To be more precise, a greedy randomized adaptive search procedure (GRASP) algorithm is developed and its performance is evaluated against optimal solutions acquired using the MIP. The GRASP algorithm is used for case studies on several public transport systems having various properties and sizes. The analysis focuses on the relation between EB ranges (battery capacity) and required charging rates (in kW) on the size of the fleet needed to cover a public transport timetable. The results of the conducted computational experiments indicate that an increase in infrastructure investment through high speed chargers can significantly decrease the size of the necessary fleets. The results also show that high speed chargers have a more significant impact than an increase in battery sizes of the EBs.

Multi-Objective Territory Design for Sales Managers of a Direct Sales Company

2019 ◽  
pp. 160-178 ◽  
Author(s):  
Elias Olivares-Benitez ◽  
Pilar Novo Ibarra ◽  
Samuel Nucamendi-Guillén ◽  
Omar G. Rojas
Keyword(s):  
Integer Program ◽  
National Average ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Sales Managers ◽  
Territory Design ◽  
Direct Sales ◽  
Sales Company ◽  
A Company

This chapter presents a case study to organize the sales territories for a company with 11 sales managers to be assigned to 111 sales coverage units in Mexico. The assignment problem is modeled as a mathematical program with two objective functions. One objective minimizes the maximum distance traveled by the manager, and the other objective minimizes the variation of the sales growth goals with respect to the national average. To solve the bi-objective non-linear mixed-integer program, a weights method is selected. Some instances are solved using commercial software with long computational times. Also, a heuristic and a metaheuristic based on simulated annealing were developed. The design of the heuristic generates good solutions for the distance objective. The metaheuristic produces better results than the heuristic, with a better balance between the objectives. The heuristic and the metaheuristic are capable of providing good results with short computational times.

scholarly journals A game-theoretic optimisation approach to fair customer allocation in oligopolies

2020 ◽  
Vol 21 (4) ◽  
pp. 1459-1486
Author(s):  
Vassilis M. Charitopoulos ◽  
Vivek Dua ◽  
Jose M. Pinto ◽  
Lazaros G. Papageorgiou
Keyword(s):  
Integer Program ◽  
Linear Constraints ◽  
Nash Bargaining ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Programming Approach ◽  
Theoretic Approach ◽  
Separable Programming ◽  
Process Industries ◽  
Game Theoretic

Abstract Under the ever-increasing capital intensive environment that contemporary process industries face, oligopolies begin to form in mature markets where a small number of companies regulate and serve the customer base. Strategic and operational decisions are highly dependent on the firms’ customer portfolio and conventional modelling approaches neglect the rational behaviour of the decision makers, with regards to the problem of customer allocation, by assuming either static competition or a leader-follower structure. In this article, we address the fair customer allocation within oligopolies by employing the Nash bargaining approach. The overall problem is formulated as mixed integer program with linear constraints and a nonlinear objective function which is further linearised following a separable programming approach. Case studies from the industrial liquid market highlight the importance and benefits of the proposed game theoretic approach.

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