Driver Scheduling Problem Research Articles

운전기사 일정계획 문제의 교환-삽입 알고리즘

본 논문은 NP-완전인 DSP에 대해 O(m)의 다항시간으로 근사 해를 찾는 규칙을 제시한 휴리스틱 알고리즘을 제안하였다. 제안된 알고리즘은 m개의 주어진 운행계획에 대해, 최소의 운전기사인 n명을 배정한 초기 배정 결과를 얻는다. 다음으로, 교환 또는 삽입의 5개 규칙들을 적용하여 초과시간 (OT)과 유휴시간 (IT)를 감소시켜 최소의 비용 (TC)을 얻었다. 제안된 알고리즘은 최적 (또는 근사) 해를 찾는 규칙을 제안한 O(m) 복잡도의 휴리스틱 다항시간 알고리즘임에도 불구하고, 5개의 실험 데이터에 적용한 결과 메타 휴리스틱 기법들과 필적하는 결과를 얻었다. 결론적으로, 본 논문에서는 CSP에 있어서 최적 해를 찾아가는 규칙이 전혀 없는 NP-완전이 아닌 다항시간의 규칙이 존재하는 P-문제가 될 수 있음을 보였다. This paper suggests O(m) polynomial time heuristic algorithm to obtain the solution for the driver scheduling problem, DSP, that has been classified as NP-complete problem. The proposed algorithm gets the initial assignment of n minimum number of drivers from given m schedules. Nextly, this algorithm gets the minimum total time (TC) using 5 rules of swap and insert for decrease of over times (OT) and idle times (IT). Although this algorithm is a heuristic polynomial time algorithm with O(m) time complexity rules to be find a optimal (or approximate) solution, this algorithm is equal to metaheuristic methods for the 5 experimental data. To conclude, this paper shows the DSP is not NP-complete problem but Polynomial time (P)-problem with polynomial time rules.

An Exact Method for Vehicle Routing and Truck Driver Scheduling Problems

In most developed countries working hours of truck drivers are constrained by hours of service regulations. When optimizing vehicle routes, trucking companies must consider these constraints to assure that drivers can comply with the regulations. This paper studies the combined vehicle routing and truck driver scheduling problem (VRTDSP), which generalizes the well-known vehicle routing problem with time windows by considering working hour constraints. A branch-and-price algorithm for solving the VRTDSP is presented. This is the first algorithm that solves the VRTDSP to proven optimality.

Innovative Crossover and Mutation in a Genetic Algorithm Based Approach to a Campus Bus Driver Scheduling Problem with Break Consideration and Embedded Overtime

The unfairness of job distribution and the ineffectiveness of break-time assignment among bus drivers are factors identified as problem issues in the bus driver management in a university campus environment. The issues affect the quality of the bus service which then pointed to the efficiency or inefficiency of the bus driver sche duling system. Thus, this study investigates the problem and constraints connected to bus driver scheduling activities as a case in a ca mpus environment. Therefore, we developed an efficient bus driver scheduling model based on the Genetic Algorithm (GA) approach. The GA model is able to schedule efficiently bus drivers to working slots and break in a particular day. It is thus, a time-saving effor t and able to satisfy equal break distribution among drivers with overtime work being considered at the same time.

An efficient solution approach for real-world driver scheduling problems in urban bus transportation

The driver scheduling problem in public transportation is defined in the following way. There is a set of operational tasks, and the goal is to define the sequence of these tasks as shifts in such a way that every task must be assigned to a shift without overlapping. In real-world situations several additional constraints need to be considered, which makes large practical problems challenging to be solved efficiently. In practice it is also an important request with respect to a public transportation scheduling system to offer several versions of quasi-optimal solutions. In this paper we present an efficient driver scheduling solution methodology which is flexible in the above sense.

The minimum duration truck driver scheduling problem

Truck driver scheduling problems are important subproblems of real-life vehicle routing and scheduling problems, because rest periods required by government regulations have a significant impact on travel and arrival times. Vehicle routes generated without considering these regulations are often practically infeasible. This paper identifies common constraints imposed by hours of service regulations world wide and presents a mixed integer programming formulation for a variant of the truck driver scheduling problem in which truck drivers may only rest at customer locations and at suitable rest areas. The objective of the problem is to find a feasible truck driver schedule with minimal duration. The model presented in this paper is very flexible and can be configured to consider different sets of rules imposed by government regulations and union contracts. A dynamic programming approach is presented and its effectiveness is demonstrated for working hour regulations in the United States and in the European Union.

The Australian Minimum Duration Truck Driver Scheduling Problem

Transport companies seek to maximise vehicle utilisation and minimise labour costs. Both goals can be achieved if the time required to fulfil a sequence of transportation tasks is minimised. However, if schedule durations are too short drivers may not have enough time for recuperation and road safety is impaired. In Australia transport companies must ensure that truck drivers can comply with Australian Heavy Vehicle Driver Fatigue Law and schedules must give enough time for drivers to take the amount of rest required by the regulation. This paper shows how transport companies can minimise the duration of truck driver schedules without violating Australian Heavy Vehicle Driver Fatigue Law. A mixed integer programming formulation is presented and effective cuts are given which provide significant reduction in computational effort.

The Minimum Duration Truck Driver Scheduling Problem

Truck driver scheduling problems are important subproblems of real-life vehicle routing and scheduling problems because rest periods required by government regulations have a significant impact on travel and arrival times. Vehicle routes generated without considering these regulations are often practically infeasible. This paper identifies common constraints imposed by hours of service regulations world wide and presents a mixed integer programming formulation for a variant of the truck driver scheduling problem in which truck drivers may only rest at customer locations and at suitable rest areas. The objective of the problem is to find a feasible truck driver schedule with minimal duration. The model presented in this paper is very flexible and can be configured to consider different sets of rules imposed by government regulations and union contracts. A dynamic programming approach is presented and its effectiveness is demonstrated for working hour regulations in the United States and in the European Union.

A multilevel variable neighborhood search heuristic for a practical vehicle routing and driver scheduling problem

AbstractThe world's second largest producer of pork, Danish Crown, also provides a fresh meat supply logistics system within Denmark. This is used by the majority of supermarkets in Denmark. This article addresses an integrated vehicle routing and driver scheduling problem arising at Danish Crown in their fresh meat supply logistics system. The problem consists of a 1‐week planning horizon, heterogeneous vehicles, and drivers with predefined work regulations. These regulations include, among other things, predefined workdays, fixed starting time, maximum weekly working duration, and a break rule. The objective is to minimize the total delivery cost that is a weighted sum of two kinds of delivery costs. A multilevel variable neighborhood search heuristic is proposed for the problem. In a preprocessing step, the problem size is reduced through an aggregation procedure. Thereafter, the aggregated weekly planning problem is decomposed into daily planning problems, each of which is solved by a variable neighborhood search. Finally, the solution of the aggregated problem is expanded to that of the original problem. The method is implemented and tested on real‐life data consisting of up to 2,000 orders per week. Computational results show that the aggregation procedure and the decomposition strategy are very effective in solving this large scale problem, and our solutions are superior to the industrial solutions given the constraints considered in this work. © 2011 Wiley Periodicals, Inc. NETWORKS, Vol. 58(4), 311–322 2011

Solving a bus driver scheduling problem with randomized multistart heuristics

The Bus Driver Scheduling Problem is an extremely complex part of the Transportation Planning System (e.g., [12]) that generally can be divided in different subproblems due to its complexity: Timetabling, Vehicle Scheduling, Crew Scheduling (Bus and Driver Scheduling), and Crew Rostering (see Figure 1 for the relationship between these subproblems). The transportation service is composed of a set of lines that corresponds to a bus traveling between two locations of the same city or between two cities. For each line, the frequency is determined by the demand. Then, a timetable is constructed, resulting in journeys characterized by a start and end point, and a start and end time. The Vehicle Scheduling Problem consists in finding a schedule for the buses, each schedule being defined as a bus journey starting at the depot and returning to the same depot. The objective is to minimize the total cost given by the cost of buses used for the service and running costs. Running costs can be minimized avoiding unnecessary deadheads, i.e., trips carrying no passengers. The daily schedule of each single bus is known as a running board (or vehicle block).

Truck driver scheduling in Canada

This paper presents and studies the Canadian Truck Driver Scheduling Problem (CAN-TDSP), which is the problem of determining whether a sequence of locations can be visited within given time windows in such a way that driving and working activities of truck drivers comply with Canadian Commercial Vehicle Drivers Hours of Service Regulations. Canadian regulations comprise the provisions found in US hours of service regulations as well as additional constraints on the maximum amount of driving and the minimum amount of off-duty time on each day. We present two heuristics and an exact approach for solving the CAN-TDSP. Computational experiments demonstrate the effectiveness of our approaches and indicate that Canadian regulations are significantly more permissive than US hours of service regulations.

Ant colony optimization for railway driver crew scheduling: from modeling to implementation

This study addresses the crew-scheduling problems for railway drivers’ duty trips on a railway timetable represented as a time–space diagram. Based on the diagram, the railway driver-scheduling problem is then transformed into an arc routing problem (ARP). Because of the special properties and features of the problem, the ARP can be treated as a typical vehicle node routing problem. The Ant Colony Optimization algorithm is employed to solve the transformed problem. Real data from the Taiwan Railways Administration are used to test the proposed models and algorithm. The results showed that the dead-heading-allowed approach is able to obtain a better solution in terms of fewer drivers and shorter idle time.

Truck driver scheduling in Australia

In September 2008 new regulations for managing heavy vehicle driver fatigue entered into force in Australia. According to the new regulations there is a chain of responsibility ranging from drivers to dispatchers and shippers and thus, carriers must explicitly consider driving and working hour regulations when generating truck driver schedules. This paper presents and studies the Australian Truck Driver Scheduling Problem (AUS-TDSP) which is the problem of determining whether a sequence of locations can be visited within given time windows in such a way that driving and working activities of truck drivers comply with Australian Heavy Vehicle Driver Fatigue Law.

A Bus Driver Scheduling Problem: a new mathematical model and a GRASP approximate solution

This paper addresses the problem of determining the best scheduling for Bus Drivers, a $\mathcal{NP}$ -hard problem consisting of finding the minimum number of drivers to cover a set of Pieces-Of-Work (POWs) subject to a variety of rules and regulations that must be enforced such as spreadover and working time. This problem is known in literature as Crew Scheduling Problem and, in particular in public transportation, it is designated as Bus Driver Scheduling Problem. We propose a new mathematical formulation of a Bus Driver Scheduling Problem under special constraints imposed by Italian transportation rules. Unfortunately, this model can only be usefully applied to small or medium size problem instances. For large instances, a Greedy Randomized Adaptive Search Procedure (GRASP) is proposed. Results are reported for a set of real-word problems and comparison is made with an exact method. Moreover, we report a comparison of the computational results obtained with our GRASP procedure with the results obtained by Huisman et al. (Transp. Sci. 39(4):491---502, 2005).

Driver scheduling problem modelling

The Drivers Scheduling Problem (DSP) consists of selecting a set of duties for vehicle drivers, such as bus, train and boat drivers or plane pilots, for the transportation of passengers or goods. This is a complex problem as it involves several constraints related to labour and company rules and may also entail different evaluation criteria and objectives. The ability to develop an adequate model for this problem, which can represent the real problem as closely as possible is an important research area. In this paper we present new mathematical models for the DSP which embody the very complexity of the drivers scheduling problem, besides demonstrating that the solutions generated by these models can easily be implemented in real situations. On the strength of extensive passenger transportation experience in bus companies in Portugal, we propose and test new alternative models to formulate the DSP. These models are based on Set Partitioning/Covering models. Moreover, they also take into account the bus operator issues and the user’s standpoint and environment.

Multi-phase dynamic constraint aggregation for set partitioning type problems

Dynamic constraint aggregation is an iterative method that was recently introduced to speed up the linear relaxation solution process of set partitioning type problems. This speed up is mostly due to the use, at each iteration, of an aggregated problem defined by aggregating disjoint subsets of constraints from the set partitioning model. This aggregation is updated when needed to ensure the exactness of the overall approach. In this paper, we propose a new version of this method, called the multi-phase dynamic constraint aggregation method, which essentially adds to the original method a partial pricing strategy that involves multiple phases. This strategy helps keeping the size of the aggregated problem as small as possible, yielding a faster average computation time per iteration and fewer iterations. We also establish theoretical results that provide some insights explaining the success of the proposed method. Tests on the linear relaxation of simultaneous bus and driver scheduling problems involving up to 2,000 set partitioning constraints show that the partial pricing strategy speeds up the original method by an average factor of 4.5.

Effective search space control for large and/or complex driver scheduling problems

For real life bus and train driver scheduling instances, the number of columns in terms of the set covering/partitioning ILP model could run into billions making the problem very difficult. Column generation approaches have the drawback that the sub-problems for generating the columns would be computationally expensive in such situations. This paper proposes a hybrid solution method, called PowerSolver, of using an iterative heuristic to derive a series of small refined sub-problem instances fed into an existing efficient set covering ILP based solver. In each iteration, the minimum set of relief opportunities that guarantees a solution no worse than the current best is retained. Controlled by a user-defined strategy, a small number of the banned relief opportunities would be reactivated and some soft constraints may be relaxed before the new sub-problem instance is solved. PowerSolver is proving successful by many transport operators who are now routinely using it. Test results from some large scale real-life exercises will be reported.

A heuristic method for analyzing driver scheduling problem

A heuristic approach, ZEST for ESTimator, is developed to analyze bus driver scheduling problems and produce an estimate of the number of drivers required for a bus schedule. Based on the observation that the maximum number of drivers is needed in the morning and afternoon peaks, ZEST divides the driver scheduling problem into morning and afternoon subproblems, solves each subproblem separately, and, finally, combines the solutions. The key techniques in ZEST derive from manual scheduling operations that examine the critical decision points in a bus schedule that are vital for a good driver schedule and use these decision points to develop chains of meal breaks that dovetail one driver's meal break with another driver's. ZEST can be used as a standalone estimator of driver duties or as a component of other driver scheduling approaches

Improved Squeaky Wheel Optimisation for Driver Scheduling

This paper presents a technique called Improved Squeaky Wheel Optimisation (ISWO) for driver scheduling problems. It improves the original Squeaky Wheel Optimisation’s (SWO) effectiveness and execution speed by incorporating two additional steps of Selection and Mutation which implement evolution within a single solution. In the ISWO, a cycle of Analysis-SelectionMutation-Prioritization Construction continues until stopping conditions are reached. The Analysis step first computes the fitness of a current solution to identify troublesome components. The Selection step then discards these troublesome components probabilistically by using the fitness measure, and the Mutation step follows to further discard a small number of components at random. After the above steps, an input solution becomes partial and thus the resulting partial solution needs to be repaired. The repair is carried out by using the Prioritization step to first produce priorities that determine an order by which the following Construction step then schedules the the optimisation in the ISWO is achieved by solution disruption, iterative improvement and an iterative constructive repair process performed. Encouraging experimental results are reported.

A Self-Adjusting Algorithm for Driver Scheduling

Public transport driver scheduling is a world wide problem, which is NP-hard. Although some mathematically based methods are being used in the transport industry, there is still much scope for improvements. This paper presents a novel evolutionary approach that simulates the self-adjusting process on a single schedule. Five factors characterized by fuzzy membership functions are first aggregated to evaluate the shift structure. This evaluating function is incorporated into a constructing heuristic to make shift selection. A self-adjusting algorithm is then designed to guide the constructing heuristic to improve a given initial schedule iteratively. In each generation an unfit portion of the working schedule is removed. Broken schedules are repaired by the constructing heuristic until stopping condition is met. Experimental results on real-world driver scheduling problems has demonstrated the success of the proposed approach.

TRACS II: a hybrid IP/heuristic driver scheduling system for public transport

We discuss the driver scheduling problem in public transport and describe a combined integer linear programming/heuristic approach to its solution. The approach has been applied successfully in many operational and planning scenarios. Recent developments in the algorithms used allow the solution of very large bus and rail problems.