A model and computational tool for crew scheduling in train transportation of mine materials by using a local search strategy

This work introduces a model of the crew scheduling problem for the operation of trains in the mining industry in the North of Chile. The model possesses particular features due to specific regulations with which train operators in mine material transportation are required to comply: every week, a fixed set of trips must be made according to current demand for the transportation of mine products and supplies. In order to balance the loads of the crews in the long term, the proposed model generates an infinite horizon schedule by means of a rotative scheme in which each crew takes the place of the previous one at the beginning of the next week. This gives rise to a medium/large size 0–1 linear optimization problem, whose solution represents the optimal assignment of drivers to trips with the number of working hours per week distributed equally among crews. The model and algorithm have been implemented with a user interface suitable for the remote execution of real instances on a High Performance Computing platform. The transportation company regularly uses this computerized tool for planning crew schedules and generating efficient assignments for emerging and changing operational conditions.     

A two-stage model for a day-ahead paratransit planning problem

We consider a dynamic planning problem for paratransit transportation. The focus is on a decision to take one day ahead: which requests to serve with own vehicles, and which requests to subcontract to taxis? We call this problem the day-ahead paratransit planning problem. The developed model is a non-standard two-stage integer recourse model. Both stages consist of two consecutive optimization problems: the clustering of requests into routes, and the assignment of these routes to vehicles. To solve this model, a genetic algorithm approach is used. Computational results are presented for randomly generated data sets.     

A Dynamic Programming Solution to a Problem of Loom Box Sequence Planning

A drop box loom has a vertical rack of four boxes on each side of the loom to hold the shuttles. When a weft pick is inserted there is a choice of empty boxes to receive the shuttle. Choosing the empty box to be used at each pick of the pattern is termed "the loom box sequence problem". For reasons of safety and wear and tear, rack movements are minimized; in particular, movements to the opposite end of the rack are to be avoided. A further constraint is that, to repeat, the shuttles must begin and end the sequence in the same boxes.This problem may be formulated simply in dynamic programming terms, but this leads to a computer storage requirement of 10¹² variables. A practical program using only 16 K storage has been written and the results for a typical problem are presented.     

Determining crane areas in intermodal transshipment yards: The yard partition problem

At rail–road transshipment yards, gantry cranes move containers from freight trains to trucks and vice versa. They constitute important entities in today’s intermodal transportation systems. Real-world yards are often partitioned into several disjunct crane areas, so that crane interferences during container transshipment are avoided. In practice, the lengths of such crane areas are typically determined by simple rules of thumb, i.e., each crane receives an equally sized area, which might result in an unleveled division of labor among cranes and, thus, prolong train processing times. This paper provides an exact solution procedure which determines disjunct yard areas of varying size for multiple gantry cranes in polynomial runtime, so that the workload for a given pulse of trains is equally distributed among cranes. Furthermore, we investigate the potential acceleration of train processing as compared to equally sized areas in a yard simulation.     

Models and algorithms for a staff scheduling problem

We present mathematical models and solution algorithms for a family of staff scheduling problems arising in real life applications. In these problems, the daily assignments to be performed are given and the durations (in days) of the working and rest periods for each employee in the planning horizon are specified in advance, whereas the sequence in which these working and rest periods occur, as well as the daily assignment for each working period, have to be determined. The main objective is the minimization of the number of employees needed to perform all daily assignments in the horizon. We decompose the problem into two steps: the definition of the sequence of working and rest periods (called pattern) for each employee, and the definition of the daily assignment to be performed in each working period by each employee. The first step is formulated as a covering problem for which we present alternative ILP models and exact enumerative algorithms based on these models. Practical experience shows that the best approach is based on the model in which variables are associated with feasible patterns and generated either by dynamic programming or by solving another ILP. The second step is stated as a feasibility problem solved heuristically through a sequence of transportation problems. Although in general this procedure may not find a solution (even if one exists), we present sufficient conditions under which our approach is guaranteed to succeed. We also propose an iterative heuristic algorithm to handle the case in which no feasible solution is found in the second step. We present computational results on real life instances associated with an emergency call center. The proposed approach is able to determine the optimal solution of instances involving up to several hundred employees and a working period of up to 6 months. Mathematics Subject Classification (2000): 90B70, 90C10, 90C27, 90C39, 90C57, 90C59     

Real-time freight locomotive rescheduling and uncovered train detection during disruption

This paper discusses rescheduling of freight train locomotives when dealing with a disrupted situation in the daily operations in Japan. Within the current framework of dispatching processes, passenger railway operators modify the entire timetables and an adjusted freight train timetable is distributed to a freight train operator. For this timetable, we solve the locomotive rescheduling problem by changing the assignment of the locomotives to all the trains and considering their periodic inspections. We then solve the uncovered train detection problem that selects unassigned trains according to their value if the rescheduling phase fails.     

Nominal and robust train timetabling problems

In this paper we survey the main studies dealing with the train timetabling problem in its nominal and robust versions. Roughly speaking, the nominal version of the problem amounts of determining “good” timetables for a set of trains (on a railway network or on a single one-way line), satisfying the so-called track capacity constraints, with the aim of optimizing an objective function that can have different meanings according to the requests of the railway company (e.g. one can be asked to schedule the trains according to the timetables preferred by the train operators or to maximize the passenger satisfaction). Two are the main variants of the nominal problem: one is to consider a cyclic (or periodic) schedule of the trains that is repeated every given time period (for example every hour), and the other one is to consider a more congested network where only a non-cyclic schedule can be performed. In the recent years, many works have been dedicated to the robust version of the problem. In this case, the aim is to determine robust timetables for the trains, i.e. to find a schedule that avoids, in case of disruptions in the railway network, delay propagation as much as possible. We present an overview of the main works on train timetabling, underlining the differences between models and methods that have been developed to tackle the nominal and the robust versions of the problem.     

Bicriteria train scheduling for high-speed passenger railroad planning applications

This paper is concerned with a double-track train scheduling problem for planning applications with multiple objectives. Focusing on a high-speed passenger rail line in an existing network, the problem is to minimize both (1) the expected waiting times for high-speed trains and (2) the total travel times of high-speed and medium-speed trains. By applying two practical priority rules, the problem with the second criterion is decomposed and formulated as a series of multi-mode resource constrained project scheduling problems in order to explicitly model acceleration and deceleration times. A branch-and-bound algorithm with effective dominance rules is developed to generate Pareto solutions for the bicriteria scheduling problem, and a beam search algorithm with utility evaluation rules is used to construct a representative set of non-dominated solutions. A case study based on Beijing–Shanghai high-speed railroad in China illustrates the methodology and compares the performance of the proposed algorithms.     

Optimizing the Simplon railway corridor

This paper presents a case study of a railway timetable optimization for the very dense Simplon corridor, a major railway connection in the Alps between Switzerland and Italy. The key to deal with the complexity of this scenario is the use of a novel aggregation-disaggregation method. Starting from a detailed microscopic representation as it is used in railway simulation, the data is transformed by an automatic procedure into a less detailed macroscopic representation, that is sufficient for the purpose of capacity planning and amenable to state-of-the-art integer programming optimization methods. This macroscopic railway network is saturated with trains. Finally, the optimized timetable is re-transformed to the microscopic level in such a way that it can be operated without any conflicts among the train paths. Using this micro-macro aggregation-disaggregation approach in combination with integer programming methods, it becomes for the first time possible to generate a profit maximal and conflict free timetable for the complete Simplon corridor over an entire day by a simultaneous optimization of all trains requests. In addition, this also allows us to undertake a sensitivity analysis of various problem parameters.     

The single-machine earliness-tardiness scheduling problem with due date assignment and resource-dependent processing times

We study the earliness-tardiness scheduling problem on a single machine with due date assignment and controllable processing times. We analyze the problem with three different due date assignment methods and two different processing time functions. For each combination of these, we provide a polynomial-time algorithm to find the optimal job sequence, due date values and resource allocation minimizing an objective function which includes earliness, tardiness, due date assignment, makespan and total resource consumption costs.     

Optimizing the periodic pick-up of raw materials for a manufacturer of auto parts

We describe a solution procedure for a special case of the periodic vehicle routing problem (PVRP). Operation managers at an auto parts manufacturer in the north of Spain described the optimization problem to the authors. The manufacturer must pick up parts (raw material) from geographically dispersed locations. The parts are picked up periodically at scheduled times. The problem consists of assigning a pickup schedule to each of its supplier’s locations and also establishing daily routes in order to minimize total transportation costs. The time horizon under consideration may be as long as 90 days. The resulting PVRP is such that the critical decision is the assignment of locations to schedules, because once this is done, the daily routing of vehicles is relatively straightforward. Through extensive computational experiments, we show that the metaheuristic procedure described in this paper is capable of finding high-quality solutions within a reasonable amount of computer time. Our main contribution is the development of a procedure that is more effective at handling PVRP instances with long planning horizons when compared to those proposed in the literature.     

Job sequencing and due date assignment in a single machine shop with uncertain processing times

This paper considers due date assignment and sequencing for multiple jobs in a single machine shop. The processing time of each job is assumed to be uncertain and is characterized by a mean and a variance with no knowledge of the entire distribution. A heuristic procedure is developed to find job sequence and due date assignment to minimize a linear combination of three penalties: penalty on job earliness, penalty on job tardiness, and penalty associated with long due date assignment. Numerical experiments indicate that the performance of the procedure is stable and robust to job processing time distributions. In addition, the performance improves when the means and variances of job processing times are uncorrelated or negatively correlated or when the penalty of a long due date assignment is significant.     

An approach for solving a class of transportation scheduling problems

An algorithm is developed for solving a class of transportation scheduling problems. It applies for a variety of problems such as: the Combining Truck Trip problem, the Delivery problem, the School Bus problem, the Assignment of Buses to Schedules, and the Travelling Salesman problem. The objective functions of the above problems differ from each other. Yet, by using the “savings method” proposed by Clarke and Wright, and extended by Gaskell, we are able to define each one of the above problems as a series of assignment problems. The cost matrix entries of each one of the assignment problems are a function of the constraints of the particular routing or scheduling problem. The solution to the assignment problem determines an upper bound of the optimal solution to the original problem. By combining the above procedure with a Branch and Bound procedure, it is possible to obtain the optimal solution in a finite number of steps. In some cases the Branch and Bound process can be eliminated due to the nature of the problem and in those cases the algorithm is efficient.     

On the online track assignment problem

This paper aims to start an analytical study of the computational complexity of some online shunting problems. We analyze the following problem. Consider a train station consisting of a set of parallel tracks. Each track can be approached from one side only or from both sides and the number of trains per track may be limited or not. The departure times of the trains are fixed according to a given time table. The problem is to assign a track to each train as soon as it arrives and such that it can leave the station on time without being blocked by any other train.We show that this problem can be modeled with online coloring of graphs. Depending on the constraints, the graphs can be overlap graphs (also known as circle graphs) or permutation graphs, and the coloring can be bounded or classical. This paper covers several combinations of these cases.     

货运列车编组调度问题的模型与算法研究

从双向编组站运输生产实际情况出发,以最大化车站发出车数和最小化车辆在站平均停留时间(中时)为目标,综合考虑解体、编组调机能力限制、到发列车车流接续、车流在站停留时间约束的影响,建立了车站货运列车编组调度问题的多目标非线性混合整数规划模型,结合该优化模型难以求解的特点,将编组调度问题分解为配流、待解车列解体和待编车列编组三个子问题,进而设计了求解该问题的分层启发式算法,对正常和特殊运输组织条件下的列车编组调度问题进行了求解.     

A genetic algorithm for robotic assembly line balancing

Flexibility and automation in assembly lines can be achieved by the use of robots. The robotic assembly line balancing (RALB) problem is defined for robotic assembly line, where different robots may be assigned to the assembly tasks, and each robot needs different assembly times to perform a given task, because of its capabilities and specialization. The solution to the RALB problem includes an attempt for optimal assignment of robots to line stations and a balanced distribution of work between different stations. It aims at maximizing the production rate of the line. A genetic algorithm (GA) is used to find a solution to this problem. Two different procedures for adapting the GA to the RALB problem, by assigning robots with different capabilities to workstations are introduced: a recursive assignment procedure and a consecutive assignment procedure. The results of the GA are improved by a local optimization (hill climbing) work-piece exchange procedure. Tests conducted on a set of randomly generated problems, show that the Consecutive Assignment procedure achieves, in general, better solution quality (measured by average cycle time). Further tests are conducted to determine the best combination of parameters for the GA procedure. Comparison of the GA algorithm results with a truncated Branch and Bound algorithm for the RALB problem, demonstrates that the GA gives consistently better results.     

Production of locomotive rosters for a multi-class single-locomotive problem

A multi-class single locomotive (MCSL) problem is defined in this paper as one involving the allocation of a single locomotive to each of a number of pre-timetabled trains, some of which can be pulled by more than one type (or class) of locomotive. This is typical of problems arising in many passenger train networks and an exact solution method exists for the general form of this problem (Forbes et al¹) This paper describes the analysis of a particular type of MCSL problem, as faced by the Public Transport Corporation (PTC) in the Australian State of Victoria, where all journeys either start or end at one location (Melbourne). Because of this feature, the problem can be solved in two separate stages. The first stage (an integer programming model) determines the type of locomotive that will hall each trip. The second stage, which can either be solved by the LP assignment algorithm or by computerised inspection, determines the locomotive rosters, (the sequence of round trips that each locomotive hauls).Splitting the problem into two stages achieves a significant reduction in problem size, resulting in greatly reduced computation time (4 seconds as opposed to a number of hours).     

Labour scheduling at an airport refuelling installation

We have developed an automatic assignment procedure for labour scheduling at a continously operating airport refuelling installation. Different types of workers are subject to different conditions on the shifts they can do (morning, evening or night), shift lengths, days-off, holidays, terms of contract and working hours. The scheduling process is carried out on a weekly basis, but there are mid-term and long-term conditions and objectives which link each week with the preceding and following weeks. Our package uses firstly a tabu search algorithm to find the best schemes of shifts/days-off to be used to cover the requirements. Secondly, an assignment problem is solved to match the schemes with available workers. Finally, the starting and finishing times for each working day are determined for each worker. The system has been designed to run on a personal computer and gives good quality solutions in very short computing times.