Optimized Workforce Scheduling in Bus Transit ...

Optimized Workforce Scheduling in Bus Transit Companies

Kimmo Nurmi

Jari Kyngäs

Satakunta University of Applied Sciences Pori, Finland

Satakunta University of Applied Sciences Pori, Finland

Zheng-Yun Zhuang

Nico Kyngäs

Chang Gung University Guei-shan, Taiwan

Satakunta University of Applied Sciences Pori, Finland

Abstract— Workforce scheduling has become increasingly important for both the public sector and private companies. Optimized shifts and rosters lower costs, utilize resources more effectively and ensure fairer workloads and distribution of shifts. This paper presents our work with workforce scheduling in bus transit companies. We present the workforce scheduling process in these companies and give an example of an optimized real-world staff rostering instance. We also give an outline of the PEAST algorithm which we use to tackle workforce scheduling problems. The algorithm has been successfully used to solve workforce scheduling problems in Finnish bus transit companies. The algorithm has been integrated into market-leading workforce management software in Finland.

papers has increased in recognized scheduling conferences in recent years. This paper presents our work with workforce scheduling in bus transit companies. The paper is composed as follows. Section 2 introduces the workforce scheduling process as we have encountered it in transportation sector. In Section 3 we outline our computational intelligence algorithm (PEAST) and its most important components. Section 4 gives an example of a challenging bus transit staff rostering instance which is solved using the PEAST algorithm. Section 5 presents conclusions.

Keywords-component; workforce scheduling; real-world scheduling; metaheuristics; PEAST algorithm

We classify the scheduling process in bus transit companies in four phases, as given in Fig. 1. Bus routing or Line planning is a preliminary phase in the development of bus service operations. In public transport the bus routes and their frequencies are defined by the city and the bus companies usually have little opportunity to influence them. Private transport operators create the bus routes based on the business opportunities. In both the public and private sectors, it is completely up to the companies to schedule their fleet of buses, roster the drivers and decide the days-off and working shifts of their drivers. An early reference on bus routing is [10].

I.

INTRODUCTION

Workforce scheduling is a difficult and time consuming task that many companies must solve, especially when employees are working on shifts or on irregular working days. The workforce scheduling problem has a fairly broad definition. Even the basic variations of the problem are NPhard and NP-complete (see for example [1]-[5]). Good overviews of workforce scheduling are published by Alfares [6], Ernst et al. [7] and Meisels & Schaerf [8]. There are hundreds of workforce scheduling solutions commercially available and in widespread use. However, most of the commercial products do not include any computational intelligence. Most of the workforce scheduling cases in which academic researchers have announced that they have closed a contract with a customer concern nurse rostering. We have also recently started a business cooperation with the Satakunta Hospital District (see [9]). The recent interest of the academic workforce scheduling community has somewhat shifted to other lines of businesses. One of these is transportation sector. The overall interest to real-world workforce scheduling has also increased; the number of presented workforce scheduling

II.

THE WORKFORCE SCHEDULING PROCESS IN BUS TRANSIT COMPANIES

Line Planning

Vehicle Scheduling

Workforce Scheduling

Driver Scheduling

Figure 1. The scheduling process in bus transit companies.

Vehicle scheduling consists of scheduling a fleet of vehicles to cover the set of bus routes at minimum cost. The

problem is solved for each day of the given time horizon separately, and the solution is a set of vehicle schedules. The vehicle scheduling problem was initially introduced by Dantzig and Ramser [11] as the truck dispatching problem. The problem has been proven to be NP-hard [10]. Good overviews of vehicle scheduling can be found in [12] and [13]. The goal in driver scheduling is to partition the vehicle schedules into operational tasks and to define the sequences of these tasks as shifts. Every task must be assigned to a shift while minimizing the cost in such a way that the daily rules are respected. A task is defined as a sequence of trips on one vehicle without a break that can be performed by a single driver without interruption. The construction of shifts is limited by a maximum total driving time, a maximum number of working hours, a maximum time period spent driving without a break, the number and length of lunch and short breaks in a scheduled time-window, etc. The measure of efficiency may be the total number of shifts used or the total cost in paid hours or a combination of both. Driver scheduling can be modeled as a set covering problem, which is NP-hard [14]. Among the few papers on driver scheduling we mention [15] and [16].

Figure 2. The workforce scheduling process.

Fig. 2 shows the phases of the workforce scheduling process. The process can be divided to preprocessing, main scheduling and supplemental phases. A. Preprocessing phases The preprocessing phases of the workforce scheduling process, workload prediction and preference scheduling, are the foundation upon which the scheduling phases are built. They may involve identifying both the needs of the employer and customers and the attributes (preferences, skills etc.) of the employees, and determining staffing requirements. This is the point in the workforce scheduling process where historical data and the schedules of previous planning horizons are most useful. Workload prediction, also referred to as demand forecasting or demand modeling, is the process of determining the staffing levels - that is, how many

employees are needed for each timeslot in the planning horizon. The staffing is preceded by actual workload prediction or workload determination based on static workload constraints given by the company, depending on the situation. In preference scheduling, each employee gives a list of preferences and attempts are made to fulfill them as well as possible. The employees’ preferences are often considered in the days-off scheduling and staff rostering phases, but may also be considered during shift generation. The nature of determining the amount and type of work to be done at any given time during the next planning horizon depends greatly on the nature of the job. If the workload is uncertain then some form of workload prediction is called for [7]. Some examples of this are the calls incoming to a call center or the customer influx to a hospital. We have simulated the randomly distributed workload based on historical data and statistical analysis to find a suitable working structure (i.e. how many and what kinds of employees are needed) over time. Computationally this approach is much more intensive than methods based on queuing theory. However, it has the benefit of being applicable to almost any real-world situation. If the workload is static, no forecasting is necessary. For example, a bus transit company might be under a strict contract to drive completely pre-assigned bus lines. It is crucial for a workforce management system to allow the employees to affect their own schedules. In general it improves employee satisfaction. This in turn reduces sick leaves and improves the efficiency of the employees, which means more profit for the employer. Hence we use an easyto-use user interface that allows the employees to input their preferences into the workforce management system. This eases the organizational workload of the personnel manager. A measure of fairness is incorporated via limiting the number and type of different wishes that can be expressed per employee. Preferences can be considered at days-off scheduling and staff rostering phases. B. Main scheduling phases The main scheduling phases, shift generation, days-off scheduling and staff rostering, can be solved using computational intelligence. Computational workforce scheduling is key to increased productivity, quality of service, customer satisfaction and employee satisfaction. Other advantages include reduced planning time, reduced payroll expenses and ensured regulatory compliance. Shift generation is the process of determining the shift structure, along with the activities to be carried out in particular shifts and the competences required for different shifts. Shift generation transforms the determined workload into shifts. This includes deciding break times when applicable. Shift generation is essential especially in cases where the workload is not static. In other cases companies often want to hold on to their own established shift building methods. A basic shift generation problem includes a variable number of activities for each task in each timeslot. Some tasks are not time-dependent; instead, there may be a daily quota to be fulfilled. Activities may require competences.

The most important optimization target is to match the shifts to the workload as accurately as possible. In our solutions we create the shifts for each day separately, each shift corresponding to a single employee’s competences and preferences. We do not minimize the number of different shifts. Days-off scheduling decides the rest days and the working days of the employees. It is based on the result of the shift generation: for each day a set of suitable employees must be available to carry out the shifts. The coverage requirement ensures that there are a sufficient number of employees on duty at all times. The regulatory requirements ensure that the employee’s work contract and government regulations are respected. The personnel’s requests are very important and should be met as well as possible; this leads to greater staff satisfaction and commitment, and reduces staff turnover. The final optimization phase of the workforce scheduling process is staff rostering, during which the shifts are assigned to the employees. The length of the planning horizon for this phase is usually between two and six weeks. The preferences of the employees are usually given a relatively large weight. The most important constraints are usually resting times and certain competences, since these are often laid down by the collective labor agreements and government regulations. C. Supplemental phases To see if there will be any chance of succeeding at matching the workforce with the shifts while adhering to the given constraints, a resource analysis is run on the data. In addition to helping the personnel manager see the problem with the data, it may help in convincing the management level that the current practices and processes of generating the schedules are simply untenable. We have developed a statistical tool for this. Some real-world datasets are huge. They may consist of hundreds of employees with a corresponding number of jobs. In these cases it is probably computationally impossible to try to roster the whole set of employees at once. We use the PEAST algorithm to intelligently partition the data. First the employees are partitioned according to their average length of working day and possibly some other criteria into a number of approximately equal-sized groups. Then the jobs are partitioned into groups so that each group of jobs corresponds to one group of employees, i.e. so that it should be relatively easy to assign the jobs of one group to the corresponding employee group. The assignments can be done in parallel. III.

THE PEAST ALGORITHM AND ITS MOST IMPORTANT COMPONENTS

The usefulness of an algorithm depends on several criteria. The two most important ones are the quality of the generated solutions and the algorithmic power of the algorithm (i.e. its efficiency and effectiveness). Other important criteria include flexibility, extensibility and learning capabilities. We can steadily note that the PEAST algorithm realizes these criteria. It has been used to solve

several real-world scheduling problems and it is in industrial use. In this section we outline the algorithm and the seven of its most important components (marked in italic). The PEAST algorithm is a population-based local search method. Population-based methods use a population of solutions in each iteration. The outcome of each iteration is also a population of solutions. Population-based methods are a good way to escape from local optima. The heart of the algorithm is the local search operator called GHCM (greedy hill-climbing mutation) [17]. The GHCM operator is used to explore promising areas in the search space to find local optimum solutions. Another important feature of the algorithm is the use of shuffling operators. They assist in escaping from local optima in a systematic way. Furthermore, simulated annealing refinement and tabu search mechanism are used to avoid staying stuck in the promising search areas too long. The pseudo-code of the algorithm is given in Fig. 3.

Set the iteration limit t, cloning interval c, shuffling interval s, ADAGEN update interval a and the population size n Generate a random initial population of schedules Si for 1