Staff scheduling in ACC at ATCC Stockholm

Department of Science and Technology Institutionen för teknik och naturvetenskap

Linköping University Linköpings universitet

LiU-ITN-TEK-G--13/075--SE

Staff scheduling in ACC at ATCC

Stockholm

Marcus Pettersson

Oscar Westgren

LiU-ITN-TEK-G--13/075--SE

Staff scheduling in ACC at ATCC

Stockholm

Examensarbete utfört i Logistik

vid Tekniska högskolan vid

Linköpings universitet

Marcus Pettersson

Oscar Westgren

Handledare Valentin Polishchuk

Examinator Tobias Andersson Granberg

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Abstract

In this report we examine the creation of staffing plans at ESOS (ATCC Stockholm). The staffing plan is the cornerstone in making the working schedule for the employees and is created with regard to the traffic flow in the Swedish airspace.

In the thesis we have come up with a model in order to create and examine staffing plans at ESOS where ATCOs (Air Traffic Controllers) will handle air traffic 55 per cent of their scheduled working hours. This would be an increase from the current staffing plan where they handle traffic

approximately 50 per cent of their time at work.

In order to create a staffing plan with the model, data on sector opening hours was received from ESOS. This data showed how many ATCOs that were handling traffic at any point in time during September 2013. By analysing the data, we obtained information about the number of hours that needed to be scheduled and also when it was appropriate to place the hours.

The result is one staffing plan which was created manually with a heuristic approach for competence group X. The staffing plan is created so that the ATCOs handle traffic 55 per cent of their working hours in a month with the traffic pattern as the one from the data.

It is important to properly investigate the effects that might occur if a staffing plan with 55 per cent time in position would be implemented. The created staffing plan is good to use as evaluation when deciding if 55 per cent time in position is something to use or not.

Table of Contents

List of Figures ... d

GLOSSARY AND DEFINITIONS ... 1

1. Introduction ... 2

Scheduling at ESOS ... 2

Purpose and Aim ... 2

Delimitations ... 2

Materials and Methods ... 3

Data on Opening Hours ... 3

Analysis of Sources ... 4

Structure of Report ... 4

2 Theory ... 5

Air Traffic Management ... 5

Personnel Management ... 7

Laws and Regulations ... 8

3 ESOS ... 9

Competence Groups ... 9

Work Time Regulations ... 9

Current Scheduling ... 10

4 Problem Formulation ... 12

Shift Assignment Problem ... 12

Starting Times For Shifts ... 12

Covering Necessary Times ... 12

Normal Opening Hours of Positions ... 12

The Minimum Number of ATCOs ... 13

Shifts Have to Overlap ... 13

Scheduled Hours ... 13

Hours in Each Shift ... 13

Number of Hours in Total ... 13

The Sum of All Shift Lengths Should be the Same as the Number of Hours in Total... 13

Adding an Objective Function ... 14

Demand of ATCOs ... 14

Shortage and Surplus of ATCOs ... 14

Minimize Shortage ... 14

Summary ... 14

5 Mathematical Model ... 16

6 Input Data Collection and Preprocessing ... 18

Creating the Inputs ... 18

Indexes ... 18

Starting Times of Shifts ... 19

Normal Opening Hours of Positions ... 20

Number of Hours in Each Shift ... 22

Number of Hours in Total ... 22

Demand of ATCOs ... 22

7 Solution Strageties ... 24

Creating a New Staffing Plan ... 24

Step 1 – Covering the Minimum Requirements ... 24

Step 2 – Making Sure That Hand Overs Can be Made ... 26

Step 3 – Adding Remaining Hours ... 27

8 Results ... 30

Presentation of New Staffing Plan ... 30

Examination of Constraints ... 30

Minimum Number of ATCOs ... 31

Shifts Have to Overlap ... 31

The Sum of All Shift Lengths Should be the Same as the Number of Hours in Total... 32

Comparison with Objective Function ... 32

Changing the Original Staffing Plan ... 33

Examination of Constraints ... 33

Minimum Number of ATCOs ... 33

Shifts Have to Overlap ... 34

The Sum of All Shift Lengths Should be the Same as the Number of Hours in Total... 35

Comparison with Objective Function ... 35

9 Analysis and Discussion ... 36

10 Conclusion ... 38 References ... I Appendix 1 – Airspace ... III Appendix 2 – Diagrams of Positions Open ... IV Appendix 3 – Calculations ... VIII A – Number of Hours that Should be Scheduled ... VIII Xk– Number of Hours in Shifts ... VIII Lij – Median Number of Positions Open ... VIII Rij – Demand of ATCOs ... IX Sijk– Set of Starting Times ... IX

Appendix 4 – Parameter Values ... XI A – Number of Hours that Should be Scheduled ... XI Xk – Number of Hours in Shifts ... XI Lij– Normal Opening Hours of Positions ... XI Rij– Demand of ATCOs ... XIV

Appendix 5 – Constraints Investigation ... XIX Minimum Number of ATCOs in Created Staffing Plan ... XIX Minimum Number of ATCOs to Handle Hand Overs in Created Staffing Plan ... XXII Minimum Number of ATCOs in Changed Staffing Plan ... XXX Minimum Number of ATCOs to Handle Hand Overs in Created Staffing Plan ... XXXIII

List of Figures

Figure 1 – Example of position times for a specific day ... 3

Figure 2 – Competence group X, number of positions open, September, Mondays... 21

Figure 3 - An example of placing 8-hour shifts as a foundation to cover minimum requirement……...24

Figure 4 - An example of placing the 7.5-hours shifts wherever the minimum requirement increases.25 Figure 5 - An example of how additional shifts were added and adjusted………..25

Figure 6 - An example of how the shift placement looked after adjustments with the overlap in starting times………..26

Figure 7 - An example of how the shift placement looked with the added extra shifts……….27

Figure 8 - Comparing minimum value to the number of scheduled ATCOs………...30

Figure 9 - Comparing scheduled ATCOs to the constraint regarding hand overs………30

Figure 10 - Comparing the input demand of ATCOs with the number of scheduled ATCOs…………..31

Figure 11 - Comparing minimum value to the number of scheduled ATCOs……….…………...33

Figure 12 - Comparing scheduled ATCOs to the constraint regarding hand overs….………33

Figure 13 - Comparing the input demand of ATCOs with the number of scheduled ATCOs…………..34

Figure 14 – Airspace in competence group X ... III Figure 15 - Competence group X, number of positions open, September, Mondays………..…………..IV Figure 16 - Competence group X, number of positions open, September, Tuesdays………IV Figure 17 - Competence group X, number of positions open, September, Wednesdays…..…….……….V Figure 18 - Competence group X, number of positions open, September, Thursdays.………..V Figure 19 - Competence group X, number of positions open, September, Fridays………..….VI Figure 20 - Competence group X, number of positions open, September, Saturdays………...…VI Figure 21 - Competence group X, number of positions open, September, Sundays……….VII

List of Tables

Table 2 - Shift explanations in competence group X ... 10

Table 3 – Competence group X, example of values on Sijk, where k = 1 ... 19

Table 4 - Opening hours of positions according to the NOM (NUAC ESOS, 2013)…...20

Table 5 – Competence group X, example of values on Lij ... 21

Table 6 – Competence group X, example of values on Xk ... 22

Table 7 – Competence group X, example of values on Rij ... 22

Table 8 – Competence group X, shifts that are 7.5 hours long ... 28

Table 9 – Competence group X, shifts that are 8 hours long ... 28

Table 10 - Created staffing plan………..29

Table 11 - Shift explanations, created staffing plan ... 29

Table 12 - Created staffing plan by changing the existing one………..32

Table 13 - Shift explanations, created staffing by changing the existing one……….32

Table 14 - All values on Xk………...XI

Table 15 – All values on Lij ... XI

Table 16 – All values on Rij ... XV

Table 17 – All values for Pij - Lij - 1 ... XIX Table 18 – All values for Pij - NOijk - Lij ... XXIII Table 19 – All values for Pij - NOijk - L(i-1)j ... XXVI Table 20 – All values for Pij - Lij - 1 ... XXX Table 21 – All values for Pij - NOijk - Lij ... XXXIII Table 22 – All values for Pij - NOijk - L(i-1)j ... XXXVII

GLOSSARY AND DEFINITIONS

For the purpose of this document the following definitions, acronyms and abbreviations shall apply: ACC Area Control Centre

ALRS Alerting Service ASM Airspace Management ATC Air Traffic Control ATCC Air Traffic Control Centre ATCO Air Traffic Controller

ATFM Air Traffic Flow Management

ATM Air Traffic Management

ATS Air Traffic Service

CFMU Central Flow Management Unit CTOT Calculated Take-Off Time

ESMM ATCC Malmö

ESOS ATCC Stockholm

FIR Flight Information Region FIS Flight Information Service

ICAO International Civil Aviation Organisation

LFV A Swedish provider of air navigation services

NOM NUAC Operations Manual TMA Terminal Control Area TMC Terminal Control

1. INTRODUCTION

The work as an ATCO (Air Traffic Controller) is highly demanding and requires a lot of focus by the individual working in position to maintain situation awareness when handling live air traffic (Rong-Chang Joua, 2013) (Y. Pecena, 2013). This makes the working situation at an ATCC (Air Traffic Control Centre) different from organisations that run their operation from nine to five. An ATCC is open 24 hours a day, all year around and it has to be able to serve the traffic at all times in a safe and efficient manner (Sköldborg, 2013). This can be a problem when it comes to scheduling ATCOs as the 24 hours of opening and an irregular traffic flow makes the task complex for the staff schedulers (NUAC Support, 2013). This report will go through the making of the staffing plan at ESOS (ATCC Stockholm). A staffing plan is the schedule with all available shifts for a period of time, which is the cornerstone when scheduling the employees (Sköldborg, 2013). In this chapter, the problem

background, the purpose and aim, our delimitations, materials and methods, analysis of sources and the structure of the report is presented.

Scheduling at ESOS

The thesis will look in to the operational part in one of the ACC-groups (Area Control Centre) at ESOS and how they create their staffing plans. Today, the ATCOs at ESOS work in shifts and the ACC part is divided in to three competence groups named X, Y and Z (Sköldborg, 2013). It is very important that the amount of ATCOs at work is sufficient enough to be able cope with the air traffic flow.

The main task that ATCOs have when working is to be in position and handling air traffic, where they ensure the safety of aircraft and expedite and maintain an orderly flow of traffic (ICAO, 2001). The time during shifts when ATCOs are not working in position is spent on other activities such as checking emails, debriefings or just having breaks (Sköldborg, 2013). According to the expert from LFV, Maria Sköldborg, the current staffing plans at ESOS are made so that ATCOs will work in position approximately 50 per cent of the time during their shifts. A shift is a working day from one to fourteen hours but more generally about 7 to 8 hours.

ATC (Air Traffic Control) is in general quite expensive to operate, therefore the ATCCs would save money by optimizing the ATCO workforce. The percentage of time an ATCO spends in position has an effect on the number of ATCOs needed to sustain a safe operation.

Purpose and Aim

The purpose of the thesis is to come up with a model for producing staffing plans at ESOS. The staffing plan has to consider parameters like; regulations, agreements, demands on sector opening hours and this thesis will discuss how to investigate whether a staffing plan meets all of these constraints. From the staffing plan the ATCOs can request how they want to work, leading to a complete schedule for every month. The aim is to create a staffing plan with 55 per cent of the time in position, as requested by LFV, to give a view on how it could look.

Delimitations

The thesis only creates a staffing plan for competence group X at ESOS and the analysis is based on that result. Competence groups which are not taken into account are groups Y and Z for the ACC part and groups Yellow and Blue for the TMC (Terminal Control) part. The model is assuming that it is a month without any special things like holidays. For example summer and Christmas are times when the staffing plan is different from normal working months due to people´s wishes to have as much time off as possible (Sköldborg, 2013). The data received in order to create a demand profile was for September of 2013 and effects from using more data are not being considered in the thesis.

In the model, some boundaries for inputs are decided without regulations to make the output more realistic. Even though adding constraints with weights is preferred for a general model, it is considered to not be enough time to do it in this thesis. Also, the model is not be used in a solver to generate a staffing plan in the thesis. Instead, the staffing plan is created manually in reference to the model.

Materials and Methods

A part of the research was studying articles and books related to scheduling and planning in general, this was done to understand important factors that needed to be considered in the staffing plan process. Research on how staff scheduling and -planning are undertaken at ESOS was made in order to get the full understanding of the specific problem at hand. The laws on working hours in Sweden and also the specific rules of ESOS were investigated to understand the rules that need to be applied in the staffing plan.

For the specific task of creating a staffing plan, data of sector opening hours was received. The data showed the exact opening hours of each sector and position during the time of September 2013, which the expert at LFV, Maria Sköldborg, thought was enough data to get an adequate picture of when the sectors usually are open. According to Maria, September is a month with a high traffic amount thus making its data on sector opening hours sufficient when creating the demand model. The

data was presented in ten minute intervals and received in paper form, which meant that it had to be implemented manually into Microsoft Excel to be used properly. The usage was to get a picture of when the sectors usually are open and the resulting need for ATCOs at work.

Data on Opening Hours

The data received from ESOS contained information about when positions had been open. 30 sheets of paper were received and each paper contained information about one day in September of 2013. In figure 1, an example of the data in its original form is shown. To the left, all of the ACC-positions are shown (the ones not open during the entire day are not shown) and at the top, the time of the day can be seen. Whenever a cell is grey, it indicates that the position was open at that specific time.

Figure 1 – Example of position times for a specific day

There were however some anomalies in the data. Sometimes, there were sudden holes between grey periods that would indicate that the position would have been closed although it was not considered likely. The same thing with some sudden grey spots that appeared in the data might not be correct

either. And while it is said that the main sectors always should be open, this was not always the case in the data. These anomalies can be explained since the positions have a log on feature when they are used. This means that the usage is not logged automatically and the data is therefore exposed to the risk of human errors.

Analysis of Sources

As a primary source, information was taken directly from ESOS, which is considered very reliable. All information about their job in staff scheduling and regulations must be correct since it is what they use. Regarding the information about ATM (Air Traffic Management), the primary sources used were from ICAO, EUROCONTROL and LFV expert Maria Sköldborg. ICAO documents are used widely over the world and EUROCONTROL is the European equivalent, also Maria Sköldborg has high knowledge in the field of ATM. The sources for the staff scheduling theory were gathered mainly from academic reports on the subject and are considered reliable.

Structure of Report

After this introduction chapter, the necessary theory about ATM, personnel management, laws and regulations followed by information about ESOS to fully understand the later work in the thesis.

In chapter 4, the problem formulation for the staffing plan is defined and in chapter 5 the model with necessary equations are summarized.

In chapter 6, details about the different inputs used and how they were defined and also the objective function is presented.

In chapter 7, a heuristic approach to solve the model is used to create a staffing plan and also a change in the existing staffing plan is presented.

In chapter 8, the results as new staffing plans are presented with an examination of the fulfilment of the constraints.

In chapter 9, the analysis and discussion are found and in chapter 10 our conclusion is presented with recommendations on future work.

2 THEORY

In this chapter, the fundamentals of ATM are explained to get a view of how the industry works. Information regarding personnel management and scheduling is described with some of the methodology behind it. Also, the basics of the existing working laws is explained. These laws are essential to understand in order to create a functioning staffing plan.

Air Traffic Management

ATM is the term that contains regulations regarding air traffic and is divided up into different sub-categories. One of them, ATS, consists of ATC, FIS (Flight Information Service) and ALRS (Alerting Service). The main objectives of ATS are to;

a) prevent collision between aircraft

b) prevent collision between aircraft on the manoeuvring area and obstructions on that area c) expedite and maintain an orderly flow of air traffic

d) provide advice and information useful for the safe and efficient conduct of flight

e) notify appropriate organisations regarding aircraft in need of search and rescue and assist such organisations as required

(ICAO, 2001)

Another of the sub-categories to ATM is ASM (Airspace Management). There are users with different needs who want to use the airspace at the same time for their specific purpose. At one hand there is the civil air traffic, on the other there is military air traffic (SKYbrary, 2013). There are also other users whom which require the use of airspace from time to time, for example military firing activities which may affect the safety of aviation in the vicinity (SKYbrary, 2011). ASM is there to coordinate,

integrate and regulate the use of airspace for these users (EUROCONTROL, 2013a).

ATFM (Air Traffic Flow Management) is a part of ATM and the main objective is to ensure that air traffic does not exceed the capacity at specific aerodromes or sectors in the air by optimizing and distributing traffic flow evenly (EUROCONTROL, 2013b). In Europe this is done by the CFMU (Central Flow Management Unit). They receive all flight plans from traffic departing within Europe and if they discover that there will be more traffic at a specific time in a specific aerodrome or sector then what ATC can handle, a slot allocation will take place (EUROCONTROL, 2005). According to the European Commission a slot is “a permission given by a coordinator to use the full range of airport infrastructure necessary to operate an air service at a coordinated airport on a specific date and time for the purpose of landing or take-off” (EC, 2013). This means that when a slot is allocated to an aircraft it has to follow it. To ensure the aircraft is where it is supposed to be at the right time a CTOT (Calculated Take-Off Time) is given (EUROCONTROL, 2011).

The provision of ATC is most commonly provided at an ACC (ICAO, 2001) or an ATCC (an ACC unit and an approach unit combined). An ACC is a unit where ATCOs are working within

a defined FIR (Flight Information Region)(ICAO, 2001). A FIR is airspace with defined dimensions, vertically and laterally, where FIS and ALRS are provided (ICAO, 2001).

A FIR is divided in to sectors, a sector is a smaller portion of the airspace; the size of the sectors depend on the amount and complexity of the traffic (CAA, 2010). A sector can contain both controlled and uncontrolled airspace. Controlled airspace is where ATC service is provided in accordance to the specific airspace classification (ICAO, 2001). In Sweden, only airspace classifications C (controlled) and G (uncontrolled) are used (LFV, 2011). Within a FIR only FIS and ALRS are provided in

uncontrolled airspace (LFV, 2013a). The sector is handed a specific radio frequency for aircraft to use in communication with ATC (Kanarish, 2012) and the sectors normally contain one to two

An ATCO’s primary task when working in position is to make sure aircraft do not collide with each other, in accordance to the ATS objectives stated in Annex 11 – Air Traffic Services. There are prescribed separation minima that never should be infringed. These separation minima are generally 5 nautical miles laterally and 1000ft vertically (ICAO, 2007). In an ACC this is done by monitoring a radar screen where every aircraft is plotted. Information about speed, flight level (altitude in standard air pressure), and direction is available for each aircraft and the information is updated once every sixth second (Pawlitzki, 2012). It is also possible to get more detailed information about each aircraft by opening the flight plan. Information regarding departure and destination aerodrome, aircraft type, aircraft equipment, planned route and requested flight level are examples of what the flight plan contains (LFV, FP). The ATCO is in direct radio communication with traffic in its own sector and instructs the aircraft from entry to exit point in the sector. The ATCO is also monitoring inbound traffic from adjacent sectors and receives and hand out coordinations regarding inbound and outbound traffic. Coordinations with aerodromes located within the sector, typically these coordinations regard aircraft departing or landing at the specific aerodrome, are also executed by the ATCO. A coordination is simply a heads up from one ATCO to another that an aircraft will affect the other in some way and contains all necessary information in order for the receiving ATCO to be able to take over control when the aircraft enters their sector (ICAO, 2007).

To both coordinate and handle traffic at the same time is capacity demanding and sometimes impossible for a single ATCO to do by itself. Instead, the work in sectors is split up between two ATCOs where one act as an executive and the other as a planner (Sköldborg, 2013). The executive is in charge of all the radio communication with the traffic and monitors the traffic in its own sector. The main responsibility of the planner is to handle all coordinations and monitor inbound traffic to get a picture of how it will affect traffic inside the sector. Executive and planner are working closely together in a team where the planner always notifies the executive about received coordinations and the executive informs the planner about coordinations he or she wishes the planner to hand out (NUAC ESOS, 2013). By separating the responsibilities, capacity in a sector is increased meaning the sector can receive a larger amount of traffic as to only having one ATCO in position (T. Kontogiannis, 2013).

An ATCO is required to undergo education for a specific sector in order to be allowed to work there, this to ensure the safe and efficient flow of air traffic. It would not be efficient having ATCOs only working in one specific sector. Instead, sectors located in vicinity of each other are often grouped together into one competence group meaning ATCOs in a specific competence group is educated in several sectors and are able to work in all of them. A positive effect of having competence in several sectors is that when traffic is low, bigger pieces of airspace can be controlled at the same time by one single ATCO (Sköldborg, 2013).

When there is a low amount of traffic and one ATCO handles traffic in several sectors, some sectors will be defined as closed. That means instead of merging the sectors, which is what is done in practice, you define one of the sectors as open and the other one as closed. When a sector is closed there are no ATCOs working exclusively with that sector. Another expression which is used is that a position is open or closed. Each sector normally consists of two positions since there can be one executive and one planner in most sectors. So the word “position” refers to either the executive or planner position in one sector (NUAC ESOS, 2013).

Even though very seldom sometimes incidents occur, it could be anything from loss of separation due to a mistake made by either ATCO or pilot, emergencies of different kinds regarding the safety of an aircraft or unlawful interference. If an incident do occur it is important that the ATCOs in position are relieved of duty as soon as the incident is handled with. It can be very stressful to handle an incident and it could affect overall performance of the ATCOs if they remain in position for a long time after the incident (Isaac, 1999). To be able to relieve ATCOs in position after an incident there have to be other ATCOs available to take over.

Personnel Management

It is important for an organisation to have the right amount of staff working at all times in order to execute the task at hand (A.T. Ernst, 2004a). If an operation is understaffed it ends up losing income, on the other hand, having too much employees will reduce the revenue due inefficient work. An organisation could save a lot of money by optimizing its work force (S.J. Sadjadi, 2011). This has proved to be very hard in many cases as there are many factors that have to be accounted for when creating a staffing plan and scheduling it.

What has to be defined is what needs to be done, how long it takes and what is required to complete the task and this is defined as “demand modelling”. The demand modelling is done for a period of time and there are different types of demands depending on what operation you are running (A.T. Ernst, 2004b). When you have a specific task and can define starting time and end time and the skill required to complete it, you have something called task based demand. Then individual tasks are paired together in order to get a sequence which a single employee can work with. The other approach to demand modelling is when you do not know exactly when tasks need to be completed. In ATC the traffic flow is changing throughout the day thus the need for ATCOs change. This specific type of demand modelling is called “flexible demand” where an estimation is made of the future demand and the result is a required amount of staff on an hourly basis throughout the day for a period of time (A.T. Ernst, 2004b) (A.T. Ernst, 2004a).

It can be very complex to plan the workforce in an organisation with flexible demand due to the fact that the need for staff can differ a lot throughout the day (Baker, 1974) (A.T. Ernst, 2004a). Also, consideration regarding competence has to be made depending on the specific task, there may only be a portion of the staff able to do it. Staff in ATCCs is often divided in to different competence groups and requires education to be able to work in one specific group (Sköldborg, 2013). Also, consideration regarding working hours has to be made; some organisations are required to have their operation up and running twenty-four hours a day all year around as to where others only have their open on a normal weekly basis.

The demand modelling is the first part of a rostering process; by estimating the need for staff on an hourly basis for a period of time, for a week or even longer, demand modelling enables an

organisation to get the picture of the amount of staff needed to complete the job. In ATC there is a need to fill positions with ATCOs in order to handle the amount of traffic. Throughout the day the amount of traffic differs a lot with peaks and lows where the need for ATCOs follow the traffic flow, the demand of ATCOs is flexible. To get the picture of how many ATCOs are needed on different times in one day an estimate is made by looking at historical traffic data or by looking at the planned amount of traffic for some time ahead. A factory is producing hammers and there is a fixed demand of 500 produced hammers per day, to create the hammers there are different tasks which have to be fulfilled. The tasks are paired in order for a single or several employees to work with. When the tasks are paired in sequences the required amount of staff is decided in order for the company to produce its 500 hammers for the day, this is task based demand. Task based and flexible demands are two

different ways of doing demand modelling, the objective for both is to estimate the required amount of staff needed in an organisation. The rostering process is everything from creating the demand model to schedule individual staff to a line of work in an organisation (A.T. Ernst, 2004b).

When the demand is defined, a staffing plan can be created from it. A staffing plan is an unassigned schedule for an organisation or part of an organisation with available shifts which employees are assigned to. Next step in the rostering process is to assign individuals to a specific line of work and the outcome of this is a schedule. A schedule is a specification of when someone is working, the length of specific shifts and days off, for a period of time (D. Ahola, 2013). Depending on how the specific organisation operates, they have the need for a specific type of schedule and it is important to match the schedule with the actual demand. Different from a staffing plan, a schedule defines who is working a specific shift rather than just defining what types of shifts that exist.

Laws and Regulations

To schedule the employees national working laws have to be taken in mind, this even though when comparing the Swedish laws to the local agreements they are less strict. The national working laws are partly constructed from directives by the European Union and comprise how much employees are allowed to work and how much breaks they need to have (Arbetsmiljöverket, 2013). One purpose of the Swedish laws on working hour is to make sure that the employees´ working periods and their leave are designed so that the employee gets enough rest to be able to perform well. If the laws are not followed the employees might be too tired to do an adequate job since fatigue in turn can lead to mistakes (T. Edwards, 2012).

The national laws are summarized and interpreted by Arbetsmiljöverket in the booklet

Arbetstidslagen. Here the relevant paragraphs from Swedish national laws are shown with comments to help in their interpretation. The actual laws are often quite brief and the comments are made with examples to suit the everyday need an employer might have for the information. The local agreements of working time are written in the LFV Affärsverksavtal. Since the national laws are both general and quite lax, the local agreements are written to be better adapted to the actual profession (Sköldborg, 2013).

Since only the scheduled time is taken in to consideration, laws about overtime and on call time, among other things, are not looked at nor explained. Some of these rules and regulations might not be directly related to creating a staffing plan but they do have an indirect effect.

The national laws allows a scheduled working time of maximum 40 hours per week. Since ATC is a profession where the work continues beyond the normal daytime hours, the employees are allowed to work as much as a maximum of 160 hours per 4 weeks’ time. There is however a possibility for the employers to negotiate an agreement with the union that allows the working time to be a bit higher in some periods and lower in others. Furthermore, the total working time per 7 day period cannot be scheduled to more than 48 hours in average per calculation period. The calculation period in this case can be 4 months at the most.

Each employee must have a scheduled leave of 11 coherent hours per 24 hour period. This leave must also, in regular cases, include the hours between midnight and 5 A.M. That is however something that would be impossible in ATC since there is need for personnel even during these hours.

A 36 hour coherent leave must be scheduled for each employee for a period of 7 days. This leave should preferably be in conjunction with the weekend. (Arbetsmiljöverket, 2011)

3 ESOS

ESOS is the designation for ATCC Stockholm which is one of the two ATCCs in Sweden today (the other is ESMM or ATCC Malmö). The ATCC is located at Arlanda International Airport and is the working place for 191 ATCOs (NUAC Support, 2013).Together with ESMM, ESOS controls most of the controlled airspace in Sweden (LFV, 2013b). In general, ESOS is responsible for the northern part of Sweden while ESMM has the southern parts but this differs a bit depending on altitude and west-east position. The main part of ESOS is ACC, which consists of 11 sectors and mostly handles the en route traffic (LFV, 2013b). There is also a section of ESOS that is responsible for Stockholm TMA.

The 11 ACC sectors that the ESOS airspace is divided in to each have at least one ATCO, the executive, when open. There is however a possibility to add another ATCO, the planner, to every sector if the traffic suggests. Often times it is the traffic that determine the need for a planner in the sector. Other times the decision to have a planner is taken before even seeing the traffic and this is done by looking at the amount of planned traffic about to enter the sector. Either way, the purpose of having a planner in the sector is to increase the capacity by relieving the executive from some of the tasks. If there are even less traffic, a decision about closing a sector can be taken meaning an ATCO in another sector handle the traffic in the closed sectors airspace as well.

Competence Groups

To handle traffic as an ATCO you must have the right competence for the airspace you work in. The airspace can sometimes be quite complex and it might take a while before an ATCO has gathered enough skill and knowledge to manage the traffic in some sectors. Therefore, the sectors have been divided into several groups called competence groups. Each ATCO gets training in one of the groups and is therefore only allowed to work in the sectors which are included in the group (Sköldborg, 2013). Every ATCO works both as executive and planner within their competence group.

There are five competence groups at ESOS and three of which that belong to the ACC part. These groups are called X, Y and Z (NUAC ESOS, 2013). Each group consists of at least three sectors and no sectors are included in more than one group. This report will focus on competence group X and in appendix 1, the airspace for this competence group is shown.

When sectors are closed, the traffic in the airspace of the closed sector is handled by an ATCO in another sector which has to be an ATCO from the same competence group. Each competence group has a main sector which is always open and this sector gets responsibility of the other sectors when they close. The main sector in competence group X is sector 3 which is therefore always open and when there is need for additional sectors, it is the traffic pattern that decides which positions that will open (NUAC ESOS, 2013).

Work Time Regulations

The working time for employees at ESOS is a bit different depending on how many nights you work where the number of hours per week varies between 34.25 and 38 hours, but it is most common to work 36 hours.

In ESOS, there has to be at least 8 hours between two working shifts. There also have to be a 30 minute break if a working shift is longer than 9.5 hours, except for the shifts that extends over the night. The longest shift is allowed to be up to 14 hours. There also has to be a free weekend (Saturday

Current Scheduling

The schedules at ESOS are created monthly but from weekly staffing plans. In the current situation, there is one staffing plan per competence group since the ATCOs handle sectors with different

opening hours. What they do have in common though is the goal that each ATCO in average should be scheduled to handle traffic 50 per cent of their time at work (NUAC Support, 2013). In table 1, the current staffing plan for group X is presented. The numbers in the cells corresponds to how many ATCOs that are planned to work that shift. In table 2, the explanations for each shift are shown. Each employee who works a shift that ends at 24:00 also works a shift that starts at 00:00 the day after.

Table 1 - Staffing plan for competence group X

X64 X4 X48 X2 R17 R14 X77 XC Monday 1 3 1 1 1 Tuesday 1 3 1 1 1 Wednesday 1 3 1 1 1 Thursday 1 3 1 1 1 Friday 1 3 1 1 1 Saturday 1 1 1 Sunday 2 1 XH XE X3 X1 XG X9 X0 X01 Monday 1 2 3 2 2 Tuesday 1 2 3 2 2 Wednesday 1 2 3 2 2 Thursday 1 2 3 2 2 Friday 3 3 2 2 Saturday 1 1 1 2 Sunday 1 1 2 1 1 2

Table 2 - Shift explanations in competence group X

Shift code Shift times Shift length Shift code Shift times Shift length

X64 0545-1315 7:30 XH 1200-2015 8:15 X4 0630-1430 8:00 XE 1200-2015 8:15 X48 0630-1445 8:15 X3 1400-2130 7:30 X2 0700-1500 8:00 X1 1430-2230 8.00 R17 0700-1500 8:00 XG 2000-2400 4:00 R14 0800-1600 8:00 X9 2200-2400 2:00 X77* 0700-1700 9:30 X0 0000-0645 6:45 XC* 0930-2015 10:15 X01 0000-0715 7:15

* Shift includes 30 minutes break

To fill these plans, ATCOs choose which shifts they want to work from the existing plans. This has to be done for every month and this phase occurs up to approximately 50 days before the first day of the month which is planned for. After that, the ATCOs themselves get to look at the requests and see which spots are empty. This is so that the ATCOs can change shifts if they feel that they are able and by doing so help to complete the schedule. Each spot in the staffing plan has to be filled so if the ATCOs themselves cannot solve the puzzle, someone has to be appointed by the schedulers to work. When the ATCOs have had two weeks’ time to look at the preliminary schedule and make changes, the requests are sent to the schedulers. They are the ones who make the final schedule after looking at the requests and correcting the errors. If there are still unfilled shifts, the schedulers assign ATCOs to those. Also, they make sure that the schedule does not break any of the rules and regulations about working times that exist. The ATCOs themselves know about these regulations when the make the

shift requests but there can sometimes be errors in the preliminary schedule anyway (NUAC ESOS, 2013).

4 PROBLEM FORMULATION

This chapter will formulate the staffing plan creation problem with its inputs, outputs and constraints. The chapter begins with a simple problem and then develops it further in every section to make it more suitable for the specific purpose of the thesis.

Shift Assignment Problem

To create a simple shift assignment problem the first input and output are defined. This problem only assigns ATCOs to shifts with no requirements at all. Every staffing plan possible would be a solution to this problem but it provides a foundation for the further work in adding constraints. This even though the problem does not have any real use in itself.

Input

- Starting times for shifts Output

- Number of ATCOs starting a shift at a specific time

- Number of ATCOs working at a specific time

Starting Times For Shifts

The input starting times for shifts are constructed to be sets of several values. Every time during the week has its own set of starting times. This set will include all possible starting times that result in an ATCO working at the specific time. For example, a time in the middle of the night probably has most of the starting times in its specific set during the evening. This means that the input for the specific time will include starting times in the evening and not in the morning. For a more concrete example and the further application in the thesis, see chapter 6.1.2.

Covering Necessary Times

The staffing plan cannot only have ATCOs scheduled without taking the opening hours of positions in to account. There always have to be enough ATCOs at work to cover all of the open positions. Also, there has to always be at least one ATCO more than the number of open positions working. To develop the shift assignment problem further, a new input and constraint must therefore be added. New input

- Normal opening hours of positions

New constraints

- Each time has a minimum number of ATCOs required

- Shifts have to overlap

Normal Opening Hours of Positions

The normal opening hours of positions have a direct effect on the amount of ATCOs that must be scheduled at a specific time. The parameter provides a value for every time and day how many positions that usually are open. The best thing would be to have exact opening hours but since that often is not applicable in ATC, the input have to settle with some kind of normal value.

The Minimum Number of ATCOs

When the number of positions open at each time has been found, it is important that there are an equal amount of ATCOs scheduled at that time. To meet the constraint, there must even be one extra ATCO every time as well to cover up if something unexpected happens.

Shifts Have to Overlap

An ATCO that is about to end a shift cannot hand over his position to another ATCO who is starting a shift at the same time the first ATCO ends his. Enough ATCOs to cover all the open positions must therefore have their shifts overlapping with other ATCOs. This is however not applicable when new positions are opened since ATCOs are considered to be able to open a new position at the same time their shift starts.

Scheduled Hours

So far, the problem formulation is trivial since the model can schedule an infinite number of ATCOs thus meeting all of the constraints. ESOS have a goal of how much time they want to schedule in the staffing plan. The sum of all the shifts put in the staffing plan should therefore not be other than this value.

New input

- Number of hours in each shift

- Number of hours in total

New constraints

- The sum of all shift lengths should be the same as the number of hours in total

Hours in Each Shift

Since the shifts can be of different length, the number of hours in each shift can also vary. It varies with the shift length and therefore gives a reason to add another index for shift length.

Number of Hours in Total

The total number of hours that should be scheduled in the staffing plan depends on how many hours the positions are open each week and how much of the working time that ATCOs are supposed to be in position. The parameter is calculated by dividing the total time of open positions during a week with the percentage you want the ATCOs to be in position. This leads to the right number of hours and no matter how they are scheduled in the staffing plan, the ATCOs will on average be in position the desired percentage.

The Sum of All Shift Lengths Should be the Same as the Number of Hours

in Total

To formulate that the shifts scheduled in the staffing plan also result in a staffing plan with the right amount of hours. The sum of hours in all shifts should simply be the same as the number of hours in total.

Adding an Objective Function

As there can be several possible outputs from the inputs and constraints the model so far consists of, some kind of objective function to optimize the output would definitely be beneficial. The question is however if it is possible to know if one staffing plan is better than the other. There might be more than one thing you could compare to try to rank staffing plans, but adding extra ATCOs at busy times was considered the best thing in this specific case.

The idea of adding extra ATCOs at busy times was that when a lot of positions are open, one extra ATCO working is not enough. To be able to open several extra positions if needed and also to allow all ATCOs to have a break once in a while, additional ATCOs should be scheduled during these times. This means that the times that already have many ATCOs should be scheduled with even more. To do this, another input had to be constructed which was highly dependent on both the time of open positions and the number of hours in total. This new input was called “demand of ATCOs”. New input

- Demand of ATCOs

New output

- Shortage of ATCOs

- Surplus of ATCOs

New objective function

- Minimize shortage

Demand of ATCOs

The input demand of ATCOs is a value on each point in time that is based on the normal opening hours of positions and numbers of hours in total. If the hours from the normal opening hours during a week are subtracted from the number of hours in total, there are some hours left as long as the

percentage in position is lower than 100. These remaining hours should be placed as well and the input specifies where the best places to put them are by providing a recommended number of ATCOs for every point in time.

Shortage and Surplus of ATCOs

The shortage and surplus of ATCOs are the difference between the demand of ATCOs and the number of ATCOs working at a specific time. If the demand of ATCOs is higher than the number of ATCOs working at a specific time there is a shortage, otherwise there is a surplus.

Minimize Shortage

The objective function in the model is to minimize the shortage which means minimize the negative difference between the demand of ATCOs and the number of ATCOs working at a specific time. This results in a staffing plan where the shifts cover as much of the demand of ATCOs as possible. Since that input represents the best value on number of ATCOs for every point in time, the more the staffing plan covers the input, the better the staffing plan.

Summary

After adding some minimum requirements, making the problem non-trivial to the original problem and adding the objective function, the entire formulation is complete.

- Starting times for shifts

- Normal opening hours of positions

- Number of hours in each shift

- Number of hours in total

- Demand of ATCOs

Output

- Number of ATCOs starting a shift at a specific time

- Number of ATCOs working at a specific time

- Shortage of ATCOs

- Surplus of ATCOs

Constraints

- Each time has a minimum number of ATCOs

- The sum of all shift lengths should be the same as the number of hours in total

- Shifts have to overlap

Objective function

5 MATHEMATICAL MODEL

This chapter presents the mathematical part of the model. The model used in this thesis is similar to a model constructed by R.Church when formulating a manpower deployment problem in emergency services in Los Angeles (R. Church, 2001). Here it has been modified to fit the specific purpose of creating a staffing plan at ESOS.

i = index for time ∈ …

j = index for day ∈ …

k = index for shift length ∈ …

Parameters:

Sijk = Set of starting times that contribute ATCOs to the coverage of (i, j) given time t and day d (t, d),

depending on shift length k

Lij = Number of positions usually open at time i and day j

Xk = Number of hours in a shift with shift length k

A = Number of hours that should be scheduled

Rij = Demand of ATCOs each time i and day j

Variables:

Pij = Number of ATCOs working at time i and day j

NOijk = Number of ATCOs starting their shift at time i, day j and shift length k

Uij = Shortage of ATCOs at time i and day j

Oij = Surplus of ATCOs at time i and day j

The objective function, minimize the shortage.

= ∑ ∑

The relationship between ATCOs working, shortage, surplus and demand.

+ − = ∀ ,

Every specific point in time has the same number of ATCOs working as the total number of ATCOs starting at starting times that means that the shifts include that specific point in time.

= ∑ ∑ ∀ ,

∈

At least the normal number of positions open plus one ATCO must work at every point in time. + ∀ ,

The sum of the hours in all shifts should be equal to the amount of hours that is supposed to be scheduled in the staffing plan.

∑ ∑ ∑ = �

There must be enough ATCOs working to cover the number of positions usually open plus the amount of ATCOs starting their shift at the same time. Since the constraint is different depending on if there is a new position opening or one already open, the constraint has to be written differently depending on

the values of Lij. So if: − ∀ > , + − − ∀ = , > + − + − ∀ = , = Then: ∑ + And if: − ∀ > , + − − ∀ = , > + − + − ∀ = , = Then: ∑ + − ∀ > ∑ + + − − ∀ = , > ∑ + + − + − ∀ = , =

Non-negativity conditions for the decision variables.

6 INPUT DATA COLLECTION AND PREPROCESSING

Creating the Inputs

To create the inputs the main help was the data on open positions that was received from ESOS. The data was used in different ways depending on which input that was supposed to be created. Even though the opening of positions very often is dependent of the traffic flow, the received data has to be relied on and assumed that these numbers reflect the normal reality and creates a foundation on which it is possible to plan for ATCOs. The five inputs that are needed in the model are the following:

- Starting times of shifts

- Normal opening hours of positions

- Number of hours in each shift

- Number of hours in total

- Demand of ATCOs

The exact calculations for each input can be found in appendix 3.

Indexes

Before starting the work with the inputs, it was important to specify the indexes. This because some of the decisions made when defining the inputs affected the input values as well. The three indexes used in the model are:

i = index for time j = index for day

k = index for shift length

The obvious one is the index for day (j). There is no reason to have any other than seven values in this index, one for each day of the week. Theoretically, you could have several weeks and create a staffing plan that was for more than one week but that would probably only complicate things and not have any advantages.

= { == = ℎ = � =

= =

The index for time (i) might not be as obvious as the index for day (j). Here it depends on how many possible solutions that are desired in the model. It is probably good to have as many available times as possible, but to have more than was provided in the data might be somewhat misleading. Since the data was in 10-minute intervals, the index was decided to also be in 10-minute intervals. Starting at time 00:00 and ending at time 23:50 lead to a total of 144 values.

= { == : … … … …: = :

= : = :

To create the index for shift length (k), the rules and regulations at ESOS had to be considered. The number of hours in each shift is very much affected by common sense but there are some concrete

rules like the maximum number of hours that a shift can be is 14. Also, if the shift is longer than 9 hours and 30 minutes, the ATCO must have a 30 minute break. Except from that, it is just common sense that creates rules. In the current staffing plan at ESOS, the shortest shifts are 7 hours and 30 minutes long. This is because shorter shifts would require ATCOs to be forced to work more than 5 days a week to be able to work a 36 hour week. Also, it is unpractical for workers to go to work for just a few hours.

Furthermore, the longest a shift is allowed to be 14 hours but it is not used at ESOS since it is considered too long. The longest shifts used today are 11 hours and 15 minutes (10 hours and 45 minutes plus 30 minutes break) which the schedulers at ESOS feel like are long enough. To make shifts even longer might have negative effects and should preferably not be done.

Since the boundaries are based on common sense, the index for shift length would benefit from having similar values as the ones used today. The lower limit was set to 7 hours and 30 minutes. As the higher boundary, since 11 hours and 15 minutes could not be chosen, 11 hours and 20 minutes (10 hours and 50 minutes plus 30 minutes break) was chosen instead. This meant that the index had 24 different values.

= { = ℎ= ℎ … … … . . = ℎ

= ℎ = ℎ

Starting Times of Shifts

There are not many concrete rules about shift starting times at ESOS. Today, the earliest starting time is 05:45 and the latest ending time is 22:30. These times are created to both help workers that

commute to work and care for the workers circadian. This is a thing to not upset the ATCOs and these times are not made up from any regulations. This means that the shifts in theory could start and end at more inconvenient times but that is something that is not preferable. To implement this in the model there should be boundaries in the starting times to have a more realistic output. These boundaries can be hard to argue regarding what they should be but it is good to try to have similar times as the ones existing today. The earliest starting and ending time in the input was set to 05:40, since 05:45 could not be chosen. As the latest starting and ending time, the same as the one used today was chosen. When the different boundaries were defined, the rest of the input was just pure mathematics. The parameter was designed to be a set of the starting times that contribute ATCOs to the coverage of different times throughout the week. The set of starting times that has the ATCO working at that a specific time is called S. The values on S can be changed depending on what starting times are acceptable. In table 3, an example of values on S is shown where k = 1. Since there are over 24,000 sets, all of them are not included in the report but in appendix 3 the general calculations for the sets are shown.

Sijk = Set of starting times indices as time t and day d (t, d) that contribute ATCOs to the coverage of

time i and day j, depending on shift length k

Table 3 – Competence group X, example of values on Sijk, where k = 1

X Time (i) Day (j) Sij1 1 2 1 {(125, 7) (126, 7) (127, 7) … (136, 7)} {(125, 7) (126, 7) (127, 7) … (136, 7)} 2 {(125, 1) (126, 1) (127, 1) … (136, 1)} {(125, 1) (126, 1) (127, 1) … (136, 1)} 3 {(125, 2) (126, 2) (127, 2) … (136, 2)} {(125, 2) (126, 2) (127, 2) … (136, 2)} 4 {(125, 3) (126, 3) (127, 3) … (136, 3)} {(125, 3) (126, 3) (127, 3) … (136, 3)}

Normal Opening Hours of Positions

The sectors and positions in ACC are not always open. As described in chapter 3.1, one sector in each competence group is always open and the rest of the sectors open when there is need for them. This is a rule with an exception though, since there is stated in the NOM (NUAC Operations Manual) that some positions shall be open during certain times. These times and positions are shown in table 4.

Table 4 - Opening hours of positions according to the NOM (NUAC ESOS, 2013)

Position Time

Planner sector 1 Monday-Thursday 08:30-16:30, Friday 08:30-12:00 Planner sector 2 Monday-Friday 06:30-18:30

Planner sector 3 Monday-Friday 06:30-21:30 Executive sector 8 Monday-Thursday 07:00-09:30

The rest of the position opening hours are decided during the actual work day. This can be a problem when creating a staffing plan since it is important that a sector or position can be opened with short notice if needed. If there are not enough ATCOs working when there is need for additional positions, the new position cannot be opened which results in poorer service to the air traffic.

This is why the data of actual opening hours was analysed in order to get the picture of what the flexible demand looks like. The data provided a picture of how the positions had been opened historically. This opening pattern was a good way of predicting how the positions would open in the future as well. Since there was no reason to believe that this was not a month with normal traffic flow, the opening hours in the data became guidelines of how opening hours look in general throughout a normal week.

To create a normal week, the median value from each of the weeks in the data was looked at. The median value was considered to better represent the opening hours than the average value since the median is less affected by abnormalities which makes it suitable to use when looking for normality. To make the values even less fluctuate, the median value at each time of the day was created by taking all values within 30 minutes from the actual time. This to ensure that only bigger peaks in traffic would result in scheduling extra personnel. In figure 2, an example of how many positions in competence group X that were open in during Mondays in September is shown. All weekdays can be viewed in appendix 2.

Figure 2 – Competence group X, number of positions open, September, Mondays

The median values and the rules from the NOM together give enough information to set a minimum number of ATCOs that have to be scheduled at each point in time. One can argue that the rules from the NOM are redundant since the median values should be affected by them anyway so it should be possible to only use the median values to create the input. The rules from the NOM however can be looked at just in case there should be flaws in the data during these times.

The median value has a direct effect on the minimum number of ATCOs working since there should always be at least one ATCO not in position at any time. This means that there always has to be at least one more ATCO at any point in time than the median value. This is so that there always is one ATCO ready to work in case of opening additional positions or due to controller incapacitation. So when the median number of positions open was gathered, the input was complete. This parameter was called L and it depends on the hour and the day. In table 5, an example of values on L is shown. All values can be found in appendix 4, with calculations in appendix 3.

Lij = Median number of positions open at time i and day j

Table 5 – Competence group X, example of values on Lij

0 1 2 3 4 5 6 7 0 0 :0 0 0 0 :5 0 0 1 :4 0 0 2 :3 0 0 3 :2 0 0 4 :1 0 0 5 :0 0 0 5 :5 0 0 6 :4 0 0 7 :3 0 0 8 :2 0 0 9 :1 0 1 0 :0 0 1 0 :5 0 1 1 :4 0 1 2 :3 0 1 3 :2 0 1 4 :1 0 1 5 :0 0 1 5 :5 0 1 6 :4 0 1 7 :3 0 1 8 :2 0 1 9 :1 0 2 0 :0 0 2 0 :5 0 2 1 :4 0 2 2 :3 0 2 3 :2 0 N u m b e r o f p o si ti o n s o p e n Time of day

Mondays (X)

02-sep 09-sep 16-sep 23-sep

30-sep Median Median +-30

X Time (i) Day (j) Lij 38 39 40 41 42 43 44 45 4 2 2 3 3 3 4 4 4 5 2 2 3 3 3 3 3 3 6 1 1 1 1 1 1 1 1 7 1 1 1 1 1 1 1 1

Number of Hours in Each Shift

The number of hours in each shift was in some sense created when the index of shift length was defined. The input is dependent on shift length but does not count the breaks that occur in some shifts as time in a shift. This number of hours was defined as X and in table 6, an example of the values is shown. All values can be found in appendix 4, with calculations in appendix 3.

Xk = Number of hours in a shift with shift length k

Table 6 – Competence group X, example of values on Xk

Number of Hours in Total

The staffing plan need to distribute ATCOs during the week and has a fixed number of hours that can be planned. This value was calculated with the purpose that the ATCOs shall be in position 55 per cent of their time at work. Therefore, the data from September 2013 was used to get a total number of the amount of hours the sectors where open. This was for competence group X an average of 21,253 minutes per week meaning that there should be 38,641 minutes scheduled each week (21253/0.55) to meet the goal of ATCOs being in position 55 per cent of their time at work. 38,641 minutes is approximately 644 hours, which was the number used as the actual input.

A = Number of hours that should be scheduled

Demand of ATCOs

To create the input demand of ATCOs, the remaining hours from the input number of hours in total when subtracting the minimum number of hours that needed to be scheduled was distributed

throughout the week depending on the median values at each point in time. Each time got a percentage added to the median value if the median was higher than two. This because the minimum number of ATCOs at work has to be two but at the same time, if the median is below two, there should not be more than two ATCOs scheduled either to achieve the goal of 55 per cent in position. The percentage that was added was calculated by taking the number of hours in input and subtracting the already scheduled hours. The difference was then divided among the hours of the times that would get to share these remaining hours.

In the model, the parameter demand of ATCOs is defined as R and in table 7, an example of the values for competence group X is shown. The full list of values can be found in appendix 4, with calculations in appendix 3.

Rij = Demand of ATCOs each time i and day j

Table 7 – Competence group X, example of values on Rij

X Time (i) Day (j) Rij 38 39 40 41 42 43 44 45 4 4 4 5 5 5 7 7 7 5 4 4 5 5 5 5 5 5 6 2 2 2 2 2 2 2 2 k 1 2 3 4 5 6 7 8 Xk 7.5 _{7 7} 8 _{8 8} 8.5 ₈

7 SOLUTION STRAGETIES

To create an example of how the output could look like, a heuristic approach was used to create a staffing plan that met all of the constraints in the model. In this chapter, a way to manually create a staffing plan is shown. Later in the chapter, another way that has less to do with the model is also shown.

Creating a New Staffing Plan

To manually create a staffing plan without the help of a solver means that the output not necessary is the optimal one. The output is however a feasible solution as long as it meets all of the constraints created for the model. The method used was a heuristic approach and all the steps are explained in this section with the results in the next chapter.

Step 1

– Covering the Minimum Requirements

The first step in the process was to cover the minimum requirements of ATCOs that each point in time had. This because it was a minimum requirement and there should therefore be lot of time available for planning to be able to cover these times. Since the absolute minimum number of ATCOs at any point in time is two, the first assignment was six 8-hour shifts each day to make it as easy as possible to cover this absolute minimum. The starting times of these shifts were not relevant at the moment since it was known that these shifts could have feasible starting times and could therefore be decided later. In figure 3, an illustration of the first part of step one is shown.

When this was done, the times that had a higher minimum value than two had to be taken in mind. This job was made through placing a 7.5-hour shift every time the minimum value was higher than for the previous time. Since the 7.5-hour shifts are the shortest ones possible they also make a good foundation for adjustments. In figure 4, an illustration of an example is shown where a few 7.5-hour shifts are assigned with consideration to the minimum value.

Figure 4 – An example of placing the 7.5-hour shifts wherever the minimum requirement increases

After that, it was just a simple matter of doing some adjustments like adding hours when a 7.5-hour shift was not enough or adding a completely new shift if there were a lot of time missing. Every day except the weekend looked pretty much the same. So in general two more 7.5-hours shifts had to be added each afternoon when the morning shifts ended and the evening shift had to be adjusted so it would start earlier to avoid ending too late. Both days during the weekend was acceptable without any changes except for one shift during Sundays that had to be extended with 10 minutes to cover the minimum value. In figure 5, an illustration of the necessary adjustments for most of the days is shown. The arrow means that the shift had to be moved to avoid ending after 22:30 and the red shifts are added since there were too much time that needed to be covered to just prolong the earlier shifts. The white area between the red and the green shifts looks empty in the figure, but it is covered by the orange shift above.

Figure 5 – An example of how additional shifts were added and adjusted

Step 2

– Making Sure That Hand Overs Can be Made

Another constraint that is connected to the minimum requirements at all times is that the staffing plan must plan for time to make the hand over between ATCOs. It might be argued that this not should be looked into before the rest of the shifts are scheduled since those shifts can help as well. That may be true but it also makes the solving a lot more complex and was therefore not used in this case.

A good thing with the method used in step one was that most of the shifts started when new positions opened and because of this there was no need for hand over time. The only exceptions were the two 7.5-hour shifts that were added in the afternoon and also the original 8-hour shifts. None of these exceptions caused any problems though, depending on how the 8-hour shifts were organized. Starting by looking at the 7.5-hour shifts just mentioned, none of these shifts started simultaneously as other shifts started and therefore the constraint is met. This because there are, in accordance with earlier constraints, always at least one more ATCO working than the median number of positions open. As just mentioned it depends on how the hour shifts are scheduled. The easiest way to schedule the 8-hour shifts was to put three shifts in a row every day and the other three shifts in a row but with 10 minutes displacement in the starting times. In that way there would be no hand over problems as long as the chosen starting times not were the same as the starting time of one of the already created shifts. In figure 6, an illustration of the overlapping is shown.