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A vacation scheduling algorithm for military flight crews: Maximizing satisfaction while maintaining military preparedness
JOURNAL
OF OPERATIONS
Vol. 5. No. 2. Fchrusry
MANAGEMEN
IYX5
A Vacation Scheduling Algorithm for Military Flight Crews: Maximizing Satisfaction While Maintaining Military Preparedness PHILIP S. CHONG, Ph.D.*
MICHAEL W. STREVELL**
EXECUTIVESUMMARY This article develops a quantitative method of assigning leave to crewmembers in an operational military flying squadron. The objective of the assignment process is to maximize crew preferences. This objective is limited by manning constraints which limit the number of crews that can be on leave at the same time. The basis of the assignment process is a point system which allows each crew to bid for the periods they prefer. The periods are then assigned to the highest bidder. In this way, each crew is assured of an influence in the leave assignment process, and the results are entirely in the hands of the crews themselves. The method now used to assign leave was developed and refined during a three year period from 1981 to 1983. The 1983 method includes a two-phase partially open bidding system. In Phase I, crews signed up on a posted calendar for the periods they wanted, but they did not assign points to the periods. During this phase, crews could change their period request as they saw what other crews requested. This allows crews to sequence themselves to avoid conflicts. At the end of Phase I, the juggling process was closed, and crews could no longer change their period request. Crews were given a week between the close of Phase I and the start of Phase II to see how many other crews they were competing with. Then in Phase II, they submitted their points via closed bid. This system was very effective in both distributing the demand and preventing “gaming.” There was a strong disincentive from changing a period request at the last minute. If they did, the competition had a week to see whom they were competing with and could then bid accordingly. It was to everyone’s advantage to avoid competition. Statistical analysis and positive feedback from crews and scheduling method to be significantly superior to the former system.
INTRODUCTION:
VACATION
personnel
have proven
this
SCHEDULING
In the 23rd Bombardment Squadron, there is a narrow spread between the number of crews required for military readiness and the number of crews available. As a result, only
* Worcester Polytechnic Institute, ** Wright-Patterson AFB, Ohio.
Worcester,
Journal of Operations Management
Massachusetts.
205
a limited number of crews can be on leave at any one time. The supply of leave is a relatively uniform distribution. In our case, we can normally afford to have only two crews on vacation. The normal demand, however, is a bimodal distribution with two peaks, at Christmas and the summer. The problem was to develop a quantitative method for distributing or scheduling the demand to fit the supply. Articles devoted to vacation scheduling are not many, no doubt because it is a specialized area of scheduling. It is apparent, however, that scheduling annual vacations is an international problem. Author Haulot, a French writer, examines problems in Europe which are a result of inefficient vacation scheduling practices [I]. The major problem is that annual leave is concentrated around certain periods of the year, notably Christmas and the summer months. The article examines the causes of this concentration and the consequences. Causes include: l l l
School calendar-primary cause. Business closures for holidays. Force of habit.
Consequences l l l l l
of this concentration
include:
Millions of workers and billions worth of equipment idle. Poor utilization of tourist facilities during off-peak periods. Overloading of transportation networks. Increase in traffic accidents. Increase in stress and less relaxing vacations because of the crowds.
Mapstone and Thamara [2] explain a vacation scheduling model used by the Eaton Corporation: “Its primary objective is to minimize the problems associated with vacation disruptions and associated production slowdowns and idle investment by spreading vacations as evenly as possible over a vacation planning period. . . . The scheduling concept is based on matching the calendar of skills required against the inventory of skills available.” After determining the skills required, vacations are assigned based primarily on seniority. The Air Force has long recognized the benefits to the organization of spreading out vacations as evenly as possible. This procedure is basically sound. It is possible, however, to vary slightly from a perfectly even distribution. Secondly, rather than using an assignment method based on seniority, as Mapstone and Thamara did [2], this study develops a method of leave assignment which gives each crew an equal chance of receiving the vacation periods they desire. PROBLEM
DESCRIPTION
As described in the introduction, the problem was to develop a quantitative method for scheduling the demand (bimodal distribution) to fit the supply (uniform distribution). Each flight crew is assigned two vacation periods during the year. In the past, each crew submitted three choices for each of the two leave periods. There were a number of problems with this method. a. When more than one crew requested the same period, there was no prescribed method for determining which crew got the period. The individual responsible for assigning the leaves had to decide arbitrarily. At best, he could only try to spread
206
APICS
out what seemed like the preferred periods among the crews. At worst, favoritism was sometimes suspected. If the crews were not happy with their assigned periods, they blamed the scheduler. b. Crews did not know what the other crews requested. An ideal system should make the demand readily apparent to allow the crews to select a lower demand period. c. Even if the demand was known, there was no incentive to request less desirable periods. To distribute the demand, an ideal system should provide an incentive for requesting a less desirable period. To correct these problems, the authors developed a totally new leave assignment process in 1982. A point system was used which allowed the crews to weight their choices [4]. Each crew was assigned 20 points to use in bidding for the two periods they wanted. The 20 points could be spread between the two periods as desired. The leave periods were assigned to the highest bidders. The more points a crew put on a period, the more likely they were to get that period. In the case of a tie, the winner was determined by a random drawing. Crews that were outbid for a period got their points back. These crews then went into a second round to rebid on the periods that were still open. This method solved most of the previous problems: a. It provided a known, prescribed, method for assigning leave periods. The highest bids got the period. If the crews were not happy with the periods they received, they could only put the blame on their own bidding decisions. And regardless of the demand pattern, it will eventually result in all crews being assigned leave periods which they have requested. b. A demand schedule from the previous year was posted. c. There was a definite incentive to avoid competing for high demand periods. It takes more points to get a high demand period. If a crew bids most of their points to get one high demand period, they will not have many points left for their second period. One problem still remained. Although the crews had a general idea where the high demand months were, they did not know which specific periods were being bid for since it was a closed bid. To correct this problem, the assignment process needed to be modified to allow the crews to see what the other crews were bidding for. The desired concept was an open market system in which all crews could see the periods the other crews want, and how many points they are bidding for that period. There would be a “juggling” phase in which crews could change their period and/or bid based on the other crews’ bids. This would enable them to use their limited resources (points) effectively in making trade-offs between period desirability and cost. If all the crews could get together at the same time, this juggling process could be accomplished in one sitting. However, due to the different schedules-ground alert, flying, crew rest, travel, leave-it would be difficult to get even most of the crews together at one time. For this reason, a posted juggling process is preferable. A problem with the completely open system is that it favors the crews who have access to the schedule just before the juggling phase is closed. They could change their bid to
Journal of Operations Management
207
outbid a crew who had bid low because they thought no one else wanted the period. The system had to be designed to discourage “gaming.” For these reasons, the 1983 bidding process was changed from a closed bid to a twophase partially open bid. In Phase I, crews signed up on a posted calendar for the periods they wanted, but they did not assign points to the periods. During this phase, crews could change their period request as they saw what other crews requested. This allows crews to sequence themselves to avoid conflicts. At the end of Phase I, the juggling process was closed, and crews could no longer change their period request. Crews were given a week between the close of Phase I and the start of Phase II to see how many other crews they were competing with. Then in Phase II, they submitted their points via closed bid. This system was very effective in both distributing the demand and preventing gaming. There was a strong disincentive from changing a period request at the last minute. If they did, the competition had a week to see who they were competing with and could then bid accordingly. It was to everyone’s advantage to avoid competition. The 1983 assignment process took three rounds. Table 1 compares the 1982 and 1983 assignment processes. With the partially open bidding process, the number of first choice leave periods assignments increased from 23 (57%) to 28 (70%). Referring to Table 1, since there were 20 crews, each allowed two leave periods a year, making a total of 40 leave periods to be assigned. Only three rounds were required to assign all leaves. All points were used by the end of the second round. OBSTACLES
ENCOUNTERED
The only problem encountered was that a few crews did not fully understand the bidding strategy. This was apparent from the (losing) bids they made in spite of the competition. When a crew does not receive the period they request, it tends to decrease user satisfaction with the assignment process, at least for that crew. This can be partially avoided by more fully explaining bidding strategy next year. Crews should try to avoid competing for high demand periods. If the number of requests exceeds the supply, someone is not going to get their desired period. The key is to get something you can live with in the first round, because by the end of the first round, most of the desired periods will be gone. Ideally, the crews would perfectly sequence themselves and everyone would get what they request. Realistically, some crews will opt to stay in competition for highly desirable periods. But they will know the consequences if they lose. Since this was the first year open bidding was used, crews will likely bid more effectively next year. They have an inherent motivation to bid wisely, since it is their vacation.
TABLE 1 Cumulative Periods Assigned
Round Round Round Round
208
I 2 3 4
FY82
FY83
23 32 35 40
28 36 40 -
APES
EVALUATION:
ANALYSIS
OF BIDS
We wish to test whether one assignment process is better than another. One method of doing this is to compare the first round supply and demand for each year. This will show how effectively the assignment process distributes the requests (demand) to conform to the given supply. What we are primarily concerned with, then, is the areas above the supply curve. This is the demand that cannot be met and must be shifted to another period. An intuitive way to compare the processes is to simply look at the area above the supply curve. The information is summarized in Table 2 below. It is apparent that the area above the curve (Demand > Supply) is less in FY83 (20) than in FY81 (42). To test the statistical significance of this difference, the chi-square test for proportions can be used [3]. If the value we calculate for chi-square exceeds the tabulated value, we can conclude that there is a statistically significant difference between the assignment processes. From the chi-square tests, it was found that the FY83 assignment process is significantly superior to both FY81 and FY82. The difference between the FY81 and FY82 methods is not significant. A likely reason for the superior performance of the FY83 method is the open bidding. It must be recognized, however, that the effectiveness of an assignment process in distributing the demand in the first round is not the only measure of an effective assignment process. If this were the only measurement, a system could be designed which would actively discourage crews from bidding for high-demand periods. For example, a process which takes away a crew’s points after they bid, whether they get the period or not, would create a strong incentive to avoid high demand periods. EVALUATION:
USER
FEEDBACK
A questionnaire for determining user satisfaction with the leave assignment process was given to each crew. In considering the results of the questionnaire, certain factors must be taken into account. There is widespread dissatisfaction with the leave program in Strategic Air Command. The two primary reasons for this dissatisfaction are the Integral Crew Concept and the manning constraints. Neither of these problems are correctable at the unit level. As one crewmember wrote on the questionnaire “. . . six people don’t want to take leave at the same time.” And even if an individual understands why he cannot have leave when he wants it, he still may not be very happy about it. So to a certain extent, polling crewmembers on leave satisfaction is perhaps more a measure of the level of dissatisfaction than satisfaction.
TABLE 2 Actual Frequencies Fy8 1 Demand > Supply Demand 5 Supply TOTAL
Fy82
FY83
Total
42 53
36 64
20 80
98 197
95
100
100
295
Journal of Operations Management
209
Considering these factors, the crew feedback from the questionnaire was very favorable. The results are shown in Table 3. Each question has a scale of five responses. The number of answers to each response is shown immediately below the response. The weighted average for each question is shown below: FAIRNESS
+.88
COMPARISON
+.69
SATISFACTION
+.53
The breakdown of ideal leave periods confirms that June/July and December are still the most favored periods, accounting for 75% of the choices. There were no suggestions for improvement. Although polls were not taken in previous years, the author has noted improvement in user satisfaction. In FYS 1, outright hostility was encountered in trying to explain why Crew X did not get their leave. In FYS3, crews were not happy when they did not get their request, but they did understand that it was because they were outbid. From the questionnaires, and also informal discussions, the author has noted a definite correlation between crewmember satisfaction with the assignment process and their understanding of the process and the manning constraints involved. Because of this, one of the most important ways of further increasing user satisfaction is through education. Crews that do not understand the process, and end up with poor leave periods tend to blame the system. They even suggest that another system be used which will penalize crews that received the good leave periods last year. They do not appear to recognize that
TABLE 3 Leave Questionnaire
Results
Fairness Neutral
Fair +2 7
Unfair
0
+1 6
-1
I Comparison
-2 1
2
to Other Methods Inferior
Neutral
Superior +2 4
+1 6
0 4
-1
-2
1
1
Satisfaction Dissatisfied
Neutral
Satisfied 4-2 5
+1 6
0 2
-1
-2
1
3
Ideal Leave Periods Jan 2
210
Feb
Mar
Apr
May
Jun
Jul
Aug
Scp
Ott
1
7
7
2
1
1
Nov
Dee
1
10
APICS
they had an equal opportunity for getting those periods. The assignment process is partial only to the extent that it favors the crews who take the time to understand the process, and bid wisely. As the crewmember better understands the method of assignment and the manning constraints, they normally conclude that this is a fair and effective way of handling a difficult situation. SUMMARY This project was very successful in developing a quantitative method of assigning leave. The method developed is very effective in maximizing crew preferences by assigning periods to the crews that want them the most. The assignment process is simple to understand and use. It puts very few restrictions on the periods crews may request, gives each crew an equal opportunity for choosing the period of their preference, and provides a logically defensible assignment method. In addition, it satisfies all scheduling and manning constraints. There are significant differences between the demand for leave in FY81 and FY83. Leave requests have shifted away from the Christmas and summer leave periods. The results of the questionnaire confirm that these periods have not become less desirable over the past two years. It is likely that the open bidding process has encouraged crews to voluntarily shift their demand. Side benefits include a more stable, longer-range alert schedule. Conflicts between leave and work schedules have been reduced. This has also created a more stable schedule for the crew force. This assignment process is directly applicable to over 50 bomber and tanker squadrons across the country.
REFERENCES 1. Haulot, A., “The Staggering of Annual Holidays with Pay,” International Labour Review, Vol. 118, No. 2, (March-April 1979), pp. 191-204. 2. Mapstone, B.E. and A. Thamara, “Vacation Scheduling,” Industrial Engineering, May 1916, pp. 21-29.
Journal of Operations
Management
3. Miller, I. and J.E. Freund, “Probability and Statistics for Engineers,” 2nd Ed., Prentice Hall, pp. 252-269. 4. Warner, D.M., “Scheduling Nursing Personnel,” Operational Research, Vol. 24, No. 5, (SeptemberOctober 1976), pp. 842-856.
211
OF OPERATIONS
Vol. 5. No. 2. Fchrusry
MANAGEMEN
IYX5
A Vacation Scheduling Algorithm for Military Flight Crews: Maximizing Satisfaction While Maintaining Military Preparedness PHILIP S. CHONG, Ph.D.*
MICHAEL W. STREVELL**
EXECUTIVESUMMARY This article develops a quantitative method of assigning leave to crewmembers in an operational military flying squadron. The objective of the assignment process is to maximize crew preferences. This objective is limited by manning constraints which limit the number of crews that can be on leave at the same time. The basis of the assignment process is a point system which allows each crew to bid for the periods they prefer. The periods are then assigned to the highest bidder. In this way, each crew is assured of an influence in the leave assignment process, and the results are entirely in the hands of the crews themselves. The method now used to assign leave was developed and refined during a three year period from 1981 to 1983. The 1983 method includes a two-phase partially open bidding system. In Phase I, crews signed up on a posted calendar for the periods they wanted, but they did not assign points to the periods. During this phase, crews could change their period request as they saw what other crews requested. This allows crews to sequence themselves to avoid conflicts. At the end of Phase I, the juggling process was closed, and crews could no longer change their period request. Crews were given a week between the close of Phase I and the start of Phase II to see how many other crews they were competing with. Then in Phase II, they submitted their points via closed bid. This system was very effective in both distributing the demand and preventing “gaming.” There was a strong disincentive from changing a period request at the last minute. If they did, the competition had a week to see whom they were competing with and could then bid accordingly. It was to everyone’s advantage to avoid competition. Statistical analysis and positive feedback from crews and scheduling method to be significantly superior to the former system.
INTRODUCTION:
VACATION
personnel
have proven
this
SCHEDULING
In the 23rd Bombardment Squadron, there is a narrow spread between the number of crews required for military readiness and the number of crews available. As a result, only
* Worcester Polytechnic Institute, ** Wright-Patterson AFB, Ohio.
Worcester,
Journal of Operations Management
Massachusetts.
205
a limited number of crews can be on leave at any one time. The supply of leave is a relatively uniform distribution. In our case, we can normally afford to have only two crews on vacation. The normal demand, however, is a bimodal distribution with two peaks, at Christmas and the summer. The problem was to develop a quantitative method for distributing or scheduling the demand to fit the supply. Articles devoted to vacation scheduling are not many, no doubt because it is a specialized area of scheduling. It is apparent, however, that scheduling annual vacations is an international problem. Author Haulot, a French writer, examines problems in Europe which are a result of inefficient vacation scheduling practices [I]. The major problem is that annual leave is concentrated around certain periods of the year, notably Christmas and the summer months. The article examines the causes of this concentration and the consequences. Causes include: l l l
School calendar-primary cause. Business closures for holidays. Force of habit.
Consequences l l l l l
of this concentration
include:
Millions of workers and billions worth of equipment idle. Poor utilization of tourist facilities during off-peak periods. Overloading of transportation networks. Increase in traffic accidents. Increase in stress and less relaxing vacations because of the crowds.
Mapstone and Thamara [2] explain a vacation scheduling model used by the Eaton Corporation: “Its primary objective is to minimize the problems associated with vacation disruptions and associated production slowdowns and idle investment by spreading vacations as evenly as possible over a vacation planning period. . . . The scheduling concept is based on matching the calendar of skills required against the inventory of skills available.” After determining the skills required, vacations are assigned based primarily on seniority. The Air Force has long recognized the benefits to the organization of spreading out vacations as evenly as possible. This procedure is basically sound. It is possible, however, to vary slightly from a perfectly even distribution. Secondly, rather than using an assignment method based on seniority, as Mapstone and Thamara did [2], this study develops a method of leave assignment which gives each crew an equal chance of receiving the vacation periods they desire. PROBLEM
DESCRIPTION
As described in the introduction, the problem was to develop a quantitative method for scheduling the demand (bimodal distribution) to fit the supply (uniform distribution). Each flight crew is assigned two vacation periods during the year. In the past, each crew submitted three choices for each of the two leave periods. There were a number of problems with this method. a. When more than one crew requested the same period, there was no prescribed method for determining which crew got the period. The individual responsible for assigning the leaves had to decide arbitrarily. At best, he could only try to spread
206
APICS
out what seemed like the preferred periods among the crews. At worst, favoritism was sometimes suspected. If the crews were not happy with their assigned periods, they blamed the scheduler. b. Crews did not know what the other crews requested. An ideal system should make the demand readily apparent to allow the crews to select a lower demand period. c. Even if the demand was known, there was no incentive to request less desirable periods. To distribute the demand, an ideal system should provide an incentive for requesting a less desirable period. To correct these problems, the authors developed a totally new leave assignment process in 1982. A point system was used which allowed the crews to weight their choices [4]. Each crew was assigned 20 points to use in bidding for the two periods they wanted. The 20 points could be spread between the two periods as desired. The leave periods were assigned to the highest bidders. The more points a crew put on a period, the more likely they were to get that period. In the case of a tie, the winner was determined by a random drawing. Crews that were outbid for a period got their points back. These crews then went into a second round to rebid on the periods that were still open. This method solved most of the previous problems: a. It provided a known, prescribed, method for assigning leave periods. The highest bids got the period. If the crews were not happy with the periods they received, they could only put the blame on their own bidding decisions. And regardless of the demand pattern, it will eventually result in all crews being assigned leave periods which they have requested. b. A demand schedule from the previous year was posted. c. There was a definite incentive to avoid competing for high demand periods. It takes more points to get a high demand period. If a crew bids most of their points to get one high demand period, they will not have many points left for their second period. One problem still remained. Although the crews had a general idea where the high demand months were, they did not know which specific periods were being bid for since it was a closed bid. To correct this problem, the assignment process needed to be modified to allow the crews to see what the other crews were bidding for. The desired concept was an open market system in which all crews could see the periods the other crews want, and how many points they are bidding for that period. There would be a “juggling” phase in which crews could change their period and/or bid based on the other crews’ bids. This would enable them to use their limited resources (points) effectively in making trade-offs between period desirability and cost. If all the crews could get together at the same time, this juggling process could be accomplished in one sitting. However, due to the different schedules-ground alert, flying, crew rest, travel, leave-it would be difficult to get even most of the crews together at one time. For this reason, a posted juggling process is preferable. A problem with the completely open system is that it favors the crews who have access to the schedule just before the juggling phase is closed. They could change their bid to
Journal of Operations Management
207
outbid a crew who had bid low because they thought no one else wanted the period. The system had to be designed to discourage “gaming.” For these reasons, the 1983 bidding process was changed from a closed bid to a twophase partially open bid. In Phase I, crews signed up on a posted calendar for the periods they wanted, but they did not assign points to the periods. During this phase, crews could change their period request as they saw what other crews requested. This allows crews to sequence themselves to avoid conflicts. At the end of Phase I, the juggling process was closed, and crews could no longer change their period request. Crews were given a week between the close of Phase I and the start of Phase II to see how many other crews they were competing with. Then in Phase II, they submitted their points via closed bid. This system was very effective in both distributing the demand and preventing gaming. There was a strong disincentive from changing a period request at the last minute. If they did, the competition had a week to see who they were competing with and could then bid accordingly. It was to everyone’s advantage to avoid competition. The 1983 assignment process took three rounds. Table 1 compares the 1982 and 1983 assignment processes. With the partially open bidding process, the number of first choice leave periods assignments increased from 23 (57%) to 28 (70%). Referring to Table 1, since there were 20 crews, each allowed two leave periods a year, making a total of 40 leave periods to be assigned. Only three rounds were required to assign all leaves. All points were used by the end of the second round. OBSTACLES
ENCOUNTERED
The only problem encountered was that a few crews did not fully understand the bidding strategy. This was apparent from the (losing) bids they made in spite of the competition. When a crew does not receive the period they request, it tends to decrease user satisfaction with the assignment process, at least for that crew. This can be partially avoided by more fully explaining bidding strategy next year. Crews should try to avoid competing for high demand periods. If the number of requests exceeds the supply, someone is not going to get their desired period. The key is to get something you can live with in the first round, because by the end of the first round, most of the desired periods will be gone. Ideally, the crews would perfectly sequence themselves and everyone would get what they request. Realistically, some crews will opt to stay in competition for highly desirable periods. But they will know the consequences if they lose. Since this was the first year open bidding was used, crews will likely bid more effectively next year. They have an inherent motivation to bid wisely, since it is their vacation.
TABLE 1 Cumulative Periods Assigned
Round Round Round Round
208
I 2 3 4
FY82
FY83
23 32 35 40
28 36 40 -
APES
EVALUATION:
ANALYSIS
OF BIDS
We wish to test whether one assignment process is better than another. One method of doing this is to compare the first round supply and demand for each year. This will show how effectively the assignment process distributes the requests (demand) to conform to the given supply. What we are primarily concerned with, then, is the areas above the supply curve. This is the demand that cannot be met and must be shifted to another period. An intuitive way to compare the processes is to simply look at the area above the supply curve. The information is summarized in Table 2 below. It is apparent that the area above the curve (Demand > Supply) is less in FY83 (20) than in FY81 (42). To test the statistical significance of this difference, the chi-square test for proportions can be used [3]. If the value we calculate for chi-square exceeds the tabulated value, we can conclude that there is a statistically significant difference between the assignment processes. From the chi-square tests, it was found that the FY83 assignment process is significantly superior to both FY81 and FY82. The difference between the FY81 and FY82 methods is not significant. A likely reason for the superior performance of the FY83 method is the open bidding. It must be recognized, however, that the effectiveness of an assignment process in distributing the demand in the first round is not the only measure of an effective assignment process. If this were the only measurement, a system could be designed which would actively discourage crews from bidding for high-demand periods. For example, a process which takes away a crew’s points after they bid, whether they get the period or not, would create a strong incentive to avoid high demand periods. EVALUATION:
USER
FEEDBACK
A questionnaire for determining user satisfaction with the leave assignment process was given to each crew. In considering the results of the questionnaire, certain factors must be taken into account. There is widespread dissatisfaction with the leave program in Strategic Air Command. The two primary reasons for this dissatisfaction are the Integral Crew Concept and the manning constraints. Neither of these problems are correctable at the unit level. As one crewmember wrote on the questionnaire “. . . six people don’t want to take leave at the same time.” And even if an individual understands why he cannot have leave when he wants it, he still may not be very happy about it. So to a certain extent, polling crewmembers on leave satisfaction is perhaps more a measure of the level of dissatisfaction than satisfaction.
TABLE 2 Actual Frequencies Fy8 1 Demand > Supply Demand 5 Supply TOTAL
Fy82
FY83
Total
42 53
36 64
20 80
98 197
95
100
100
295
Journal of Operations Management
209
Considering these factors, the crew feedback from the questionnaire was very favorable. The results are shown in Table 3. Each question has a scale of five responses. The number of answers to each response is shown immediately below the response. The weighted average for each question is shown below: FAIRNESS
+.88
COMPARISON
+.69
SATISFACTION
+.53
The breakdown of ideal leave periods confirms that June/July and December are still the most favored periods, accounting for 75% of the choices. There were no suggestions for improvement. Although polls were not taken in previous years, the author has noted improvement in user satisfaction. In FYS 1, outright hostility was encountered in trying to explain why Crew X did not get their leave. In FYS3, crews were not happy when they did not get their request, but they did understand that it was because they were outbid. From the questionnaires, and also informal discussions, the author has noted a definite correlation between crewmember satisfaction with the assignment process and their understanding of the process and the manning constraints involved. Because of this, one of the most important ways of further increasing user satisfaction is through education. Crews that do not understand the process, and end up with poor leave periods tend to blame the system. They even suggest that another system be used which will penalize crews that received the good leave periods last year. They do not appear to recognize that
TABLE 3 Leave Questionnaire
Results
Fairness Neutral
Fair +2 7
Unfair
0
+1 6
-1
I Comparison
-2 1
2
to Other Methods Inferior
Neutral
Superior +2 4
+1 6
0 4
-1
-2
1
1
Satisfaction Dissatisfied
Neutral
Satisfied 4-2 5
+1 6
0 2
-1
-2
1
3
Ideal Leave Periods Jan 2
210
Feb
Mar
Apr
May
Jun
Jul
Aug
Scp
Ott
1
7
7
2
1
1
Nov
Dee
1
10
APICS
they had an equal opportunity for getting those periods. The assignment process is partial only to the extent that it favors the crews who take the time to understand the process, and bid wisely. As the crewmember better understands the method of assignment and the manning constraints, they normally conclude that this is a fair and effective way of handling a difficult situation. SUMMARY This project was very successful in developing a quantitative method of assigning leave. The method developed is very effective in maximizing crew preferences by assigning periods to the crews that want them the most. The assignment process is simple to understand and use. It puts very few restrictions on the periods crews may request, gives each crew an equal opportunity for choosing the period of their preference, and provides a logically defensible assignment method. In addition, it satisfies all scheduling and manning constraints. There are significant differences between the demand for leave in FY81 and FY83. Leave requests have shifted away from the Christmas and summer leave periods. The results of the questionnaire confirm that these periods have not become less desirable over the past two years. It is likely that the open bidding process has encouraged crews to voluntarily shift their demand. Side benefits include a more stable, longer-range alert schedule. Conflicts between leave and work schedules have been reduced. This has also created a more stable schedule for the crew force. This assignment process is directly applicable to over 50 bomber and tanker squadrons across the country.
REFERENCES 1. Haulot, A., “The Staggering of Annual Holidays with Pay,” International Labour Review, Vol. 118, No. 2, (March-April 1979), pp. 191-204. 2. Mapstone, B.E. and A. Thamara, “Vacation Scheduling,” Industrial Engineering, May 1916, pp. 21-29.
Journal of Operations
Management
3. Miller, I. and J.E. Freund, “Probability and Statistics for Engineers,” 2nd Ed., Prentice Hall, pp. 252-269. 4. Warner, D.M., “Scheduling Nursing Personnel,” Operational Research, Vol. 24, No. 5, (SeptemberOctober 1976), pp. 842-856.
211