Research Article  Open Access
Hesham K. Alfares, "Multiobjective Scheduling of RemoteArea Employees with Minimum Cost of Transportation", Journal of Industrial Engineering, vol. 2014, Article ID 978347, 11 pages, 2014. https://doi.org/10.1155/2014/978347
Multiobjective Scheduling of RemoteArea Employees with Minimum Cost of Transportation
Abstract
An integer programming model and optimal solution procedure are presented for assigning employees to the (10, 14) daysoff schedule. This schedule is used by a large oil company to schedule employees in remote work locations. The primary objective is to minimize the total number of employees. Since employees are flown to their remote work sites, the company also aims to minimize transportation cost. Therefore, secondary objectives include (1) minimizing the number of active daysoff work patterns, (2) consistently using the same set of active daysoff patterns, (3) assigning work schedules fairly among employees, and (4) avoiding the use of specialized optimization solvers. A rotation schedule is used in which two scheduling rules are enforced: a minimum proportion of weekend days off needs to be given and a maximum limit on the number of successive workdays cannot be exceeded. Utilizing the problem structure, simple optimal procedures are developed to solve this unique complex scheduling problem.
1. Introduction
This paper presents a mathematical programming model and an optimal solution methodology for a reallife daysoff scheduling problem. Specifically, the focus is on the (10, 14) daysoff work schedule used for remotearea employees of a large oil company in the Middle East. The company’s work operations include all aspects of the oil business, from exploration to producing, and cover a vast area of geographical expanse. Many permanent and temporary work sites such as drilling sites, oil wells, processing plants, pipelines, service stations, and oil platforms are located in remote areas both onshore and offshore. The company provides transportation to these remote areas by its own fleet of helicopters and small fixedwing aircraft. The company’s first objective is to reduce the labor cost by minimizing the workforce size in each work site. The second objective is to reduce the transportation cost by minimizing the total number of flights. In order to minimize the number of flight trips per week, the company applies certain work schedules for remotearea employees. Such schedules, including the (10, 14) schedule, are designed to have a lower frequency of daysoff breaks.
Under the (10, 14) daysoff work schedule, each employee works for 10 consecutive days and takes a break of 4 consecutive off days during a 14day work cycle. For each employee, this means one daysoff break instead of two breaks in the twoweek cycle and consequently half the number of flight trips. In order to avoid work stoppage, employees cannot take their four off days all at the same time. Any work interruption is not acceptable, as it may reduce revenue and undermine oil supply to the market. In order to keep the work running continuously, the fourday break times may be different for different employees. It should be noted that there is a roundtrip flight for each break time (start and end day), regardless of the number of employees. This makes it important to minimize the number of different break times, that is, the number of daysoff work patterns that are active (assigned to employees). In order to reduce the number of flights further, employees that have the same break times can be pooled together from different (nearby) work sites. To allow such pooling, the same set of active daysoff patterns (same break times) should be selected as consistently as possible, although labor demands may vary from one work site to another.
From the company’s point of view, the (10, 14) daysoff schedule has the advantage of reducing the number of flights to remote work locations. From the employees’ perspectives, however, the (10, 14) schedule keeps them away longer from their families. Moreover, this schedule can cause employees to miss weekends with their families because their breaks may not always coincide with weekends. Employees obviously prefer to have some of their daysoff breaks on weekends, when their families are home all day. Therefore, for the sake of keeping up employee morale, each employee is assured at least 50% of weekend days off.
Naturally, some daysoff patterns (breaks) are going to be more desirable than others. Therefore, for fairness, employees should take turns (rotations) on all active (assigned) daysoff patterns. In going through the rotations, with each new twoweek cycle, employees may switch from one dayoff pattern to another. This makes it possible to have more than 10 consecutive workdays straddling two cycles. To maintain employee morale and productivity, the maximum work stretch (continuous work period) is not allowed to exceed 14 days. Most of the remotearea employees and supervisors concerned with the (10, 14) schedule are technicians who are not familiar with optimization tools. Therefore, the company would like a simple scheduling tool that eliminates the need to use specialized optimization software.
This paper presents an integer programming (IP) model of the abovedescribed (10, 14) daysoff scheduling problem, as well as an optimal solution methodology. Details of the problem, the model, and the solution procedure are given in subsequent sections according to the following order. First, recent relevant daysoff scheduling literature is surveyed in Section 2. The IP model of the multiobjective (10, 14) daysoff scheduling problem is formulated in Section 3. The minimum workforce size to satisfy all objectives and constraints is determined in Section 4. The optimal procedure for determining daysoff assignments to satisfy different labor demands is described in Section 5. A reallife application and an example are presented in Section 6. Finally, conclusions and suggestions are given in Section 7.
2. Literature Review
Employee scheduling is a challenging optimization problem that has major implications on workforce cost, size, productivity, and morale. Therefore, employee scheduling is a wellstudied applied optimization problem. The problem is generally classified into three types: shift (timeofday) scheduling, daysoff (daysofweek) scheduling, and tour (timeofday and daysof week) scheduling. Alfares [1] and Ernst et al. [2] provide comprehensive reviews of literature on employee scheduling. Brunner [3] gives a more recent but specialized review, focusing on the scheduling of physicians in hospitals. This section is mostly concerned with employee dayoff scheduling literature published since 2005.
Although the daysoff scheduling problem is NPcomplete according to Brucker et al. [4], mathematical properties of particular problem versions are utilized to develop efficient solution algorithms. Jarray [5] applies discrete tomography principles to develop a threestep, polynomialtime daysoff scheduling algorithm. First, a set of linear equations is solved, then a binary matrix is constructed, and finally a greedy procedure is used. Costa et al. [6] apply another polynomialtime algorithm to determine optimum daysoff schedules to satisfy variable daily labor demands. The daysoff schedule for each employee is subject to several conditions: fixed number of workdays, two or three consecutive off days per week, and at least three consecutive off days per month. Jarray [7] develops a threestep decomposition algorithm to solve a compressed workweek (34 workdays) version of the problem that also includes weekendoff frequency constraints.
There are several applications of daysoff scheduling in the service sector, especially in maintenance. Lilly et al. [8] develop a 4day workweek schedule for maintenance employees at a power plant in Nigeria. They estimate that 10% savings in labor cost could be obtained by switching from five to four workdays per week for maintenance crews. Alfares [9] constructs a simulation model to evaluate alternative daysoff schedules for a multicraft pipeline maintenance workforce. Assuming stochastic daily demands for each craft, the model suggests a daysoff schedule to reduce average completion times of maintenance orders. Considering limits on the number of workdays, weekends work, and maximum work stretch, Elshafei and Alfares [10] apply dynamic programming (DP) to determine optimal daysoff assignments. The DP model assumes daily labor demands to be variable and costs of daysoff patterns to be dependent on the given sequence of work and off days.
Transportation is a major service sector with several applications of daysoff scheduling algorithms. Klinkert [11] uses an IP model with soft and hard constraints to construct daysoff schedules for multiskilled airport ground handling employees. To facilitate solution, soft constraints are incorporated in the objective function, while a preprocessing IP model is used to identify the most critical hard constraints. Maenhout and Vanhoucke [12] address the airline crewscheduling problem, in which crew members are assigned to flight duties in order to satisfy a variable workload. Several approaches are presented for assigning airline crews to fixed daysoff patterns, including cyclical schedules and ad hoc schedules. Kyngäs and Nurmi [13] apply a modified version of the cooperative local search method to generate optimal daysoff schedules for employees in a Finnish bus transportation company.
Air transportation applications of employee scheduling is an active area of research. Addressing a problem similar to Klinkert [11], Lusby et al. [14] formulate a cutting stockbased IP model for daysoff scheduling of ground crews of an airline company. Assuming a schedule of six work days followed by three off days per cycle, decomposition and columngeneration heuristics are used to develop efficient sixmonth employee schedules. Abdoul Soukour et al. [15] decompose airport security staff scheduling into three stages: daysoff scheduling, shift scheduling, and staff assignment. A memetic algorithm is integrated with an evolutionary algorithm and local search techniques to solve this staff assignment problem.
By definition, employee tour scheduling involves a daysoff scheduling component. A number of tour scheduling algorithms have noteworthy and distinctive daysoff scheduling features. Using implicit programming techniques, Rong [16] develops monthly tour schedules for a mixed workforce using both binary and general integer programming models. The unique feature of Rong’s models is the inclusion of weekend off frequency constraints to maintain employees’ morale. Assuming random labor demands for each department, Campbell [17] presents a twostage stochastic IP approach for tour scheduling of crosstrained employees. In the first stage, daysoff scheduling is used to allocate workdays, while in the second stage, shift scheduling is used to allocate work hours.
3. Model Formulation
As stated in Section 1, the company’s main objective is to minimize the workforce size. The secondary objectives are (1) minimizing the number of active daysoff work patterns, (2) assigning the same set of daysoff patterns, (3) allocating work assignments fairly among employees, and (4) avoiding the need to use specialized optimization solvers. The objective function of the IP model, formulated below, explicitly includes only the minimum workforce size and the minimum number of daysoff work patterns. The remaining secondary objectives are implicitly addressed in the overall solution process.
3.1. Assumptions
The optimization algorithm presented in this paper applies to a singleshift, 14daycycle daysoff schedule according to the following conditions.(1)Each employee is assigned 10 consecutive workdays and 4 consecutive off days per twoweek cycle.(2)The maximum work stretch is 14 consecutive workdays.(3)During the rotation period, at least 50% of the daysoff breaks include weekends.(4)The first objective is to minimize the total workforce size, and the second objective is to minimize the number of active daysoff patterns.(5)The demand for employees has one constant level for all five regular workdays and another constant level for the two weekend days.(6)A cyclic rotation schedule is used, in which all employees take turns on the assigned daysoff patterns.
3.2. Model Variables and Parameters
3.2.1. Decision Variables
number of employees assigned to daysoff work pattern , workforce size, that is, total number of assigned employees.
3.2.2. Given Parameters
and correspond to weekdays, correspond to the weekend, and corresponds to weekendoff frequency constraint (8).
Table 1 shows matrix , small positive constant , number of workers required on each weekday, number of workers required on each weekend day (), actual proportion of weekendcontaining days off, that is, lefthand side of (8), a large number, , set of daysoff patterns with weekend days off per cycle, and ,

3.3. The Integer Programming Model
According to assumptions stated above, the integer programming model of the (10, 14) daysoff scheduling problem is shown as follows: The primary objective in (4) is to minimize workforce size, which is the total number of employees , while the secondary objective is to minimize the total number of active daysoff patterns. Constraints (5) and (6) guarantee assigning at least the minimum number of required employees on workdays and weekends, respectively. Logical constraints (7) ensure that the binary variable is equal to 1 only if daysoff pattern is active, that is, pattern is assigned to employees , and is equal to 0 if pattern is not active, .
The constraint on weekend work frequency (8) ensures that at least 50% of the daysoff assignments contain weekends off. Numerator coefficients in constraint (8) indicate that patterns from the set contain half a weekend off, while patterns from the set contain a full weekend off. Constraint (8) can be alternatively expressed as follows: Thus Constraints (9) enforce the maximum limit on work stretch length. In order for the work stretch not to exceed 14 consecutive days, some daysoff patterns can be immediately followed only by certain subsets of patterns. Daysoff pattern , off on days , can be followed only by patterns and patterns . Based on this rule, patterns can be followed by any pattern. Therefore, the work stretch constraints (9) are applied only to patterns . Constraints (9) make sure that if pattern is assigned , then at least one of the feasiblyfollowing patterns must also be assigned.
4. The Minimum Workforce Size
4.1. Bounds on Workforce Size
Since the primary objective is to minimize workforce size , it is necessary to initially focus on this objective and temporarily ignore the secondary objective. Therefore, at this stage, the objective function (4) is replaced by The removal of the secondary objective entails the removal of the associated binary variables and all related constraints. Therefore, the reduced IP model contains objective (14) subject only to labor demand constraints (5) and (6) weekendsoff frequency constraints (8). Next, the dual model of this reduced primal model is formulated. Subsequently, using the procedure of Alfares [18], dual solutions are cyclically enumerated, and the dominant dual solutions are identified. The dominant dual solutions identified from the simplified (10, 14) model are associated with the following lower bounds on the workforce size .(1)First, the workforce size must be greater than the labor demand on any given day; thus (2)Since each employee is assigned 10 workdays per twoweek cycle, the total persondays assigned are equal to . This assignment must be greater than the total persondays required for two weeks, which is equal to ; thus (3)The third bound can be obtained in several different ways. This bound is obtained by adding four daily labor demand constraints from (5) and (6). There are many fourday combinations (sets) that can be used to obtain this bound. When the four constraints in each set are added up, they give exactly on the lefthand side and the sum of four daily demands on the righthand side. For any , we define circular sets denoted by . Since the (10, 14) schedule has a 14day cycle, are all mod 14 cyclic sets. Referring to matrix in Table 1, each variable has at most three nonzero coefficients in the four rows of each set. For example, the sum of rows (1, 5, 8, and 12) from constraints (5) gives , while the sum of rows (2, 6, 9, and 13) from constraints (5) and (6) gives . Therefore (4)The fourth bound has to do with satisfying both weekend labor demands and weekendsoff frequency requirements. Adding up weekend labor demand constraints (rows 6, 7, 13, and 14) and weekend off constraint (row 15) of Table 1, we obtain . Therefore It is clear that the bound (15) is dominated by bounds (16) and (18). Choosing the highest of all applicable bounds and rounding up to the nearest integer value, the minimum workforce size is obtained as follows where rounded up to the nearest integer.
At this point, it should be noted that, in all remote work locations where the company applies the (10, 14) schedule, weekend labor demand never exceeds workdays labor demand; thus . Dividing the arguments in (19) by and plotting them as functions of , we obtain Figure 1. From the figure, it is clear that the last two functions in (19) are always dominated and hence not applicable for . Therefore, for , the minimum workforce size is given by
4.2. Effect of Other Objectives and Constraints on
Before proceeding further, it is essential to verify whether adding the remaining objectives and constraints can affect the minimum workforce size specified by (20). From the discussion on the different bounds on , especially (17), it is clear that the integer programming model of the (10, 14) daysoff scheduling problem is expected to have many alternative optimum solutions. Taking advantage of the existence of alternative optimum solutions, it is possible to select the optimum (minimum) solutions with the following features: (1) the minimum number of assigned daysoff patterns, (2) similar sets of active daysoff patterns for satisfying different labor demands and , and (3) feasible work stretch lengths. Work stretch constraints are satisfied as long as a feasiblyfollowing daysoff pattern (such as 12, 13, and 14) is active. Since some of the alternative solutions always contain these patterns, workstretch constraints do not affect workforce size .
4.3. Rotation Scheme for the Employees
A cyclic rotation scheme is used to make sure weekendoff and workstretch constraints are not violated and that the workload is equally distributed. Let us assume the workforce size and the number of employees assigned to each daysoff pattern are given. A feasible cyclic sequence of daysoff assignments is then determined to guarantee the work stretch constrains are satisfied. This cyclic sequence determines the order in which daysoff pattern is assigned. Since each daysoff assignment lasts for 2 weeks, each employee will be assigned daysoff pattern for weeks. Therefore, the length of the rotation cycle for all employees is weeks. During this cycle, all employees follow the same cyclic sequence but start in different weeks. Employee starts the sequence on week , which is given by
5. Assigning Employees to DaysOff Patterns
Given the values of labor demand levels for weekdays and weekends, and , first the workforce size is calculated by (20). According to the applicable function in (20), primarydual complementary slackness rules are applied on the dual solution to identify basic variables and binding constrains in the corresponding primal model. Taking advantage of the high degeneracy of the (10, 14) problem, selection of the alternative primal solutions is directed towards assigning the same minimum set of active daysoff patterns while satisfying work stretch constraints. Based on extensive numerical experimentation with different values of and , five distinct solutions are identified. These five solutions, in which the number of active daysoff patterns is equal to 4, 7, 8, 10, or 11, are presented below.
5.1. Four Active Patterns
This solution applies when under certain conditions to be discussed below. Given that , we can select a minimum of four active daysoff patterns (4, 6, 10, 14). On each weekday, three out of these four patterns are working. In the first weekend (days 6 and 7), however, only patterns 10 and 14 are working. Assuming and and ignoring dominated constraints, the applicable labor demand constraints for weekdays (5) and weekends (6) can be expressed as where Combining (22b) with (22d) gives Combining (22d) with (22a) gives Combining (22d) with (22c) gives A feasible fourpattern solution exists if the lower bound in (23a) is not greater than the upper bounds in (23b) and (23c). Considering (23a) with the upper bound in (23b) and setting we obtain This is redundant since . Therefore, (23b) is redundant and can be ignored.
Considering (23a) with the upper bound in (23c) and setting we obtain Therefore, the conditions for four active daysoff patterns (4, 6, 10, and 14) areIf the two conditions in (28a)(28b) are satisfied, then from (23a) and (23c) the bounds on are given by If the interval between the bounds in (29) contains integer values, then is set equal to the maximum integer value in this interval, that is, the upper bound rounded down. Otherwise, is set equal to the nearest integer to the interval, that is, the lower bound in (29) rounded up. Feasible assignments to the four daysoff patterns (4, 6, 10, and 14) are calculated as follows: where rounded down to the nearest integer.
The above solution has to be checked to verify that weekendoff frequency constraints are satisfied. Noting that patterns 10 and 14 belong to while patterns 4 and 6 belong to and using (8), the actual proportion of weekendcontaining daysoff breaks is given by If is approximated by in (28b), we obtain . Since (30d) gives and since and , then is approximated as shown below. Since this proportion is greater than 0.5, weekendoff frequency constraints are satisfied: Next, the fourpattern solution needs to be checked against work stretch constraints. The presence of daysoff patterns 10 and 14 guarantees the satisfaction of work stretch constraints by assuring a feasible rotation sequence. As noted before, pattern 10 may precede any pattern, while pattern 14 can either follow or precede any pattern. Many feasible cyclic rotation sequences exist for the four patterns that satisfy work stretch constraints. The only restriction is to avoid following pattern 4 immediately by pattern 10. For example, the simple sequence (461014) is feasible in terms of satisfying work stretch constraints.
5.2. Seven Active Patterns
If any of the conditions in (28a)(28b) are not satisfied, then assignment to four daysoff patterns is not feasible. Under certain conditions, assignment to seven daysoff patterns (2, 4, 6, 8, 10, 12, and 14) is feasible for both arguments of specified in (20). Assuming and and ignoring redundant constraints, the daily labor demand constraints are represented as follows: where Combining (32a) with (32c) gives Combining (32b) with (32c) gives Setting the lower bound in (33a) less than or equal to the upper bound in (33b) gives the following condition for seven active daysoff patterns: If the above condition is satisfied, then the values are set equal to the maximum integer value in or nearest to the interval defined by (33a)(33b). The remainder of is assigned to patterns 2, 8, and 12, giving priority to pattern 12 because it has a full weekend off. Assignments to all seven patterns are calculated as follows:Using (8), it can be shown that the percentage of weekendcontaining days off is approximately 75% . There are many feasible cyclic rotation sequences for the seven daysoff patterns. For example, the rotation sequence (2468101214) guarantees that work stretch limits are not exceeded.
5.3. Eight Active Patterns
If and assignment to four or seven daysoff patterns is not feasible, then it may be possible to allocate the employees among eight patterns (3, 4, 6, 7, 10, 11, 13, 14). Assuming and and ignoring redundant constraints, the daily labor demand constraints can be expressed as where Combining (36c) with (36d) gives Combining the sum of (36a) and (36b) with (36d) gives The first condition for a feasible solution with eight daysoff patterns (3, 4, 6, 7, 10, 11, 13, and 14) is Setting the lower bound in (37a) less than or equal to the upper bound in (37b) leads to the second condition for eightpattern assignment: If (38a)(38b) is satisfied, the values are set equal to the maximum integer value in or nearest to the interval defined by (37a)(37b). In assigning patterns (3, 7, 11, 13), priority is given to patterns 11 and 13 because they contain full weekends off. Assignments to the eight daysoff patterns are calculated as follows:The proportion of weekend days off can be shown to be approximately equal to 0.75. To satisfy work stretch constraints, there are many feasible cyclic rotation sequences, such as the sequence (346710111314).
5.4. Ten Active Patterns
Assignment to 10 daysoff patterns (2, 3, 4, 6, 7, 9, 10, 11, 13, 14) is applicable when and a sevenpattern solution is not feasible. Assuming , , and , the active daily labor demand constraints can be expressed as follows: where The linear combination 2 (40a) + (40c) − 2 (40d) gives The linear combination − (40a) − (40b) + 1.5 (40d) gives The first condition for a 10pattern solution is Setting the lower bound in (41a) less than or equal to the upper bound in (41b) gives the second condition: After fixing as the maximum integer value inside or nearest to the interval defined by (41a)(41b), the bounds on , the average value of are found in terms of the value. First, the labor constraints system (40a)–(40d) is written as follows: where The linear combination 2 (43a) – (43d) gives Subtracting (43d) − (43b) gives Subtracting (43d) − (43c) gives It can be shown that the upper bound in (44c) dominates the one in (44b) because if , then , or . Since (41a) specifies , then , or , which is always true for 10pattern solutions according to condition (42b).
The limits on in (44a) and (44c) are bounds on the average value of the variables , not necessarily bounds on the individual value of each variable. If the interval between the bounds in (44a) and (44c) contains integer values, then are set equal to the maximum integer value of in this interval. Otherwise, if the interval contains only one point, specifying a fractional value for , then will take different values. Giving priority to patterns 11 and 13 to maximize weekends off, assignments to the 10 daysoff patterns are calculated as follows:The proportion of weekend days off for the 10pattern schedule can be shown to be roughly 0.75, assuring weekend off constraints are satisfied. Work stretch constraints are easily satisfied by many rotation sequences, including the sequence (23467910111314).
5.5. Eleven Active Patterns
This solution is applicable when and assignment to 7 or 10 patterns is not feasible. In this case, employees are assigned to 11 daysoff patterns (1, 3, 4, 5, 6, 7, 9, 10, 11, 13, and 14). Assuming , , and , the daily labor demand constraints can be written as where The linear combination 6 (46a) + (46c) − 5 (46d) gives The linear combination −6 (46b) − (46c) + 5 (46d) gives The first condition for a feasible 11pattern solution is Setting the lower bound in (47a) less than or equal to the upper bound in (47b) leads to This condition is redundant since . After fixing the values of within the bounds in (47a)(47b), the bounds on can be calculated in terms of as follows: where Constraint (50a) dominates (50b) because if , then , but since (47a) specifies , then , or , which is always true according to (16).
The linear combination 3 (50a) − 2 (50d) gives Subtracting (50d) − (50c) gives The values of are set equal to the maximum integer value between the bounds in (51a)(51b). Giving priority to patterns 5, which has a full weekend off, employees are assigned to the 11 daysoff patterns as follows: Applying (8), it can be shown that the 11pattern schedule satisfies the weekendoff constraints because the proportion of breaks with weekends off is approximately equal to 0.75. Work stretch constraints are easily satisfied by many rotation sequences, including the sequence (1234567910111314).
The results obtained in Section 5 are summarized in Table 2. It is clear that one set of active patterns (4, 6, 10, and 14) is used consistently for all cases, while other sets such as patterns (3, 7, 11, and 13) are used to satisfy most labor demands variations.

6. Application and Example
6.1. The Scheduling Process
The optimal solution results, obtained in Sections 4 and 5 and summarized in Table 2, have been incorporated into a simple spreadsheet tool. This userfriendly tool can be easily used to find the optimal schedule directly, without having to run any optimization solver. By simply entering the weekday and weekend daily labor demands and , respectively, the spreadsheet immediately shows the workforce size, the number of daysoff patterns, and the number of employees assigned to each pattern. Because most remote area employees are technicians with low IT skills, the spreadsheet tool avoids the use of specialized optimization software. The spreadsheet is easy to use and has been well accepted by the concerned employees and their supervisors. To illustrate the calculations used to find the optimum (10, 14) schedule, a reallife example from one of the locations areas is solved below.
6.2. A RealLife Example
For a remote work site, daily labor demand is nine employees during regular weekdays and seven employees during weekends. The daysoff schedule is determined as follows.
Given using (20), Checking 4pattern condition (28b): (infeasible); checking 7pattern condition (34): (infeasible); checking 8pattern condition (38b): (feasible);calculating the bounds on for 8 patterns: using (37a): , using (37b): ,using the equation system (39a)–(39e), using (8), Following the cyclic sequence (346710111314) and using a cycle of 24 weeks, the 12 employees are rotated on the 8 daysoff patterns as shown in Table 3. The numbers inside each cell indicate the assigned daysoff patterns for the given employee in the particular week. Shaded cells indicate assignment to a daysoff pattern, that is, two weekend days off.

7. Conclusions and Extensions
A model and optimum solution have been presented for a reallife employee daysoff scheduling problem with unique features. An innovative practical approach has been used, in which simple practical solutions are developed to deal with theoretically complex issues. The problem is to assign remotearea employees to the cyclic (10, 14) daysoff schedule, primarily in order to minimize workforce size. The secondary objective is to reduce the costs of employee air transportation by minimizing the number of active daysoff patterns. The constraints include daily labor demands, weekend off frequency requirements, work stretch limitations, and fair workload distribution. This optimization problem has been modeled as a biobjective pureinteger linear programming model with both binary and general integer variables. The distinctive structure of the model and the given reallife values of problem parameters have been utilized to develop a simple solution procedure that eliminates the need to use integerprogramming solvers.
The work presented in this paper can be extended in several directions. For example, different labor demands for each day can be considered instead of two fixed demand levels ( for workdays and for weekends). Another possibility is to consider the case where weekend labor demands are higher than weekday demands. These two extensions are not applicable to the current reallife problem presented in this paper but might be applicable either in the future or in other reallife scheduling situations. Finally, integrating transportation (flight) scheduling and employee scheduling for multiple work locations presents an interesting and challenging research opportunity.
Conflict of Interests
The author declares that there is no conflict of interests regarding the publication of this paper.
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Copyright
Copyright © 2014 Hesham K. Alfares. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.