Integrated Workforce Planning Considering Regular and
Overtime Decisions
Shrikant Jarugumilli
Department of Engineering Management & Systems Engineering
Missouri University of Science & Technology, Rolla, MO - 65409, USA
Abstract
We consider the integrated workforce planning and allocation problem for a high volume manufacturing facility that operates in two non-overlapping shifts of twelve hours each day, with twenty eight shifts for a two week planing period. In such facilities, operational workforce planning is typically carried out in two steps consisting of the multi-shift assignments and the single-multi-shift allocation. The multi-multi-shift decisions balance the regular and overtime worker assignments to individual shifts based on capacity plans and worker availability during the two week planning pe-riod. The single-shift decisions ensure the worker-machine group allocations satisfy the qualification and skill-level requirements. In this paper, we present an integrated workforce planning model that makes these decisions for all the shifts during the two week planning period. Analyzing the regular and overtime allocation report provides insights in designing the cross-training programs.
Keywords
Multi-shift workforce planning, Single-shift worker allocation, Overtime planning, Integrated workforce planning.
1. Introduction and Literature Review
Managing highly skilled workforce in facilities that operate twenty-four hours a day in multiple-shifts not only presents challenges, but also opportunities in cost savings if done correctly. Workforce planning decisions for a two week planning period include the assignment of regular and overtime workers to several shifts based on the worker roster, anticipated factory loading, factory overtime policy, and the labor laws specific to a geographic region. For each shift, the number of regular workers can be obtained from the worker roster, while the number of required workers is estimated based on the anticipated factory loading determined by the capacity plans. If there is a shortage of workers in a shift, workers from other shifts are assigned as overtime workers to fill the temporary gap.
While making overtime assignments the planners should ensure that the company overtime policies and the re-gional labor laws are strictly adhered to, which specify the maximum number of overtime hours for an individual worker and the entire factory. The individual overtime policies are designed to maintain a right balance between the regular and overtime assignments for an individual worker in order to minimize the loss of motivation to work caused by fatigue. By limiting the total factory overtime, the extra overtime operational costs can drastically be reduced.
Assigning workers to shifts, becomes essential and has been extensively used in modeling application areas such as nurse scheduling, police patrolling, fire fighter scheduling and other manufacturing settings that operate 24 hours a day and 7 days a week with multiple shifts per day. The planners have the task of assigning workers to shifts based on the worker requirement and skill sets of the workers while ensuring regulatory constraints such as minimum number of days off and maximum number of work hours per week. In the literature, the variants of the shift scheduling problems have been studied under regular and compressed work week category. In [1] and [2], an optimal algorithm to solve the multiple shift workforce scheduling considering a 3 - 4 day work week is presented. In [3], a three-step method for assigning the daily work for fulltime employees working on one shift is described. In the first step, the minimal workforce is calculated such that the demand is satisfied. In the second step, the feasibility of timetable for workers is ensured by giving a minimum number of days off to each worker. Finally, in the third step, the workers are allocated to the work days. In [4], a constraint programming algorithm for construction of rotating schedules is presented.
Once the workers are assigned to a given shift, the single-shift decisions include the allocation of workers to respec-tive machine groups based on the worker qualification and other factory constraints. The various factory constraints for the single-shift worker planning include the allocation of workers to machine groups based on the qualification, efficiency, and certification matrix. The number of workers with the desired skill-level at a machine group is deter-mined by the man-machine ratio and the skill-level ratio. Further, the factory layout imposes restrictions on certain
worker-machine group allocations that should be considered in the model. With the increased attention gained by cellular manufacturing and group technology during the past decade, there exists vast literature that has focused on worker assignment problems. In [5], an IP formulation of the cellular manufacturing worker assignment problem considering worker cross-training, multiple skill levels, and multiple training levels is presented. The model considers both worker assignment and cross training decisions in the single model. Other practical aspects of cross-training, such as associated training costs and time, have been included in the model as constraints. However, the authors suggest use of alternative heuristics for large data instances. In an earlier work presented in [6], integer programming formulations are presented for assigning workers to cells and determining the training requirements for the workers. The worker assignment to cells along with the aggregate training requirement is handled by the first model, while the second model determines the individual training schedule. However, the authors report that the larger test instances could not be solved optimally. In another work, [7] present an IP to formulate the long-term allocation of workers to machines considering fluctuating demand and worker absenteeism. In [8], a two-phase hierarchical methodology to find the optimal operator assignment to manufacturing cells is proposed. A mixed integer program was developed to generate alternative operator levels and an IP model was used to achieve optimal operator assignment to the cells.
In the literature, the operational workforce planning models are classified as multi-shift assignment models and single-shift allocation models. In order to develop efficient operational workforce plans considering overtime deci-sions, it is essential to link the multi-shift planning models to the single-shift allocation models. In this paper, we present an integrated workforce planning model that makes both the multi-shift and the single-shift decisions simulta-neously for the two-week planning horizon. At the start of each shift, overtime candidate availability and capacity plans are updated before using the model. The worker-shift assignments for the first few immediate shifts are frozen, so that a fluctuation in the updated capacity plan does not impact the regular and overtime worker assignments. Based on the regular and overtime worker assignments to shifts and the worker-machine group allocations, effective cross-training programs can be designed and implemented. Some of the benefits of the integrated planning approach include: high worker utilization, efficient overtime assignments resulting in reduced operational costs and worker-shift assignment conflicts, provisions for workers to take planned leaves, and meeting the production targets for the planning horizon.
The remainder of the paper is organized as follows: Section 2 presents the Problem Description followed by prob-lem formulation of the Integrated Workforce Planning Model in Section 3. In Section 4, we present the Results from the implementations followed by the Conclusions and Future Work in Section 5.
2. Problem Description
In this paper, we consider an Assembly-Test facility of a major semiconductor manufacturer that operates in two non-overlapping shifts of twelve hours each day, with twenty eight shifts in the two-week planning period. These twenty eight shifts are classified into four shift types based on the start times as: Shift Type 1 (Day Shift starting Sunday(ST1)), Shift Type 2 (Night Shift starting Sunday(ST2)), Shift Type 3 (Day Shift starting Thursday(ST3)), and Shift Type 4 (Night Shift starting Thursday(ST4)). Each worker is assigned to one of these shift types and is considered as a regular worker for that particular shift type. A worker on an average works for forty-two hours per week during his/her regular shift, working either thirty-six hours one week followed by forty-eight hours the next week (or vice-versa), taking the day off on alternate Wednesdays as illustrated in Table 1.
Table 1: Shift Types during two-week planning horizon
Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa
Day Shift ST1 ST1 ST1 ST1 ST3 ST3 ST3 ST1 ST1 ST1 ST3 ST3 ST3 ST3
Most of the operations in this facility are labor intensive requiring workers to manage the capital intensive equip-ment. The level of automation and reliability is equipment specific, thus the number of skilled workers required at each machine group may vary accordingly. Further, a machine group can be utilized for production if and only if the minimum numbers of skilled workers are allocated to operate it. Hence, the number of workers required every shift can be estimated using the number of operating machine groups in a given shift. The variation in the worker requirement is caused due to planned and unplanned worker absenteeism or change in the number of operational machine groups based on the capacity plans, preventive maintenance schedules, setup operations, and machine failures.
Since, the duration of a shift is twelve hours, great care needs to be taken while making the overtime assignments to avoid potential conflicts between a worker’s regular and overtime shift assignments. To avoid such conflicts, the overtime workers for a given shift are selected from the other two shift types that do not operate during the same day. Also, while making overtime allocations, the planners are interested in ensuring that a day(or night) shift is filled using overtime worker from another day(or night) shift, such an allocation is referred to as primary overtime call. In case, the primary overtime call is not available, overtime for the day(or night) shift is filled using the night(or day) shift that does not operate during the same day, and is referred to as secondary overtime call.
The inputs for multi-shift and single-shift planning include: factory calendar, estimated weekly tool-count, worker roster, equipment report, process plan, worker certification, historical allocations, and worker-operation preferences. The factory calendar gives details about the operational shifts during the planning period, and the overtime (OT) candidates from the primary OT call and the secondary OT call. The estimated tool-count is based on the rough-cut capacity plan that depends on the factory loading. The worker roster gives the details about the planned and unplanned leaves for the worker. The equipment report gives specific data about the man-machine ratio and the skill-level ratio at each machine group. The process plan gives details about the critical operations. Finally, the worker certification report gives information about the worker qualification, historical allocation gives the history of worker-machine group allocations from previous shifts, and the worker-operational stage preference gives the preference of an individual worker to perform a given operation.
Once the regular and overtime workers are assigned to the shifts, the next task is to allocate these workers to machine groups for all the shifts during the two week planning horizon. The worker-machine group allocations for a single-shift are based on the detailed capacity and process plans. In a facility with a series of operational stages, often there exist bottlenecks that control the rate of production; these operational stages are referred to as critical operations. Hence, worker allocation to such operational stages takes priority over the other operational stages in the facility. Each machine group, based on its reliability and criticality, requires a minimum number of workers with specific skill levels. Based on these rules, along with the allocation rules, the worker requirement for a desired skill level and qualification at a machine group is determined and is assumed to be constant for a shift. At a given operational stage, the worker requirement based on the skill-level varies based on the reliability of the machine group. In some real-world scenar-ios, the shift-supervisor has to either allocate workers to machine groups manually due to considerations beyond the mathematical models or reallocate a group of workers to a set of machine groups due to an unexpected event, e.g., tool failure or unavailability of WIP. In such cases, it is essential to allocate the workers to the remaining machine groups optimally; we refer to such scenarios as partial allocations, which is presented in the next section.
3. Integrated Workforce Planning Model
The integrated workforce planning model considers both the overtime planning decisions and the worker machine-group allocation decisions simultaneously. This model can be used at least once at the beginning of every shift and in case, there is a change in the capacity plan for future shifts the user has the flexibility to reallocate the regular and overtime workers to the shifts as required. However, this flexibility might also cause last minute changes to the over-time requests for the immediate shifts that follow in the planning horizon. Thus to avoid such situations, the allocation of regular and overtime workers to the shifts that immediately follow the current shift are frozen using the partial allocation constraints. This strategy offers the integrated model both the flexibility and robustness in worker planning during the two-week planning horizon. Further, the overtime constraint parameters are adjusted and automatically updated every time the model is used.
Notation: Set Indices
i∈ {1, 2, . . . , I} the set of workers;
n∈ {1, 2, . . . , N} the set of operational stages;
r∈ {1, 2, . . . , R} the set of machine groups at an operational stage; l∈ {1, 2, . . . , L} the set of skill levels;
k∈ {1, 2, . . . , K} the set of shifts; Decision Variables
Xlk
irn: is the percentage of the shift duration for which a regular worker i with skill level l is allocated at machine group
rat an operational stage n during shift k; OTlk
irn: is the percentage of the shift duration for which an overtime worker i with skill level l is allocated at machine
group r at an operational stage n during shift k;
Zirnlk =
1 if regular worker i with skill-level l is assigned to the machine group r at operational stage n during shift k, 0 otherwise;
Yirnlk=
1 if overtime worker i with skill-level l is assigned to the machine group r at operational stage n during shift k, 0 otherwise;
Uirnlk =
1 if the worker allocation at a machine group exceeds the minimum allowable threshold limit, 0 otherwise;
Deviational Variables
sk+/−lrn : is the deviational variable indicating the excess / shortage of workers with skill level l at a given machine group rand operational stage n during shift k;
Parameters
clkirn: is the preferential cost coefficient of a regular worker i with skill level l to operate a machine group r at an operational stage n during a given shift k;
colkirn: is the preferential cost coefficient of an overtime worker i with skill level l to operate a machine group r at an operational stage n during a given shift k;
pk+/−lrn : is the cost coefficient of the deviational variable sk+/−lrn ;
Rlkrn: is the worker requirement for skill level l at a machine group r at an operational stage n during a given shift k; τki: is the maximum number of operations a regular worker can be assigned during a given shift k;
∂ki: is the maximum number of operations an overtime worker can be assigned during a given shift k; ωlkirn: is the minimum amount of time a worker can be allocated to a given operation during a given shift k; ξi: is the maximum allowable overtime hours for an individual worker i during the two week period;
ξf actory: is the maximum allowable overtime hours for all workers in the factory during the two week period;
ϕlkirn: is the percentage of the shift duration for which the worker i with skill-level l is partially allocated to machine group r at operational stage n during a given shift k;
Objective Function: Minimize
∑
l
∑
i∑
r∑
n∑
k(clkirn.Xirnlk) +
∑
l
∑
i∑
r∑
n∑
k(colkirn.OTirnlk) +
∑
l
∑
r∑
n∑
k (pk+lrn.sk+lrn) +∑
l∑
r∑
n∑
k (pk−lrn.sk−lrn) (1) Subject to:∑
i (Xirnlk+ OTirnlk) + slrnk−− sk+lrn= Rlkrn, ∀l, r, n, k (2) Zirnlk ≥∑
l∑
n∑
r Xirnlk, ∀i, k (3)∑
l∑
n∑
r Zirnlk ≤ τk i, ∀i, k (4) Yirnlk ≥∑
l∑
n∑
r OTirnlk, ∀i, k (5)∑
l∑
n∑
r Yirnlk ≤ ∂k i, ∀i, k (6)∑
l Xirnlk ≤ 1, ∀i, l, k (7)∑
l OTirnlk≤ 1, ∀i, l, k (8)Uirnlk ≤ Xirnlk.(1/(ωlkirn)), ∀i, l, r, n, k (9)
Xirnlk ≤ M.Uirnlk, ∀i, l, r, n, k (10)
Uirnlk ≤ OTlk
irn.(1/(ωlkirn)), ∀i, l, r, n, k (11)
OTirnlk≤ M.Ulk irn, ∀i, l, r, n, k (12)
∑
l∑
i∑
r∑
n∑
k OTirnlk≤ ξf actory−∑
l∑
i∑
r∑
n k−1∑
k=k‘ OTirnlk (13)∑
l∑
r∑
n∑
k OTirnlk≤ ξi−∑
l∑
r∑
n k−1∑
k=k‘ OTirnlk, ∀i (14)ϕlkirn≤ Xirnlk ≤ 1, ∀i, l, r, n, k (15)
ϕlkirn≤ OTirnlk≤ 1, ∀i, l, r, n, k (16)
0 ≤ Xirnlk ≤ 1, ∀i, l, r, n, k (17)
0 ≤ OTirnlk≤ 1, ∀i, l, r, n, k (18)
sk−lrn, sk+lrn≥ 0, ∀i, l, r, n, k (19)
Zlkirn,Yirnlk,Uirnlk ∈ {0, 1}, ∀i, r, n, k, l (20)
The objective function in Equation (1) minimizes the penalty cost of deviation in the number of workers allocated with a skill level l, from the actual worker requirement at the machine group r at a given operational stage n; and the cost of allocation of regular and overtime workers to the machine groups for all the shifts during the planning horizon. The cost coefficients of the deviational variables are assigned based on the criticality of the operational stage and the reliability of the machine group, such that the deviation between the allocated and the required number of workers at the critical operation is much greater than those at the non-critical operation. Constraint set (2) matches the worker requirement for all machine groups at each operational stage for every shift with the regular and OT workers. Con-straint sets (3) and (4) restrict the movement of the regular workers to a limited number of operations during a given shift. Constraint sets (5) and (6) restrict the movement of the overtime workers to a limited number of operations
during a given shift. Constraint set (7) ensures that the number of hours a regular worker is allocated during a given shift is less than the shift duration. Constraint set (8) ensures that the number of hours an OT worker is allocated during a given shift is less than the shift duration. Constraint sets (9) and (10) ensure that the allocation of the regular worker to a machine group during a given shift exceeds the minimum threshold allocation duration set by the shift supervisor. Constraint sets (11) and (12) ensure that the allocation of the overtime worker to a machine group during a given shift exceeds the minimum threshold allocation duration set by the shift supervisor. Constraint set (13) ensures that the total number overtime hours for all workers does not exceed the factory overtime limit. Constraint set (14) ensures that the total overtime assignment for each individual worker does not exceed the individual overtime limit. Constraint sets (15) and (16) are used for setting the partial allocations for the regular and OT workers respectively. Constraint sets (17) and (18) impose the non-negativity and the upper bounds for the allocations during a given shift for the regular and overtime workers respectively. Constraint set (19) imposes the non-negativity restrictions on the deviational variables. Constraint set (20) imposes the binary restrictions on the auxiliary decision variables.
4. Results
In this section, we present the results for a data instance obtained from one of the Assembly-Test facility of a semi-conductor manufacturing company. We consider a small portion of the facility consisting of 26 regular workers/shift type, ten operational stages and three machine groups at each stage. The worker qualification and roster, skill-level requirements, individual and factory overtime, shift types, and capacity plans for each shift during the planning hori-zon is presented in [9]. For any given shift, the worker requirement is fulfilled using the regular workers(R), primary overtime call(P), and secondary overtime call(S) based on their availability and qualification. Workers qualified for a given operational stage are classified as Skill Level 1 or Skill Level 2 workers. Each qualified worker has a preference on a scale of 1 − 3 to work at an operational stage, where 1 denotes most preferred operational stage and 3 denotes the least preferred operational stage. Based on the skill-levels and the worker preference for an operational stage, the technological cost coefficients for the decision variables (regular and overtime) are assigned. The worker requirement based on the skill levels 1 and 2, at each operational stage for the planning horizon consisting of 8 shifts is listed in the Tables 2 and 3, respectively. Operational stages 3 and 5 have been identified as critical operations and the worker allocation at these operational stages cannot be violated under any circumstances.
The results generated by the integrated model determines the fraction of the shift a worker is allocated to a given machine group, along with any shortages at a given operational stage during the planning horizon. Table 4 presents the number of regular workers, primary OT call, and secondary OT call with Skill Levels 1 and 2 needed to fulfill the worker requirements for the eight shifts. Table 5 presents a sample of the detailed worker-operational stage allocation based on the skill-levels 1 and 2 for the first shift. The detailed results of specific worker-machine group allocation for each of the eight shifts is presented in [9].
Analyzing the results in Tables 4 and 5 the decision makers can identify the prospective set of workers and set of operational stages for which cross-training might have a positive impact. The set of workers with lower utilization can be considered as candidates for the cross-training programs. Also, the set of operational stages that require frequent allocation of overtime workers can be included in the cross-training programs. Hence, this model also helps decision makers to identify the set of workers and operational stages to be included in the cross-training programs.
Table 2: Skill 1 Worker Requirement Operational Stage
Shift 1 2 3 4 5 6 7 8 9 10 Total Requirement
1 1.50 0.30 1.20 1.60 1.40 2.10 2.40 1.00 0.90 0.80 13.20 2 1.47 0.29 1.18 1.57 1.37 2.06 2.35 0.98 0.88 0.78 12.94 3 1.10 0.22 0.88 1.18 1.03 1.54 1.76 0.74 0.66 0.59 9.70 4 1.67 0.33 1.33 1.78 1.55 2.33 2.66 1.11 1.00 0.89 14.65 5 1.28 0.26 1.02 1.36 1.19 1.79 2.04 0.85 0.77 0.68 11.22 6 0.90 0.18 0.72 0.96 0.84 1.26 1.44 0.60 0.54 0.48 7.92 7 0.98 0.20 0.78 1.04 0.91 1.37 1.56 0.65 0.59 0.52 8.58 8 1.05 0.21 0.84 1.12 0.98 1.47 1.68 0.70 0.63 0.56 9.24
Table 3: Skill 2 Worker Requirement Operational Stage
Shift 1 2 3 4 5 6 7 8 9 10 Total Requirement
1 2.00 0.40 1.60 2.13 1.86 2.79 2.19 1.00 0.50 0.30 14.77 2 1.96 0.39 1.56 2.09 1.82 2.74 3.13 1.30 1.17 1.04 17.20 3 1.47 0.29 1.17 1.56 1.37 2.05 2.35 0.98 0.88 0.78 12.90 4 2.21 0.44 1.77 2.36 2.07 3.10 3.54 1.48 1.33 1.18 19.49 5 1.70 0.34 1.36 1.81 1.58 2.37 2.71 1.13 1.02 0.90 14.92 6 1.20 0.24 0.96 1.28 1.12 1.68 1.92 0.80 0.72 0.64 10.53 7 1.30 0.26 1.04 1.38 1.21 1.82 2.07 0.86 0.78 0.69 11.41 8 1.40 0.28 1.12 1.49 1.30 1.96 2.23 0.93 0.84 0.74 12.29
Table 4: Regular, Primary OT, and Secondary OT Worker Allocation
Skill Level 1 Skill Level 2
Shift Regular Primary OT Secondary OT Total Regular Primary OT Secondary OT Total
1 9.90 2.00 1.30 13.2 10.68 1.90 2.19 14.77 2 8.50 2.31 2.13 12.94 10.2 4.30 2.70 17.20 3 9.00 0.70 0.00 9.70 10.70 2.20 0.00 12.9 4 9.40 2.15 3.10 14.65 10.30 6.30 2.89 19.49 5 9.65 1.57 0.00 11.22 11.0 2.10 1.82 14.92 3 7.92 0.00 0.00 7.92 10.46 0.00 0.00 10.46 7 8.58 0.00 0.00 8.58 10.50 0.91 0.00 11.41 8 9.24 0.00 0.00 9.24 11.0 1.29 0.00 12.29
Table 5: Worker-Machine Group Allocation for Shift 1
Operation Skill 1 Worker Id. Skill 2 Worker Id.
Requirement [Allocation][Shift] Requirement [Allocation][Shift]
1 1.50 9[1.00][R] 2.00 1[1.00][R] 17[0.50][R] 22[1.00][R] 2 0.30 100[0.30][S] 0.40 8[0.40][R] 3 1.20 5[0.20][R] 1.60 25[1.00][R] 20[1.00][R] 60[0.60][P] 4 1.60 8[0.60][R] 2.13 12[1.00][R] 85[1.00][S] 3[0.13][R] 65[1.00][P] 5 1.40 4[0.40][R] 1.86 23[1.00][R] 56[1.00][P] 3[0.86][R] 6 2.10 7[0.10][R] 2.79 13[1.00][R] 26[1.00][R] 14[1.00][R] 53[1.00][P] 24[0.79][R] 7 2.40 10[1.00][R] 2.19 95[1.00][S] 11[1.00][R] 79[1.00][S] 16[0.40][R] 100[0.19][S] 8 1.00 6[1.00][R] 1.0 2[1.00][R] 9 0.90 7[0.90][R] 0.5 17[0.50][R] 10 0.80 5[0.80][R] 0.3 60[0.30][P]
5. Conclusions and Future Work
In this paper, we presented an integrated workforce planning model that generates both multi-shift worker-shift assignments and single-shift worker-machine group allocations for a two-week planning period based on overtime, qualification and skill-level constraints. The model presented in the paper, helps the decision makers to identify and assign overtime workers to shifts with worker shortages and allocate workers to machine groups based on qualification and skill-level constraints. The output reports help the decision makers to identify the set of operational stages and workers for designing effective cross-training programs. These cross-training programs can help in the reduction of overtime allocation and worker idle time due to uncertainties such as: tool failure, fluctuations in capacity plans, and unplanned worker absenteeism. Further, the model also has provisions for making partial allocations for any shift during the planning horizon.
The integrated workforce planning model presented in this paper does not consider the implementation of the cross-training programs during the two-week planning period. Making provisions for implementation of cross-training programs is an interesting extension. Other interesting extensions include modeling the overlapping shift structure and the use of contract workers to meet the temporary shortage of workers during the planning horizon.
Acknowledgements
The author would like to thank personnel from Intel Corporation for providing data and insights. Also, the author thanks the Intel Research Council for funding this project.
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