Article Contents
Article Contents

# Cost of fairness in agent scheduling for contact centers

• We study a workforce scheduling problem faced in contact centers with considerations on a fair distribution of shifts in compliance with agent preferences. We develop a mathematical model that aims to minimize operating costs associated with labor, transportation of agents, and lost customers. Aside from typical work hour-related constraints, we also try to conform with agents' preferences for shifts, as a measure of fairness. We plot the trade-off between agent satisfaction and total operating costs for Vestel, one of Turkey's largest consumer electronics companies. We present insights on the increased cost to have content and a fair environment on several agent availability scenarios.

Mathematics Subject Classification: Primary: 90B90; Secondary: 90-10.

 Citation:

• Figure 1.  Forecasted Intraday Call Volumes

Figure 2.  Required and Working Agents

Figure 3.  Demand Volumes

Figure 4.  Preference Scores

Figure 5.  Distribution of Agents in Shifts

Figure 6.  Cost and Fairness Values for P1

Figure 7.  Total Understaffed and Working Hours for P1

Figure 8.  Cost and Fairness Values for P2

Figure 9.  Total Understaffed and Working Hours for P2

Table 1.  Model Inputs and Outputs

 Inputs Outputs Demand for a Theoretical Day Scheduling/Planning Horizon Number of Agents in Each Shift Time Intervals and Possible Shifts Total Employee Cost Break Time Distribution Rules Total Shuttle Cost Shuttle (Transportation) Costs Understaffed Hours Agent Wages and Undesirability Cost of Shifts Agent-Shift Assignments Cost of Understaffing Total Satisfaction Score Shift Preference Scores of Agents Fairness Score Distribution Fairness Bounds

Table 2.  Inputs and a Sample Assignment

Table 3.  Break Time (Effectiveness) Factor

Table 4.  Preference Scoring Sample

 $\textbf{Preference Priority}$ Preference Score First 8 Second 4 Third 2 Fourth 1 Not preferred 0

Table 5.  Preference Matrix Sample

 $\textbf{agents}$ shift 1 shift 2 shift 3 shift 4 shift 5 shift 6 shift 7 shift 8 agent 1 8 4 0 0 1 0 0 2 agent 2 8 4 0 0 0 0 2 1 agent 3 4 8 0 2 0 0 0 1 agent 4 4 2 0 1 0 0 8 0 agent 5 4 2 0 1 0 8 0 0 agent 6 2 1 8 4 0 0 0 0 agent 7 1 2 0 4 8 0 0 0 agent 8 0 0 1 2 4 0 0 8 agent 9 0 8 0 4 2 0 0 1

Table 6.  Model Parameters

 Description Parameter Week Index in Planning Horizon $w$ Shift Index $s$ Time Interval Index in a Day $t$ Agent Index $i$ Individual Fairness Lower Limit $h$ Overall Fairness Lower Limit $H$ Weekly Cost Per Agent $c^\text{agent}$ Cost Estimation for 1% of Understaffing $c^{\text{understaff}}$ Cost of Shift Undesirability $c^{\text{undesirable}}_s$ Average Per Person Arrival Shuttle Cost for Intervals $c^{\text{v}}_t$ Average Per Person Departure Shuttle Cost for Intervals $c'^{\text{v}}_t$ Break Time Factor (Effectiveness) of Agent in Intervals of Shift $a^s_t$ Demand in Intervals of Weeks $d^w_t$ Agents' Preference Value of Shifts $p_{is}$ Starting Interval Binary of Shifts $s_t^s$ Ending Interval Binary of Shifts $e_t^s$

Table 7.  Decision Variables

 Description Notation Binary Variable of Agents' Shift in Weeks $Y_{isw}$ Individual Average Fairness Score Auxiliary Variable of Working Weeks $A_{iw}$ Individual Average Weekly Fairness Score Variable $Z_i$ Number of Agents Variable in Shifts of Weeks $X^w_s$ Understaffed Level Variable in Intervals $U^w_t$

Table 8.  Shift Descriptions

Table 9.  Shuttle Costs

Table 10.  Parameter Values

 Description Parameter Value Number of Weeks $|W|$ 4 Number of Shifts $|S|$ 17 Number of Time Intervals $|T|$ 24 Number of Agent $|I|$ 150 Agent Cost $c^{\text{agent}}$ ＄200 Understaffing Coeffcient $c^{\text{understaff}}$ ＄10

Table 11.  Fairness Distribution

 $Z_i$ Range/$h$ 0 1 2 3 4 5 6 7 8 [0-1) 83 0 0 0 0 0 0 0 0 [1-2) 19 62 0 0 0 0 0 0 0 [2-3) 35 68 120 0 0 0 0 0 0 [3-4) 8 9 14 89 0 0 0 0 0 [4-5) 3 8 12 61 130 0 0 0 0 [5-6) 0 1 3 0 14 81 0 0 0 [6-7) 0 2 1 0 6 68 149 0 0 [7-8) 0 0 0 0 0 0 1 77 0 [8] 2 0 0 0 0 1 0 73 150 Total Satisfaction Score 178 289 370 519 640 824 904 1123 1200 Cost (in ＄1000) 139 139 139 139 140 143 157 522 618

Table 12.  Comparison of P1 and P2

 Overall Fairness Score 640 824 904 1123 P1 Cost (＄1000) 140 143 157 522 P2 Cost (＄1000) 139 139 141 304 (P1 Cost - P2 Cost) / P2 Cost 0.7% 2.3% 10.9% 71.5%

Table 13.  Fairness Distribution for P2

 $Z_i$ Range/$H$ 640 824 904 1123 [0-1) 23 16 17 0 [1-2) 10 7 6 2 [2-3) 25 9 7 3 [3-4) 5 4 2 0 [4-5) 19 17 7 11 [5-6) 11 6 3 0 [6-7) 17 20 12 1 [7-8) 2 5 12 0 [8] 38 66 84 133 Cost (in ＄1000) 139 139 141 304

Table 14.  Available Shifts for Agent Groups

 Shifts Unrestricted Pregnant Disabled Student Distant 1 $\bullet$ $\bullet$ $\bullet$ $\bullet$ 2 $\bullet$ $\bullet$ $\bullet$ 3 $\bullet$ $\bullet$ $\bullet$ 4 $\bullet$ 5 $\bullet$ $\bullet$ 6 $\bullet$ 7 $\bullet$ 8 $\bullet$ 9 $\bullet$ 10 $\bullet$ 11 $\bullet$ 12 $\bullet$ 13 $\bullet$ 14 $\bullet$ 15 $\bullet$ $\bullet$ 16 $\bullet$ $\bullet$ $\bullet$ 17 $\bullet$ $\bullet$ $\bullet$

Table 15.  Number of Agents in Groups

 Scenario Unrestricted Pregnant Disabled Student Distant high restriction 30 20 20 20 60 med. restriction 90 10 10 10 30 low restriction 120 5 5 5 15 no restriction 150 0 0 0 0

Table 16.  Cost of Restriction

 no rest. low rest. medium rest. high rest. total cost (＄1000) 139 139 139 159 cost gap - 0% 0% 14%

Table 17.  Cost of Fairness Levels with Restriction in ＄1000

 no rest. low rest. med. rest. high rest. h=4 140 140 140 193 h=5 143 144 155 224 h=6 157 160 176 243

Table 18.  Efficient Solutions for Fairness Levels with Restriction

 Cost Acceptable Solution 1 Solution 2 Tolerance Cost (＄1000) 0% 139 h=0|medium rest. scenario N/A 1% 140 h=4|medium rest. scenario 2% 141 3% 143 h=5|no rest. scenario 4% 144 5% 146 10% 153 15% 160 h=5|medium rest. scenario h=6|low rest. scenario

Table 19.  Solution Times for Instances

 Restrictions Preferences Bound $h$ for P1 $H$ for P2 Time (sec) None Individual – P1 0 3 1 7 2 17 3 1257 4 117 5 126 6 49 7 14 8 5 Overall – P2 640 12 824 18 904 16 1123 10 Low Individual – P1 0 5 4 20 5 30 6 20 Medium 0 3 4 12 5 14 6 9 High 0 2 4 7 5 9 6 6
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