Cost of fairness in agent scheduling for contact centers

Onur Şimşek; O. Erhun Kundakcioglu

doi:10.3934/jimo.2021001

Article Contents

2022, Volume 18, Issue 2: 872-896. Doi: 10.3934/jimo.2021001

This issue Previous Article Coordinating a supply chain with demand information updating Next Article A model and two heuristic methods for The Multi-Product Inventory-Location-Routing Problem with heterogeneous fleet

Cost of fairness in agent scheduling for contact centers

Onur Şimşek and
O. Erhun Kundakcioglu^,

Department of Industrial Engineering, Ozyegin University, Istanbul, 34794, Turkey

^* Corresponding author: erhun.kundakcioglu@ozyegin.edu.tr
^* Corresponding author: erhun.kundakcioglu@ozyegin.edu.tr

Received: November 30, 2019

Revised: September 30, 2020

Early access: December 2020

Published: March 2022

Abstract Full Text(HTML) Figure(9) / Table(19) Related Papers Cited by

Abstract

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.

Keywords:

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

Citation:

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Figure 1. Forecasted Intraday Call Volumes

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Figure 2. Required and Working Agents

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Figure 3. Demand Volumes

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Figure 4. Preference Scores

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Figure 5. Distribution of Agents in Shifts

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Figure 6. Cost and Fairness Values for P1

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Figure 7. Total Understaffed and Working Hours for P1

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Figure 8. Cost and Fairness Values for P2

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Figure 9. Total Understaffed and Working Hours for P2

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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

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Table 2. Inputs and a Sample Assignment

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Table 3. Break Time (Effectiveness) Factor

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Table 4. Preference Scoring Sample

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

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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

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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 $

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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 $

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Table 8. Shift Descriptions

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Table 9. Shuttle Costs

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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

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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

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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%

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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

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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 $

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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

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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%

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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

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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

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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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