Traditional and fuzzy goal programming approaches for resource dependent assembly line balancing problem

Yakup Atasagun; Alper Döyen; Gözde Can Atasagun

doi:10.3934/naco.2023003

Article Contents

2024, Volume 14, Issue 1: 214-226. Doi: 10.3934/naco.2023003

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Traditional and fuzzy goal programming approaches for resource dependent assembly line balancing problem

Konya Technical University, Industrial Engineering Department, Konya, Turkey

^*Corresponding author: Yakup Atasagun
^*Corresponding author: Yakup Atasagun

The paper is handled by Gerhard-Wilhelm Weber as guest editor.

Received: March 2022

Revised: December 2022

Early access: February 6, 2023

Published online: February 6, 2023

An earlier version of this paper including only the traditional goal programming approach, has been published at Proceedings of 2nd International Conference on Applied Mathematics in Engineering (ICAME'21) and has been selected to be evaluated for possible publication in a Special Issue by Numerical Algebra, Control and Optimization NACO.

Abstract / Introduction Full Text(HTML) Figure(1) / Table(4) Related Papers Cited by

Abstract

In this study, two goal programming models are proposed for balancing resource dependent assembly lines with precise and fuzzy goals in order to provide flexibility for decision makers based on their decision environment and preferred priorities. Three conflicting goals, namely, total number of utilized workstations, cycle time and total cost of additional resources (equipment and assistant workers) are considered. The proposed models are validated on illustrative examples and scenario analyses are performed with different priority levels of the goals. The results show that the proposed goal programming formulations are valid and useful for balancing resource dependent assembly lines.

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Mathematics Subject Classification: Primary: 90B50; Secondary: 90C29.

Citation:

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Figure 1. Final Solution of the Illustrative Problem (Traditional GP)

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Table 1. Illustrative Problem Data

$ i $	$ IP_i $	Task Completion Times					$ i $	$ IP_i $	Task Completion Times
		Assistant	Equipment							Assistant	Equipment
		Assistant	No	1	2	3			No	Assistant	1	2	3
1	-	Yes					6	2, 5	Yes
1	-	No	5			4	6	2, 5	No	8	6		6
2	-	Yes	7				7	6	Yes
2	-	No	10	7	8		7	6	No	7
3	-	Yes	13				8	7	Yes
3	-	No					8	7	No	4			3
4	1	Yes	3				9	3, 7	Yes	5
4	1	No	5				9	3, 7	No
5	4	Yes					10	9	Yes
5	4	No	6				10	9	No	13

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Table 2. Final Results of the Illustrative Problem (Traditional GP)

Workstation	Assigned tasks	Workload	Assigned equipment	Assistant	Cost of additional resources
1	1, 3	18	-	Yes	6
2	2, 4, 5	18	$ \# $1	No	3.3
3	6, 7, 8	16	$ \# $3	No	1.5
4	9, 10	18	-	Yes	6
Total cost of additional resources					16.8

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Table 3. Scenario Analysis by Changing the Priority Levels of the Goals (Traditional GP)

Scenario	Priority Order	$ d^+ $	$ f^+ $	$ g^+ $	Unsatisfied Goals	Total Number of Workstations	Cycle Time	Cost of additional resources
1	G1-G2-G3	0	3	0.8	G2, G3	4	18	16.8
2	G1-G3-G2	0	4	0	G2	4	19	15
3	G2-G1-G3	1	0	2.3	G1, G3	5	15	18.3
4	G2-G3-G1	2	0	0	G1	6	15	13.5
5	G3-G1-G2	0	4	0	G2	4	19	15
6	G3-G2-G1	2	0	0	G1	6	15	13.5

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Table 4. Scenario Analysis by Changing the Priority Levels of the Goals (Fuzzy GP)

Scenario	Priority Order	$ d^- $	$ h^- $	$ g^- $	Total Number of Workstations	Cycle Time	Cost of additional resources
1	G1-G2-G3	0	0.8	0.38	4	18	16.8
2	G1-G3-G2	0	1	0	4	19	12.3
3	G2-G1-G3	0.67	0	0.2	6	14	15
4	G2-G3-G1	1	0	0	7	14	12
5	G3-G1-G2	0	1	0	4	19	12.3
6	G3-G2-G1	1	0	0	7	14	12

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