ORGANIZING BUSINESS FORUMS WITH INTEGER LINEAR PROGRAMMING

Pessanha, José Francisco Moreira; Santos, Narcisa Maria Gonçalves dos

doi:10.1590/0101-7438.2019.039.03.0379

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Articles • Pesqui. Oper. 39 (3) • Sep-Dec 2019 • https://doi.org/10.1590/0101-7438.2019.039.03.0379 copy

ORGANIZING BUSINESS FORUMS WITH INTEGER LINEAR PROGRAMMING

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Business associations often promote forums between entrepreneurs. One strategy for establish contacts among participants is to organize them into small groups assigning them to tables so that participants in the same group can present their companies and projects. After an interval, a new round begins with new groups in order to establish new contacts. The repetition of this strategy allows each participant to expand his/her business network, but the repeated contacts between participants should be avoided. We present an Integer Linear Programming model that minimizes the repeated contacts when the participants are successively assigned to new groups. The model was implemented in R programming language and it has been applied to organize business forums. In order to illustrate the model application, this paper shows the results from a case study with 108 participants.

Keywords:
integer programming; business networking; business forums

108 participants	110 participants	111 participants	112 participants	114 participants
$1 x 108$	$1 x 110$	$1 x 111$	$1 x 112$	$1 x 114$
$2 x 54$	$2 x 55$	$3 x 37$	$2 x 56$	$2 x 57$
$3 x 36$	$5 x 22$		$4 x 28$	$3 x 38$
$4 x 27$	$10 x 11$		$7 x 16$	$6 x 19$
$6 x 18$			$8 x 14$
$9 x 12$

Tables m	Participants per table p	Duration of each round (minutes) $d = 3 p$	*Number of rounds s = f loor(180/d)*	Total duration ds (minutes)	Contacts performed by each participant $s (p - 1)$
12	9	27	6	162	48
18	6	18	10	180	50
11	10	30	6	180	54
14	8	24	7	168	49
16	7	21	8	168	48

Participants	108	108	110	112	112
Tables	12	18	11	14	16
Participants per table	9	6	10	8	7
Number of rounds	6	10	6	7	8
Elapsed time to achieve the optimal solution (seconds)	369	740	370	380	483
Repeated contacts up to round 2	0	0	0	0	0
Repeated contacts up to round 3	0	0	0	0	0
Repeated contacts up to round 4	5	0	17	0	0
Repeated contacts up to round 5	23	1	57	4	0
Repeated contacts up to round 6	58	1	148	16	2
Repeated contacts up to round 7		2		49	11
Repeated contacts up to round 8		5			27
Repeated contacts up to round 9		13
Repeated contacts up to round 10		27

Round	Number of Binary variables $p (m - s + 1)$	Number of Integer variables $(s - 1) (m - 1) m$	Number of variables	Number of constraints $m + n + (s - 1) (m - 1) m$	Elapsed time to solve the ILPP (seconds)
s=2	1188	132	1320	252	<1
s=3	1080	264	1344	384	1
s=4	972	396	1368	516	121
s=5	864	528	1392	648	121
s=6	756	660	1416	780	123

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[1] *Corresponding author: José Francisco Moreira Pessanha - E-mail: professorjfmp@hotmail.com