A heuristic approach to optimize the production scheduling of fruit-based beverages

Toscano, Alyne; Ferreira, Deisemara; Morabito, Reinaldo; Trassi, Murilo

doi:10.1590/0104-530X4869-20

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ORIGINAL ARTICLE • Gest. Prod. 27 (4) • 2020 • https://doi.org/10.1590/0104-530X4869-20 copy

A heuristic approach to optimize the production scheduling of fruit-based beverages

Abordagem heurística para otimizar a programação da produção de bebidas à base de frutas

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract:

In this paper, the fruit-based beverage production scheduling problem is studied. The aim is to determine the lot sizing and scheduling production, optimizing inventory costs, backorders and cleanings. Fruit-based beverage production processes typically consist of two production stages, beverage preparation and pasteurization/filling/beverage packaging, including the following characteristics: an intermediate inventory in the second stage, temporal cleanings in both stages and the need for synchrony between the two stages. An effective heuristic based on a two-phase mathematical model is proposed to solve the problem in situations where item changeovers in the tanks (Stage 1) and in the lines (Stage 2) are sequence-dependent on the production. In the first stage, the heuristic searches for feasible solutions, while the second is an improvement stage. Computational tests were run using data based on real instances of a beverage company in two variants of the heuristic and both are promising because they are able to find good solutions to the problem in computational times acceptable in practice.

Keywords:
Production scheduling; Fruit-based beverages; Lot sizing and scheduling; Heuristics

Set	Instances (I1/I2/I3)	Modifications
01	I1-01/I2-01/I3-01	Instances based on the company’s data
02	I1-02/I2-02/I3-02	Filling speeds doubled
03	I1-03/I2-03/I3-03	Filling speeds tripled
04	I1-04/I2-04/I3-04	Filling speeds doubled and $C a p_{m t}$ reduced by 50%
05	I1-05/I2-05/I3-05	$C a p_{m t}$ was reduced by 10%
06	I1-06/I2-06/I3-06	$C a p_{m t}$ was reduced by 15%
07	I1-07/I2-07/I3-07	$C a p_{m t}$ was reduced by 20%
08	I1-08/I2-08/I3-08	For period $t$ with a smaller demand, $C a p_{m t} = 0$ , for all $m$
09	I1-09/I2-09/I3-09	For period $t$ with a smaller demand, $C a p_{1 t} = 0$
10	I1-10/I2-10/I3-10	For period $t$ with a smaller demand, $C a p_{2 t} = 0$
11	I1-11/I2-11/I3-11	For period $t$ with a larger demand, $C a p_{m t}$ was reduced by 50%, for all $m$
12	I1-12/I2-12/I3-12	$U B_{j}$ was reduced by 25%
13	I1-13/I2-13/I3-13	$U B_{j}$ was doubled
14	I1-14/I2-14/I3-14	$U B_{j}$ was doubled, we considered only one filling line with a doubled filling speed

Set of Instances	FIHRMS-S		FIHRMS-R
Set of Instances	Objective Function	Time (seconds)	Objective Function	Time (seconds)
1	709,701.78	2,253.70	786,091.00	1,401.60
2	23.67	601.01	23.67	600.85
3	23.67	600.91	23.67	600.75
4	2,320,791.67	1,421.55	2,420,923.36	885.80
5	4,698,305.67	2,011.11	4,476,281.86	1,800.59
6	11,344,844.55	3,601.14	12,335,577.83	1,600.43
7	21,993,070.67	2,600.92	22,145,036.98	1,400.68
8	35,486,463.11	3,000.66	36,288,029.67	1,200.41
9	6,665,317.33	1,640.48	4,741,822.50	1,223.19
10	2,458,900.39	2,800.87	2,586,598.34	1,783.41
11	16,638,709.45	3,572.59	17,247,266.67	1,200.37
12	694,423.67	2,452.33	786,091.00	1,354.07
13	786,088.00	1,482.90	413,746.08	2,276.82
14	25.00	266.60	25.00	264.22
Average	7,414,049.21	2,021.91	7,444,824.12	1,256.66

Set	FIHRMS-R				FIHRMS-S
Set	%Back	%Inv	%TC	%Cap	%Back	%Inv	%TC	%Cap
01	0.59%	0.05%	3.36%	81.69%	0.54%	0.06%	3.38%	82.47%
02	0.00%	0.00%	0.63%	47.73%	0.00%	0.00%	0.61%	47.42%
03	0.00%	0.00%	0.57%	43.13%	0.00%	0.00%	0.44%	43.43%
04	1.80%	0.00%	1.96%	89.18%	1.46%	0.01%	2.10%	89.67%
05	3.97%	3.16%	4.10%	92.97%	3.24%	0.28%	3.73%	91.65%
06	8.55%	8.12%	3.62%	88.23%	7.49%	1.16%	4.07%	96.88%
07	3.09%	6.22%	3.25%	99.00%	14.66%	1.61%	3.73%	99.78%
08	27.42%	4.57%	3.87%	99.01%	25.41%	5.25%	4.97%	99.78%
09	5.09%	1.71%	4.37%	94.10%	3.21%	1.24%	3.78%	94.63%
10	2.04%	0.25%	3.95%	92.06%	1.57%	0.37%	3.90%	92.73%
11	12.27%	15.09%	3.09%	92.45%	11.49%	15.02%	3.91%	93.52%
12	0.58%	0.05%	3.34%	81.75%	0.58%	0.01%	3.51%	82.52%
13	0.64%	0.05%	3.12%	81.80%	0.35%	0.00%	3.19%	81.69%
14	0.00%	0.00%	3.33%	80.01%	0.00%	0.00%	3.33%	79.83%
Med	6.54%	2.80%	3.04%	83.08%	5.00%	1.79%	3.19%	84.00%

Universidade Federal de São Carlos Departamento de Engenharia de Produção , Caixa Postal 676 , 13.565-905 São Carlos SP Brazil, Tel.: +55 16 3351 8471 - São Carlos - SP - Brazil
E-mail: gp@dep.ufscar.br

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[1] Source: The authors.