OPTIMIZATION OF ECONOMIC INDICATORS IN A CARPENTRY COMPANY THROUGH INTEGER PROGRAMMING

Freitas, Luis Carlos de; Barros, Ana Paula da Silva

doi:10.1590/1806-908820210000019

Luis Carlos de Freitas ^**Corresponding author.

Universidade Estadual do Sudoeste da Bahia, Departamento de Fitotecnia e Zootecnia, Vitória da Conquista, BA - Brasil. E-mail: <luisfreitas@uesb.edu.br>.

http://orcid.org/0000-0002-8448-0843

Ana Paula da Silva Barros

Universidade Estadual do Sudoeste da Bahia, Programa de Pós-Graduação em Ciências Florestais, Vitória da Conquista, BA - Brasil. E-mail:<apsbarros_eng3@hotmail.com>.

http://orcid.org/0000-0002-1665-9454

*Corresponding author.

6. AUTHOR CONTRIBUTIONS

Luís Carlos de Freitas: methodological design, analysis of results, discussion of results, technical review and writing.Ana Paula da Silva Barros: data collection, bibliographic research and writing.

Table 1 Annual cost in the frames manufacturing process in the evaluated carpentry company.

Cost items of the carpentry company	Values (US$)
Labor	32,661.00
Jequitiba wood	9,833.33
Jatoba wood	14,988.88
Machinery depreciation	199.10
Machinery maintenance	3,007.20
Fuel	870.00
Administrative costs	740.52
Other inputs (nails, glue, sandpaper and energy)	841.32
Total	63,141.35

Table 2 Quantity of each assortment produced by carpentry company from Jequitiba wood (A) and Jatoba wood (B) after application of the operational research.

Rows= 9 vars = 6 No. Integer vars = 6 (all are linear) // Nonzeros = 30 Constraint nonz= 18 (12 are +- 1) Density=0.476 // Smallest and largest elements in absolute value= 0.972000E-02 1008.00 // No. <: 2 No. = : 0 No. > : 6, Obj=MAX, GUBs < = 6 // Single cols = 0		(A)
Optimal solution found at step:	6
Objective value:	54790.99
Branch count:	2
Variable	Value	Reduced Cost
X1	0.0000000E + 00	118.7000
X2	106.0000	90.74000
X3	153.0000	0.0000000E + 00
X4	576.0000	0.0000000E + 00
X5	125.0000	0.0000000E + 00
X6	48.00000	0.0000000E + 00
Row	Slack or surplus	Dual Price
OBJ	54790.99	1.000000
2	0.0000000E + 00	120.3700
3	0.1421526E - 02	0.0000000E + 00
4	0.0000000E + 00	-94.44000
5	0.0000000E + 00	-7.410000
6	0.0000000E + 00	-33.33000
7	114.0000	0.0000000E + 00
8	0.0000000E + 00	0.0000000E + 00
9	106.0000	0.0000000E + 00
Rows= 6 vars = 3 No. Integer vars = 3 (all are linear) // Nonzeros = 15 Constraint nonz= 9( 6 are +- 1) Density=0.625 // Smallest and largest elements in absolute value= 0.900000E-02 564.000 // No. < : 2 No. = : 0 No. > : 3, Obj=MAX, GUBs < = 3 // Single cols = 0		(B)
Optimal solution found at step:	7
Objective value:	32669.64
Branch count:	0
Variable	Value	Reduced
Cost
X4	432.0000	0.0000000E+00
X5	47.00000	-43.52626
X7	0.0000000E + 00	16.66375
Row	Slack or surplus	Dual Price
OBJ	32669.64	1.000000
2	85.00000	0.0000000E+00
3	0.2819580E - 02	0.0000000E+00
4	0.0000000E+00	0.0000000E+00
5	47.00000	0.0000000E+00
6	0.0000000E+00	0.0000000E+00

Table 3 Annual revenue before and after operational research modeling using Linear Integer Programming.

Products	Real DataStandard production					Data after operational research modeling using Linear Integer Programming (LIP)
Products	Qty.	Mean Volume (m³)	Total Volume	Average price Unit. (US$)	Annual Revenue (US$)	Qty.	Total Volume	Annual revenue (US$)
Jequitiba wood
Cladding	12	0.00972	0.11664	18.00	216.00	0	0	0
Tilt and turn windows	12	0.012320	0.14784	29.63	355.56	106	1.30592	3,140.78
Windows/window frames	48	0.052080	2.49984	120.37	5,777.76	153	7.96824	18,416.61
Frames/casings	720	0.024570	17.6904	25.93	18,669.6	576	14.15232	14,935.68
Doors/door frames	156	0.07602	11.85912	112.96	17,621.76	125	9.5025	14,120.00
Doors	60	0.051450	3.08700	87.04	5,222.40	48	2.4696	4,177.92
Baseboards	-	-	-	-	-	-	-	-
Total	1008	-	35.40	-	47,863.08	1008	35.40	54,790.99
Jatoba wood
Cladding	-	-	-	-	-	-	-	-
Tilt and turn windows	-	-	-	-	-	-	-	-
Windows/window frames	-	-	-	-	-	-	-	-
Frames/casings	540	0.024570	13.2678	51.85	27,999.00	432	10.61424	22,399.20
Doors/door frames	12	0.07602	0.91224	218.52	2,622.24	47	3.57294	10,270.44
Doors	-	-
-	-	-	-	-
Baseboards	12	0.0009	0.0108	2.78	33.36	0	0	0
Total	564	-	14.20	-	30,654.60	479	14.18	32,669.64

Table 4 Evaluation of economic indicators of evaluated carpentry company before and after operational research modeling.

Economic indicators	Scenario before operacional research	Scenario after operational research
NPV (US$) /30 anos	213,565.76	336,466.98
EPV (US$)	15,515.32	24,443.96
R/C	1.24	1.38

Table 5 Sensitivity analysis for the economic indicators before and after operational research modeling.

NPV (US$)/30 years			EPV (US$)		R/C
Change of the parameters	Scenario before the operational research	Scenario after the operational research	Scenario before the operational research	Scenario after the operational research	Scenario before the operational research	Scenario after the operational research
Interest rate (%)
6% WSA*	213,565.76	336,466.98	15,515.32	24,443.96	1.24	1.38
8%	174,668.11	275,184.81	15,515.32	24,443.96	1.24	1.38
10%	146,261.59	230,431.12	15,515.32	24,443.96	1.24	1.38
Labor cost (US$)
WSA*(32,661.00)	213,565.76	336,466.98	15,515.32	24,443.96	1.24	1.38
Reduction of 10%	258,523.08	381,424.30	18,781.42	27,710.06	1.31	1.46
Reduction of 5%	236,044.42	358,945.64	17,148.37	26,077.01	1.27	1.42
Addition of 5%	191,087.10	313,988.32	13,882.27	22,810.91	1.21	1.35
Addition of 10%	168,608.45	291,509.67	12,249.22	21,177.86	1.18	1.31
Wood cost (US$)
WSA*(24.822,21)	213,565.76	336,466.98	15,515.32	24,443.96	1.24	1.38
Reduction of 10%	247,717.68	370,618.90	17,996.41	26,925.05	1.29	1.44
Reduction of 5%	230,641.72	353,542.94	16,755.86	25,684.50	1.27	1.41
Addition of 5%	196,489.80	319,391.02	14,274.77	23,203.40	1.22	1.36
Addition of 10%	179,413.84	302,315.06	13,034.22	21,962.86	1.19	1.33

\begin{matrix} \sum_{i = 1}^{n} X_{i} \leq S \max_{[k]} & \begin{matrix} {X i \geq 0.8 X i, i = 3.6, X i \geq 0, i = 1.2} jequitiba wood \\ {X i \geq 0.8 X i, i = 4, X i \geq 0, i = 5.7} jatoba wood \\ k = 1.2 \end{matrix} \end{matrix}

[1] *Corresponding author.

Brasil

Brasil

OPTIMIZATION OF ECONOMIC INDICATORS IN A CARPENTRY COMPANY THROUGH INTEGER PROGRAMMING

OTIMIZAÇÃO DE INDICADORES ECONÔMICOS EM UMA CARPINTARIA PELO USO DA PROGRAMAÇÃO INTEIRA

ABSTRACT