INTEGRATED LOTSIZING, SCHEDULING AND BLENDING DECISIONS IN THE SPINNING INDUSTRY

Camargo, Victor C. B.; Almada-Lobo, Bernardo; Toledo, Franklina M. B.

doi:10.1590/0101-7438.2021.041s1.00233486

Acessibilidade / Reportar erro

Brasil

Español English

sumário « anterior atual seguinte »

Sumário

ARTICLES • Pesqui. Oper. 41 (spe) • 2021 • https://doi.org/10.1590/0101-7438.2021.041s1.00233486 copy

INTEGRATED LOTSIZING, SCHEDULING AND BLENDING DECISIONS IN THE SPINNING INDUSTRY

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

In this paper, the relevance of integrated planning concerning decisions of production and blending in a spinning industry is studied. The scenario regards a plant that produces several yarn packages over a planning horizon. Each yarn type is produced using a blend of several cotton bales that must contain attributes to ensure the quality of the produced yarns. Three approaches to managing production and blending are compared; the first deals with the solution to the production scheduling and blending problems in a single integrated model. The second approach hierarchically addresses these problems. The third procedure combines features from the integrated and hierarchical approaches. These approaches are applied to a real-world problem, and their respective performances are analyzed. The third approach proved to deal with lot sizing, scheduling and blending in the spinning industry more efficiently. Moreover, the results indicate the importance of coordinating production and blending decisions.

Keywords:
production planning; lotsizing and scheduling problem; blending problem; spinning industry

Product	Family k	d _it			p _mi	c _itt'
Product	Family k	t = 1	t = 2	t = 3	p _mi	*t < t'*	t > t'
i = 1	1	4,666	0	0	0.000150	0.0017	0.17
i = 2	1	20,000	10,247	0	0.000097	0.0017	0.17
i = 3	1	0	4,067	0	0.000540	0.0017	0.17
i = 4	2	0	0	3,243	0.000185	0.0017	0.17
i = 5	2	0	0	15,815	0.000141	0.0017	0.17

Product	1	2	3	4	5
1	0.0/0.0	0.031/3.1	0.039/3.9	0.066/6.6	0.060/6.0
2	0.047/4.7	0.0/0.0	0.042/4.2	0.066/6.6	0.050/5.0
3	0.045/4.5	0.040/4.0	0.0/0.0	0.060/3.0	0.070/5.0
4	0.063/6.3	0.063/6.3	0.063/6.3	0.0/0.0	0.030/3.0
5	0.065/6.5	0.062/6.2	0.060/6.0	0.050/5.0	0.0/0.0

		Color grade
		White	Light spotted	Spotted	Tinged
Initial inventory ( $I_{g}^{0}$ )		230	250	200	50
Number of bales used in latest load ( f _gk )	k = 1	91	8	1	0
Number of bales used in latest load ( f _gk )	k = 2	62	18	18	2
Minimum limit ( $α_{g k}$ )	k = 1	0.85	0	0	0
Minimum limit ( $α_{g k}$ )	k = 2	0.6	0	0	0
Maximum limit ( ${\bar{α}}_{g k}$ )	k = 1	1	0.16	0	0
Maximum limit ( ${\bar{α}}_{g k}$ )	k = 2	1	0.25	0.2	0.02

		Color grade
		White	Light spotted	Spotted	Tinged
Final inventory ( $I_{g}^{f}$ )		0	200	180	50
Used bales (F _gk )	k = 1	85	15	0	0
Used bales (F _gk )	k = 2	60	20	20	0
Variation between blends (ℋ_gk )	k = 1	0	0	0.1	0
Variation between blends (ℋ_gk )	k = 2	0.2	0.7	0.2	0.2

Sociedade Brasileira de Pesquisa Operacional Rua Mayrink Veiga, 32 - sala 601 - Centro, 20090-050 Rio de Janeiro RJ - Brasil, Tel.: +55 21 2263-0499, Fax: +55 21 2263-0501 - Rio de Janeiro - RJ - Brazil
E-mail: sobrapo@sobrapo.org.br

Acompanhe os números deste periódico no seu leitor de RSS

[1] *Corresponding author

Indices
i = 1,..., N	yarn types;
k = 1,..., K	yarn families - blend quality types;
m = 1,..., M	spinning machines;
t,t'= 1,..., T	periods;
l = 1,..., L	blend loads available within the planning horizon.

Parameters
c _itt'	cost of producing one kilogram of yarn i in period t to fulfill the demand of period t ^l ;
σ _mij	setup cost of a changeover on machine m from yarn i to yarn j;
r _l	cost of one kilogram of residue of the lth blend load;
d _it'	demand (kilograms) of yarn i in period t ^l ;
s _mij	fraction of a single period consumed for the production setup of a changeover on machine m from yarn i to yarn j;
p _mi	fraction of a single period consumed for production on machine m, of one kilogram of yarn i;
C	opening-and-blending machine capacity (kilograms) for one blend load;
S(k)	yarn set belonging to the same family k.

Variables
X _mitlt'	production (kilograms) on machine m of yarn i in period t using the lth blend load to meet demand in period t ^l ;
Y _mijtl	takes 1, if a changeover occurs on machine m from yarn i to j in period t using the lth blend load; 0 otherwise;
R _l	raw cotton residue (kilograms) of the lth blend load;
U _lk	takes 1, if the lth blend load satisfies the quality for yarn family k; 0 otherwise;
$u_{l}^{s}$	starting time of the lth blend load;
$u_{l}^{f}$	finishing time of the lth blend load;
$μ_{m i t l}^{s}$	production starting time on machine m of yarn i in period t using the lth blend load;
$μ_{m i t l}^{f}$	production finishing time on machine m of yarn i in period t using the lth blend load;
α _mitl	takes 1, if machine m is set up for production of yarn i in period t using the lth blend load; 0 otherwise;
$P_{t l}^{s}$	takes 1, if the lth blend load starts before the end of period t (that is, instant time t); 0 otherwise;
$P_{t l}^{f}$	takes 1, if the lth blend load ends after the beginning of period t (that is, instant time t − 1); 0 otherwise.

Indices
g = 1,..., G	color grade levels (fiber attribute).

Parameters
$I_{g}^{0}$	initial bale inventory level of color grade attribute g;
Z ⁰	total number of bales in the initial inventory;
w	weight of one cotton bale;
q	amount of cotton bales for a blend load: $q = ⌈C / w⌉$ ;
${\bar{α}}_{g k}$	maximum percentage of the color grade attribute g in the blend of type k;
$α_{g k}$	minimum percentage of the color grade attribute g in the blend of type k;
f _gk	amount of bales with color grade g used in the last blend load of type k;
${\bar{v}}_{g k}$	maximum variation allowed for the color grade attribute g in the blend of type k (in percentage).

Variables
$I_{g}^{f}$	final inventory level of bales with color grade g;
Z ^f	total number of bales in the final inventory;
𝒜_g	variation (in percentage) of bales with color grade g in the inventory;
ℋ_gk	variation of bales with color grade g between blends of type k;
D _k	number of blend loads of type k needed for production;
B _k	takes 1, if one or more blend loads of type k is used; 0 otherwise;
F _gk	number of bales with color grade g used in the blend load of type k.

	t = 1	t = 2	t = 3
m = 1	α₁₁₁₁ = 1	α₁₃₂₂ = 1	α₁₃₃₃ = 1
	$μ_{1111}^{s} : μ_{1111}^{f} = 0 : 0.7$	$μ_{1322}^{s} : μ_{1322}^{f} = 1 : 2$	Y₁₃₅₃₃ = 1
	X₁₁₁₁₁= 4667	X₁₃₂₂₂= 1851.9	$μ_{1533}^{s} : μ_{1533}^{f} = 2 : 3$
	Y₁₁₃₁₂ = 1		X₁₅₃₃₃= 6595.7
	$μ_{1313}^{s} : μ_{1312}^{f} = 0.7 : 1$
	X₁₃₁₂₂= 474.4
m = 2	α₂₂₁₁ = 1	α₂₃₂₂ = 1	α₂₄₃₃ = 1
	$μ_{2211}^{s} : μ_{2211}^{f} = 0 : 0.7$	$μ_{2322}^{s} : μ_{2322}^{f} = 1 : 1.94$	$μ_{2433}^{s} : μ_{2433}^{f} = 2 : 2.6$
	X₂₂₁₁₁= 7266.2	X₂₃₂₂₂= 1740	X₂₄₃₃₃= 3243
	$μ_{2212}^{s} : μ_{2212}^{f} = 0.7 : 1$	Y₂₃₄₂₂ = 1	Y₂₄₅₃₃ = 1
	X₂₂₁₂₁= 2424.5	$μ_{2422}^{s} : μ_{2422}^{f} = 1.94 : 2$	$μ_{2533}^{s} : μ_{2533}^{f} = 2.6 : 3$
	Y₂₃₃₁₂ = 1		X₂₅₃₃₃= 2624.4
m = 3	α₃₂₁₁ = 1	α₃₂₂₂ = 1	α₃₂₃₃ = 1
	$μ_{3211}^{s} : μ_{3211}^{f} = 0 : 0.7$	$μ_{3222}^{s} : μ_{3222}^{f} = 1 : 2$	Y₃₂₅₃₃ = 1
	X₃₂₁₁₁= 7266.2	X₃₂₂₂₂= 10247	$μ_{3533}^{s} : μ_{3533}^{f} = 2 : 3$
	$μ_{3212}^{s} : μ_{3212}^{f} = 0.7 : 1$		X₃₅₃₃₃= 6737.6
	X₃₂₁₂₁= 3043.1
Stock level	X₁₃₁₂₂= 474.41
Residue level	R₁ = 801.63	R₂ = 218.37	R₃ = 942
Value of solution: 33.33