Optimization approaches for sugarcane harvest front programming and scheduling

Junqueira, Rogério de Ávila Ribeiro; Morabito, Reinaldo

doi:10.1590/0104-530X1882-16

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Articles • Gest. Prod. 24 (2) • Apr-Jun 2017 • https://doi.org/10.1590/0104-530X1882-16 copy

Optimization approaches for sugarcane harvest front programming and scheduling

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

The production of sugar, ethanol, and electricity from sugarcane necessarily involves harvesting and transportation of raw materials, which are expensive and complex operations that affect industrial efficiency. The present study proposes optimization approaches to support programming and scheduling harvest front decisions, based on considering the representation of the lot sizing and scheduling problem on parallel machines with sequence-dependent setup times and costs, a modeling technique widely reported in the literature. We carried out real data experiments in order to verify the adequacy and consistency of this representation. The results show that the proposed approaches adequately represent the conceptual model studied and have great potential to reduce cost in real-life situations.

Keywords:
Sugarcane harvesting planning; Programming and scheduling of harvest fronts; Lot sizing and scheduling; Mixed integer programming

Symbol	Definition
$i, j$	harvest block
m	type of harvesting belonging to set M=(man,mec)
$l$	harvest front
$t$	macro-period
$S_{t}$	set of micro-periods s belonging to the macro-period t
$S 0_{t}$	set with the first micro-period s of period t
$F_{m}$	set of the harvest fronts l belonging to the type of harvesting m
$B l_{j l}$	set of the blocks j that can be harvested by the harvest front l
$B s_{j t}$	set of the blocks j that can be harvested in the macro-period t
$V_{j}$	set of the blocks j that can be irrigated with vinasse

Symbol	Definition
$d e m_{m t}$	mill demand per type of harvesting m in the period t (tons)
$p_{j}$	production of block j (tons)
$f_{j m}$	area of block j that can be harvested with the type of harvesting m
$v i n_{t}$	minimum area with vinasse to be left by the harvesting in the macro-period t
$T C H_{j}$	productivity of block j (tons per hectare)
$f i_{j}$	area of block j that allows the use of vinasse
$c o l_{m j}$	harvesting capacity of block j with the type of harvesting m (tons per hour)
$N p$	vehicle for equipment transportation (step-deck trailer)
$N m_{l}$	harvesting machines (harvesters) of harvest front l
$H t_{m}$	number of hours of machine operation per type of harvesting m
$s t_{i j}$	time required for a harvest front to move from block i to j
$K_{t}$	harvest front capacity in period t (time)
$t r a n s p_{m j}$	transportation capacity of block j with the type of harvesting m (tons per hour)
$N t$	transportation vehicle (transportation trucks)
$H t t$	number of hours worked in transportation
$b m_{l j}$	minimum area of block j to enable the shift of harvest front l (tons)
T	total number of macro-periods
F	total number of harvest fronts
B	total number of blocks

Symbol	Definition
$x_{l j s}$	production of block j in the micro-period s by harvest front l (tons)
$y_{l j s}$	${\begin{cases} 1, i f h a r v e s t f r o n t l i s i n t h e b l o c k j i n t h e m i c r o - p e r i o d s \\ 0, o t h e r w i s e \end{cases}$
$z_{l i j s}$	${\begin{cases} 1, i f h a r v e s t f r o n t l m o v e s f r o m n o d e i t o j i n t h e m i c r o - p e r i o d s \\ 0, o t h e r w i s e \end{cases}$

	Is sugarcane already planted?	Cycle	Last cutting/ planting	4	5	6	7	8	9	10	11
1	X	Early maturing	Early-season	5	5	4
2	X	Early maturing	Mid-season			5	4	3	2
3	X	Early maturing	Late-season					4	3	3	2
4	X	Medium maturing	Early-season	2	3	4	5	5	4
5	X	Medium maturing	Mid-season			4	5	5	4
6	X	Medium maturing	Late-season				3	4	5	4	3
7	X	Late maturing	Early-season	0	1	1	1	1	4	5	4
8	X	Late maturing	Mid-season				2	3	4	5	5
9	X	Late maturing	Late-season						3	5	5
10				5	5	5	5	5	5	5	5
Aggravating factors		Risk of fire		2	2	1	0	-2	-2	-2	-2
		Risk of flooding		-2	-2	1	2	2	1	-2	-2
		Sandy soil		2	1	1	-2	-2	1	2	2
		Paved road		2	2	1	0	0	1	2	2
		Dirt road (clay)		-2	-2	1	2	2	1	-2	-2

Symbol	Definition
$[m i n d_{m t}, m a x d_{m t}]$	Mill minimum and maximum demand per type of harvesting m in the period t (tons)
$m o$	parameter that considers the influence of loss of grinding capacity in the objective function (cost of a ton of sugarcane left unground)
$b s$	parameter that considers the influence of loss of raw material left in field in the objective function (cost of a ton of sugarcane left unharvested)
md	parameter that considers the influence of the distance traveled by the harvest front to move from one block to another in the objective function (cost of one km traveled in transporting equipment/machine)
$d i s t_{i j}$	Distance between blocks i and j (km)

Symbol	Definition
$w m_{m t}$	tonnes of sugarcane left unground of the type of harvesting m in the period t
$w b_{j}$	tonnes of raw material left unharvested in block j

Blocks	Prod (t)	X'	Y'	Dist. (km)	Vel. (km/h)	Field (min)	Mill (min)	Cycle (h)	Loads	Tonnes (ton/load)	Transp. (ton/h)	Harv. (ton/h)
1	17.000	0	-15	15.0	30	35	25	2.0	2	32	32	30
2	17.000	-5	5	7.1	30	35	25	1.5	2	32	43	42
3	17.000	0	-5	5.0	20	35	25	1.5	2	32	43	42
4	17.000	-5	-15	15.8	30	35	25	2.1	2	32	31	30
Total	68.000	Average		10.7	28	35	25	1.8	2	32	37	36

Parameters	R1	R2	Unit
Harvester average speed	4.5	5.0	km/h
Productivity	76.0	62.0	t/ha
Average length of the area harvested	0.60	0.30	Km
Spacing	1.5	1.5	M
Average time spent on maneuvering	1.5	2.0	min
t/h Total average	43.2	29.9	t/h/mach

	distance in km-dist (i,j)				Time in hours-dist (i,j)
Blocks	b1	b2	b3	b4	b1	b2	b3	b4
b1	0	27	13	7	0.0	2.0	1.6	1.4
b2	27	0	15	26	2.0	0.0	1.6	1.9
b3	13	15	0	15	1.6	1.6	0.0	1.6
b4	7	26	15	0	1.4	1.9	1.6	0.0

	$B s_{j t}$		$γ_{j t}$
	P1	P2	P1	P2
b1	1		5
b2	1	1	5	4
b3	1	1	4	5
b4	1		5

	Exp. 1.2		Exp. 1.3
	P1	P2	P1	P2
b1	5	4	5	4
b2	5	4	5	4
b3	4	5	4	5
b4	5	4	5	3

Experiment	Model	Production (t)	Obj. Func. of Model 1	Score
1.4	1	66.375	283.375	4.27
1A.1	1A	63.000	267.750	4.25
1B.1	1B	66.375	281.250	4.24
1.5	1	68.000	323.000	4.75
1A.2	1A	63.000	298.462	4.74
1B.2	1B	68.000	321.750	4.73

Exp.	Number of harvesters	Number of tractor trailers	Cost of grinding loss (R$)	Cost of harvester idleness (R$)	Cost of tractor trailer idleness (R$)	B1 harvested in P2
1B.3	10	9	0	30,405	20,651	Yes
1B.4	9	9	0	0	20,651	Yes
1B.5	8	9	514,944	0	20,651	Yes
1B.6	9	8	0	0	0	Yes
1B.7	9	7	367,200	0	0	Yes
1B.8	9	9	385,300	0	0	No
1B.9	9	8	209,300	0	0	No

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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