Harvest scheduling algorithm to equalize supplier benefits: A case study from the Thai sugar cane industry

Page 1

Computers and Electronics in Agriculture 110 (2015) 42–55

Contents lists available at ScienceDirect

Computers and Electronics in Agriculture

journal homepage: www.elsevier .com/locate /compag

Harvest scheduling algorithm to equalize supplier benefits: A case studyfrom the Thai sugar cane industry

http://dx.doi.org/10.1016/j.compag.2014.10.0050168-1699/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Tel./fax: +66 43 202697.E-mail addresses: [email protected] (S. Thuankaewsing), sakdakhamjan@

gmail.com (S. Khamjan), [email protected] (K. Piewthongngam), [email protected] (S. Pathumnakul).

1 Tel.: +66 43 202697.2 Tel.: +66 43 202401.

S. Thuankaewsing a,1, S. Khamjan b,1, K. Piewthongngam c,2, S. Pathumnakul a,⇑,1

a Supply Chain and Logistics System Research Unit, Faculty of Engineering, Khon Kaen University, Khon Kaen 40002, Thailandb Faculty of Science and Engineer, Kasetsart University Chalermphrakiat Sakonnakhon Province Campus, Sakhonnakhon 47000, Thailandc Esaan Center for Business and Economic Research, Faculty of Management Science, Khon Kaen University, Khon Kaen 40002, Thailand

a r t i c l e i n f o

Article history:Received 27 January 2014Received in revised form 16 September2014Accepted 5 October 2014

Keywords:Grower clusteringOptimization modelHeuristic algorithmSugar caneTabu search

a b s t r a c t

In this study, the harvest scheduling problem of a group of cane growers in Thailand is addressed. Eachmember in a group is required to consistently supply sugar cane to a mill for the entire harvest season.However, the current scheduling does not account for the time-variant cane production of each cane field,which leads to unequal opportunities for growers to harvest. A portion of growers could have the oppor-tunity to harvest in periods that provide higher sugar cane yields, while others in the same group do not.This inefficient harvest scheduling causes conflicts between growers and unnecessary loss of sugar caneand sugar yields. An artificial neural network is applied to estimate cane yield over a harvest season.Then, an optimization model and a heuristic algorithm with the objective of maximizing the estimatedsugar cane yield under the condition of fair benefits for all of the growers in the group were developedto determine the most suitable sugar cane harvest schedule for a cluster of sugar cane fields. For the heu-ristic, the initial solution is first constructed based on the yield trends, and the solution is then improvedby the tabu search approach. The results indicated that there are potential benefits from applying themodel to cane scheduling within a group of heterogeneous yield trends. Sensitivity analysis showed thatthe more that the yield trends in a group differ from one another, the higher the benefit the group is likelyto gain from adopting the proposed framework.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Harvest scheduling has become one of the most important tasksin the sugar cane industry. It is obvious that an efficient harvestschedule could increase the sugar yield, which improves theprofitability of the entire supply chain. Research related to thesugar cane harvesting problem has steadily increased (e.g.,Higgins et al. (1998), Salassi et al. (2002), Jiao et al. (2005),Grunow et al. (2007), Piewthongngam et al. (2009), Stray et al.(2012)). As with other agricultural products, the complexity ofthe harvest scheduling problem can be attributed to the biologicalcharacteristics of sugar cane, which are uncertain and variable, andproduction variations, such as a grower’s skill and the number offarms involved in the scheduling plan.

Although researchers agree on the benefit of collaborationbetween the sugar mill and cane growers, different concepts totackle harvest operations plans have been proposed. The conceptsproposed in the past are usually around situations that pertain toinvolving parties in each of the sugar-producer countries. Forexample, in Australia, most growers are large scale. Hauler and railsystems are the main transportation modes. Growers implementeda self-rotation strategy such that no grower finishes harvestingahead of others (Higgins, 1999). In Venezuela, Brazil and otherSouth American countries, mills own and administer a large shareof the cane field. Grunow et al. (2007) proposed a harvest plan forthe South American case by designing a cultivation plan that, inturn, roughly set a harvesting time slot for each field. They dividedthe harvest plan into three levels: cultivation, harvesting decisionsand the dispatching of harvest equipment. While the model por-trays innovative and holistic concepts in the South American case,it encompasses a plan for large size fields for which all of the deci-sions, including the decisions to use equipment and transportation,are not under the control of the mill. Due to the large field sizes,harvesting a plot in the case of South Africa could take several days.Each plot is harvested in a single round. As stated by Stray et al.

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S. Thuankaewsing et al. / Computers and Electronics in Agriculture 110 (2015) 42–55 43

(2012), this case is not in a sugar cane-producing country such asSouth Africa or Thailand, where small farm growers make theirown decisions with regard to their cultivation plan. In South Africaand Thailand, a central plan was implemented by the Mill GroupBoard for South Africa and by the millers for Thailand.

For the case that is proposed here, there is a small scale withhighly different environments and constraints. We propose todevelop a flexible yield estimation model that can account forthe heterogeneous conditions in the fields. To maintain the maxi-mum cane production for the whole joined operation group, it isnot necessary to maintain individual members’ maximum profits.Some members in the group must unequally sacrifice to harvesttheir cane far beyond their highest yield. Hence, to maintain max-imum cane production for each cane grower, we propose the con-cept of finding the optimum point at which each grower harvestsan equivalent amount less than his/her maximum yield. In otherwords, suppose that one’s maximum production is 100 tons andanother’s is 200 tons. Additionally, the model suggests harvestingat 98% of the maximum production of each. Hence, the grower with100 tons should be assigned to harvest until he obtains 98 tons ofcane, while the latter should harvest until the time at which he has196 tons of cane. In this sense, the maximum yield of the wholegroup also means that each one sacrifices its own maximum yieldproportionately. Although this study addresses a group harvestrotation in the cane industry, the concept is applicable to othercrops for which a large number of growers share harvestequipment and schedules.

Group rotation system for the Thai cane industry

In Thailand, sugar cane is grown mainly in the northeasternregion of the country, where there are thousands of farms supply-ing sugar cane to a sugar mill. Most of these farms are small, andtheir sugar cane production is less than 300 tons per crop year.To simplify the harvest planning, a sugar mill planner organizesthe small farms into groups. Growers are asked to form a groupvoluntarily. Each group is a set of farms whose total estimatedsugar cane production is greater than or equal to the transporta-tion quota specified by the mill. For example, if the transportationquota is 1000 tons, then the farms whose sugar cane yield is lessthan 1000 tons will be grouped with others. The number of grow-ers in each group varies, ranging from 2 to 8 growers and covering10 to 50 fields per group. The members in a group share theirresources such as laborers, harvesting equipment and trucks. Typ-ically, as in this study, a group of growers has only one force oflaborers and a delivery truck to be shared. Additionally, the har-vesting operation is performed manually by a labor force and nota harvesting machine.

The harvest season in Thailand usually starts at the end ofNovember or the beginning of December, and it ends in early- tomid-April. To ensure that a mill will have a supply of cane that isequal to its capacity for the entire season, the sugar mill dividesthe harvest season into many rounds, typically 100–120 rounds,where each round lasts 25–28 h. Each farm group must consistentlysupply sugar cane for the entire season. Currently, the growerswithin a group decide the harvest schedule among themselves.Basically, the harvest schedule is a simple calculation. For example,in a harvest season, the number of transportation round-trips is setto 100, and the transportation quota is approximately 1000 tons.Consider a farm group that consists of 2 growers and assume that

Table 1The traditional harvest schedule of the farmer group.

Transportation round 1 2 3 4 5 6Farmer no. 1 1 1 1 2 1

the estimated sugar cane supplied to a sugar mill for the entire har-vest season is 800 tons for grower 1 and 200 tons for grower 2. If a10-ton truck is used to transport the sugar cane from the farms tothe mill, then the number of transportation round-trips requiredfor this group is 100. The number of round-trips to transport theharvest for grower 1 will be 4 times greater than that for grower2. The harvest schedule is shown in Table 1. The schedule can bealtered among the growers based on various criteria such as thesugar cane ripening time, the financial needs of the members, orthe availability of laborers, but this pattern is typical. Moreover,for the purpose of harvest labor management, two main harvestingpatterns are always practiced in the harvest scheduling within agroup. In the first pattern, once the harvesting of a field has started,all of the cane in that field must be harvested without interruption.In the second pattern, no more than one field is harvested in thesame harvest period, except for in the period where harvestinghas finished in one field and has started in another field. This pat-tern is based on the situation that the group of growers shares alabor force and a delivery truck. The field-by-field harvesting oper-ation is practiced to prevent the mixing of cane from different fieldsin one delivery truck. Several examples of practical and impracticalharvesting patterns are shown in Figs. 1 and 2, respectively.

The current practice does not consider which harvest periodsprovide the highest sugar productivity. This shortcoming leads tounequal opportunities for growers to harvest: some growers couldhave opportunities to harvest in periods that provide higher sugarcane yields than those of the others in the same group. In theworst-case scenario, none of the growers have the chance to har-vest at the best time. This problem appears to be trivial, and ithas been overlooked by the sugar industry in the past. In fact, inef-ficient harvest scheduling within the groups causes many prob-lems, including conflicts between growers and the unnecessaryloss of sugar cane and sugar productivity. These problems signifi-cantly affect both the growers and sugar mills, especially whenthere are many small-scale farms clustered into groups, as in Thai-land. Therefore, it is necessary for the sugar industry to manage theharvest schedule within the farm groups. To efficiently schedulethe harvests, the sugar cane yield throughout the harvest periodof each sugar cane field must be known. The integration of a sugarcane yield estimation method and a harvest scheduling algorithmis required to solve this problem.

In the literature on the sugar cane harvesting problem, severalstudies have attempted to combine yield estimation and an opti-mization model or a heuristic algorithm to optimize the sugar canecultivation or harvest scheduling, such as Salassi et al. (2002), Jiaoet al. (2005), Piewthongngam et al. (2009) and Stray et al. (2012).The spatial variation of cane yield is known and is found to behighly effective for harvest productivity (Le Gal et al., 2004). Inan attempt to explain cane yield variation, Lawes et al. (2004)employed two multivariate techniques, the 3-way mixture methodof clustering and the 3-mode principle component analysis to iden-tify meaningful relationships between farms that performed simi-larly for both cane yield and CCS for whole mill productivityimprovement. Le Gal et al. (2004) compared the recoverable valuerate (RV%) in different areas of South Africa. Hence, a number ofcane yield estimations have been studied. The estimated yield isusually the forecasted sugar cane yield and/or the sugar yield(expressed as a Commercial cane sugar (CCS) or sucrose), depend-ing on the objective of the optimization problem. For example,Salassi et al. (2002) estimated the sugar cane stalk weight and

7 8 9 10 . . .. . . 99 1001 1 1 2 . . .. . . 1 2

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Field No. Harvesting Period1 2 3 4 5 6 7 8 9 10

1 � �

2 � � �

3 � �

4 � � �

(a)

Field No. Harvesting Period1 2 3 4 5 6 7 8 9 10

1 � �

2 � � � �

3 � � �

4 � � � �

(b)

Field No. Harvesting Period1 2 3 4 5 6 7 8 9 10

1 � � � � �

2 �

3 �

4 � � � � � �

(c)

Field No. Harvesting Period1 2 3 4 5 6 7 8 9 10

1 � �

2 � �

3 �

4 � �

(d) Fig. 1. Practical harvesting patterns.

44 S. Thuankaewsing et al. / Computers and Electronics in Agriculture 110 (2015) 42–55

the sugar per stalk to forecast the tonnage and sugar yields, whichwere used to determine the optimal sugar cane harvest system.Jiao et al. (2005) used the forecasted CCS, which was derived froma regression model, to plan the harvest schedule. Piewthongngamet al. (2009) employed a crop growth model (DSSAT) to estimatethe sugar cane yields, which were the basis for determining anoptimal sugar cane cultivation plan. Stray et al. (2012) constructedregression models of cane yield and RV% to find a suitable harvestschedule.

To plan the cultivation or harvest schedule in these studies,optimization and/or a heuristic algorithm were used to determinethe schedule that maximized sugar cane yield, sugar yield or profit.Salassi et al. (2002) used mixed integer programming to select theharvest system (either whole stalk or combined) that would max-imize the total net returns of the farms. Yosnual and Supsomboon(2004) developed an integer programming approach to schedulethe cane supply for each vehicle type and to obtain the optimalnumber of harvesters for each harvest round. Jiao et al. (2005) usedlinear programming to optimize the proportions of the fields thatwould be allocated for harvesting on each farm in each harvestround, to maximize the CCS across all of the farms within the farmgroup. Piewthongngam et al. (2009) used linear programming todetermine the planting dates, the cultivars and the harvesting per-iod, where the objective of their model was to maximize the over-all sugar production subject to the limitations of the mill’s capacityand the cane-growing areas. Stray et al. (2012) presented a math-ematical programming model and a metaheuristic algorithm tofind the harvest schedule that maximized the total profit.

Various types of optimization-based techniques have beenapplied in harvesting operations and production scheduling in

many other agricultural problems, such as pig procurement plans(Khamjan et al., 2013), harvesting and distribution for perishableproducts (Ahumada and Villalobos, 2011), production schedulingin a sawmill for the timber industry (Maturana et al., 2010), andwine grape harvest scheduling (Ferrer et al., 2008).

Although the previous approaches provide the increment ofsugar cane yield or sugar yield, the opportunity to harvest withinthe group remains a problem. Certain growers could have anadvantage over others in the group, which causes resentmentamong the growers. To solve the inequality among the growers,Higgins (1999) proposed a solution in the case of Australian caneharvesting. In Higgins’ work, cane from each farm is also suppliedon a rotational basis. Each farm within a harvesting group suppliesan equal percent of its cane to the mill for each round. A harvestinggroup cannot be ahead of the others in terms of the percentage ofcane supplied to the mill. For example, a harvesting group cannothave supplied 60% of cane from its farms to the mill when anotherhas only supplied 25%. This approach results in all of the harvestinggroups within a mill region to finish supplying cane to the mill onapproximately the same date (Higgins, 1999). Hence, equality inthe Australian case is an equal proportion of cane harvested in eachround. Our study explores a different equality aspect in terms of anequal percentage lower than its highest productivity at which toharvest the cane. Therefore, the concept involves estimating yieldtrends and their highest productivity and developing an optimiza-tion model to set a harvest schedule while accounting for equalopportunities to all members of a group. The sugar cane yield esti-mation method, which is based on an artificial neural network(ANN) that was introduced in the work of Thuankaewsing et al.(2011), was applied to forecast the sugar cane yield of each field

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Field No.Harvesting Period

1 2 3 4 5 6 7 8 9 101 � � �

2 � � � �

3 � � �

4 � � � �

(a) All canes in a field are not continuously harvested

Field No.Harvesting Period

1 2 3 4 5 6 7 8 9 101 � � � �

2 � � � � �

3 � � � � �

4 � � � � � �

(b) Fields are simultaneously harvested

Field No.Harvesting Period

1 2 3 4 5 6 7 8 9 101 � � �

2 � � � � �

3 � � � � �

4 � � � �

(c) Fields are simultaneously harvested

Field No.Harvesting Period

1 2 3 4 5 6 7 8 9 101 � � � �

2 � �

3 � �

4 � � � � �

(d) Fields are simultaneously harvested

Fig. 2. Impractical harvesting patterns.

S. Thuankaewsing et al. / Computers and Electronics in Agriculture 110 (2015) 42–55 45

throughout the harvest season, and these forecasted yields wereemployed in the optimization model to determine the harvestschedule. The optimization determines the harvest sequence, theharvest periods and the amount of sugar cane to be harvested ineach harvest period for each field in the group throughout the har-vest season. The objective in the optimization model is to maxi-mize the total tonnage of cane that is harvested by each growerin the harvest plan. Additionally, this plan ensures the equality ofharvesting opportunities among the growers in the group; i.e., allof the growers in the group can harvest in the time periods thatwill produce equal yields and profits.

2. Sugar cane yield prediction

In this study, the sugar cane yields in the harvest periods wereestimated using an ANN-based sugar cane prediction model(Thuankaewsing et al., 2011). In this model, a three-layer, feed-for-ward, back propagation neural network (which consists of an inputlayer, a hidden layer and an output layer) is used to find a relation-ship between the input parameters and the output parameter ofthe problem. Nine ANN models were constructed according tothe crop class (rattoon crop or cultivated crop, which is dividedinto late rainy season and irrigated) and farming skills (i.e., high,medium, or low). The common input parameters for a rattoon cropand a cultivated crop are the cultivars (e.g., K 84-200, LK 92-11, K88-92, KK3), the soil type (i.e., clay, silky loam and loamy sand), theuse of irrigation (i.e., yes and no), the age of the cane in days fromcultivation to harvest, the average value of the daily minimumtemperature (Celsius), the average value of the daily maximumtemperature (Celsius), the average daily rainfall (mm.), and theaccumulated daily rainfall since germination (mm.). All of the

qualitative inputs are entered into the model as a binary matrix.For the farming skills, we asked a mill agronomy team to rate theirresponsible growers into groups of high skill (A), medium skill (B)and low skill (C). The models were developed based on data from1600 fields in the 2011/2012 growing season at a selected mill,one of the largest sugar mills in Thailand. Some example data areshown in Table 2.

All of the models were developed using the commercial soft-ware MATLAB 2007b. The scaled conjugate gradient and theFletcher–Powell conjugate gradient algorithms were used to mini-mize the error function during the training process. The data wereseparated into three sets: training, model-validating and testing.For the purpose of training the models, approximately 70% of thesamples were randomly selected, 20% were used for testing pur-poses, and the remaining 10% were used for validation and earlytermination of the training process. Note that early terminationprevented over-fitting of the neural network models. The beststructures and the performances of the 9 models are presented inTables 3 and 4, respectively. The mean absolute percent error(MAPE) of the models was approximately 10.98% compared withthe actual data.

3. Optimization model for the harvest plan

3.1. Model

In this section, the optimization model is formulated to solvethe scheduling problem. In the optimization model, the estimatedcane yields (over the harvesting period for each field), which arerequired for the optimization model, are obtained from the pro-posed ANN model. The following notation is used in the model:

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Table 2Example of data used in sugar cane yield prediction model.

Grower no. Farmingskill

Field no. Area(raisa)

Cropclassb

Cultivar Soil type Irrigationsystem

Cultivationdate

Harvestingdate

Daily rainfall Temperature Cane yield(tons/rai)

Average Accumulated Averageminimum

Averagemaximum

101021 B 101021002 6.05 IC LK 92-11 Loamy sand Yes 18/2/2011 15/9/2011 4.51 947.80 24.09 32.72 9.90101132 B 101132046 9.21 5th RC K 84-200 Clay No 2/3/2011 19/9/2011 4.93 996.50 24.14 32.58 11.10101136 B 101136004 10.20 IC KK3 Clay Yes 8/3/2011 12/10/2011 5.56 1217.50 24.18 32.29 10.60101163 A 101163014 10.61 IC KK3 Silky loam No 9/3/2011 13/9/2011 4.72 891.80 24.15 32.55 15.10101227 A 101227016 4.86 IC KK3 Clay Yes 25/3/2011 12/10/2011 6.03 1217.50 24.39 32.34 15.70101482 B 101482019 5.98 2nd RC K 95-84 Clay Yes 1/5/2011 14/9/2011 6.34 868.50 24.72 32.39 10.30101501 A 101501043 3.60 2nd RC LK 92-11 Silky loam Yes 27/12/2010 14/9/2011 2.23 584.10 22.85 32.19 18.60101563 B 101563014 5.17 4th RC K 88-92 Clay Yes 11/4/2011 16/9/2011 5.86 932.50 24.69 32.71 11.30101585 A 101585008 10.43 IC KK3 Silky loam Yes 27/4/2011 12/10/2011 6.82 1152.00 24.66 32.17 18.50101668 B 101668011 6.69 IC KK3 Loamy sand Yes 12/4/2011 15/9/2011 5.45 856.00 24.71 32.70 9.10101937 B 101937019 5.52 IC LK 92-11 Clay Yes 11/3/2011 14/9/2011 5.16 969.50 23.50 32.63 9.20101949 A 101949012 8.14 LC KK3 Silky loam Yes 27/12/2010 13/9/2011 3.99 1041.50 21.73 32.13 16.80103162 A 103162006 5.90 LC LK 92-11 Silky loam Yes 13/9/2010 15/9/2011 3.36 1238.00 20.76 30.79 16.50103463 C 103463005 4.31 IC LK 92-11 Silky loam Yes 24/1/2011 15/9/2011 4.87 1130.13 21.81 31.70 7.50103502 B 103502008 1.44 LC LK 92-11 Loamy sand Yes 5/11/2010 12/10/2011 3.77 1180.37 20.52 30.88 10.50104227 A 104227202 5.87 IC K 84-200 Silky loam Yes 19/1/2011 28/12/2011 4.21 1023.04 22.98 33.01 17.60104291 C 104291001 19.69 2nd RC K 88-92 Loamy sand Yes 30/3/2011 29/12/2011 5.43 939.13 24.12 33.11 5.10104463 C 104463002 5.47 LC K 92-72 Silky loam Yes 15/12/2010 12/10/2011 3.50 962.80 22.75 32.11 4.50104518 C 104518008 10.47 1st RC LK 92-11 Silky loam No 6/5/2011 15/9/2011 5.40 729.00 24.69 32.27 5.40112099 C 112099003 3.09 LC KK3 Silky loam Yes 18/1/2011 15/9/2011 4.22 1013.84 22.92 33.01 5.60112099 C 112099003 3.09 LC KK3 Silky loam Yes 18/1/2011 12/10/2011 4.70 1260.54 23.02 32.90 7.70113884 B 113884003 3.07 LC LK 92-11 Loamy sand Yes 23/1/2011 14/9/2011 5.14 1177.74 21.74 31.72 11.80114189 A 114189001 6.63 4th RC K 84-200 Clay No 20/1/2011 10/1/2012 3.72 1323.80 22.86 31.82 15.36114258 C 114258007 4.62 IC K 92-72 Loamy sand Yes 1/4/2011 12/10/2011 3.65 710.90 24.59 32.58 7.40114318 C 114318002 7.06 IC LK 92-11 Clay Yes 6/3/2011 12/10/2011 5.01 977.50 24.15 32.56 4.80114433 C 114433017 9.35 1st RC LK 92-11 Loamy sand Yes 3/3/2011 13/9/2011 4.79 1313.18 23.86 32.15 5.63

a 1 rai = 0.16 ha.b IC: irrigated cane, LC: late rainy season cane, RC: rattoon cane.

46S.Thuankaew

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TaSu

Table 4Performance of the ANN models.

S. Thuankaewsing et al. / Computers and Electronics in Agriculture 110 (2015) 42–55 47

Sets and indices:

Model Mean absolute percent error (MAPE)

i

ble 3mmary

Mode

Late rLate rLate rIrrigatIrrigatIrrigatRattooRattooRattoo

index of growers within a group, i = 1, 2, 3, . . ., I.

j index of cane fields that belong to each grower, j e J(i).

Train Validation Test Overall

t index of the harvest period, t = 1, 2, 3, . . ., T. Late rainy season cane with farming 11.51 11.80 11.86 11.72 J(i) set of fields that belong to grower i.

skill ALate rainy season cane with farming 7.03 12.81 11.94 10.59

Parameters:

skill B

aij land area of field j of grower i (unit area). Late rainy season cane with farming 0.40 0.86 2.84 1.37 fijt

skill C

estimated cane yield of field j of grower i if harvested inperiod t (tons/unit area).

Irrigated cane with farming skill A 13.16 11.42 13.20 12.59

mij Irrigated cane with farming skill B 14.69 14.23 14.70 14.54Irrigated cane with farming skill C 6.45 12.57 11.9 10.31Rattoon cane with farming skill A 7.95 10.69 10.58 9.74

maximum cane production that can be harvested fromfield j of grower i (tons), the highest estimated yieldobtained from the ANN.

Rattoon cane with farming skill B 10.48 12.27 12.93 11.89

rijt Rattoon cane with farming skill C 15.94 15.85 16.38 16.06

number of periods required to harvest the entire area offield j of grower i if harvesting begins in period t.

TQ

maximum tonnage of cane for each harvest periodassigned by the mill (tons/period).

P

the minimum yield proportion allowed for all growers inthe group. The yield proportion is the ratio of totalharvested cane yield to the highest cane yield ifharvested in the best period.

M1

a positive large number. M2 a positive number that is equal to the number of total

fields in the group.

Decision variables: xijt area proportion of cane field j of grower i harvested in

period t.

Intermediate variables: yijt equal to 1 if field j of grower i is harvested in period t and

0 otherwise.

sijt equal to 1 if the harvesting of field j of grower i begins in

period t and 0 otherwise.

eijt equal to 1 if the harvesting of field j of grower i is

completed in period t and 0 otherwise.

The optimization model is formulated as follows:

MaximizeXI

i¼1

X

j2JðiÞ

XT

t¼1

xijtaijf ijt ð1Þ

Subject to

XI

i¼1

X

j2JðiÞxijtaijf ijt 6 TQ 8t ð2Þ

XT

t¼1

xijt ¼ 1 8i; j 2 JðiÞ ð3Þ

of the results of the ANN models.

l Input layer Hiddenlayer

Transferfunction

No. ofneurons

No. ofneurons

ainy season cane with farming skill A 15 164 Logsigainy season cane with farming skill B 15 152 Tansigainy season cane with farming skill C 15 148 Tansiged cane with farming skill A 15 96 Tansiged cane with farming skill B 15 60 Tansiged cane with farming skill C 15 163 Logsign cane with farming skill A 24 261 Logsign cane with farming skill B 24 305 Tansign cane with farming skill C 24 96 Tansig

Pj2JðiÞ

PTt¼1xijtaijf ijtP

j2JðiÞmij� P 8i ð4Þ

xijt 6 yijt 8i; j 2 JðiÞ; t ð5Þ

M1 � xijt � yijt 8i; j 2 JðiÞ; t ð6Þ

Xt

t0¼1

sijt0 � yijt 8i; j 2 JðiÞ; t ð7Þ

XT

t0¼t

eijt0 � yijt 8i; j 2 JðiÞ; t ð8Þ

XT

t¼1

sijt ¼ 1 8i; j 2 JðiÞ ð9Þ

XT

t¼1

eijt ¼ 1 8i; j 2 JðiÞ ð10Þ

XI

i¼1

X

j2JðiÞ

Xt

t0¼1

sijt0 � eijt0� �

6 1 8t ð11Þ

XI

i¼1

X

j2JðiÞ

Xt0�1

t00¼tþ1

sijt00 6 M2 � ð1� sijtÞ þM2 � 1� eijt0� �

8i; j 2 JðiÞ; tjrijt > 1; t0 ¼ t þ rijt � 1; t þ rijt ð12Þ

Xminftþrijt ;Tg

t0¼t

eijt0 � sijt 8i; j 2 JðiÞ; tjrijt > 0 ð13Þ

xijt � 0 8i; j 2 JðiÞ; t ð14Þ

yijt ; sijt; eijt 2 0;1f g 8i; j 2 JðiÞ; t ð15Þ

The objective function in (1) is the total cane production of thegroup. The constraint that the harvested cane should not exceedthe maximum tonnage of cane that was agreed upon for each har-vest period is given in (2). The constraint that all fields should beharvested within the harvest season is given in (3). Constraint (4)ensures that the proportion of the total cane production for all ofthe growers should be at least P; i.e., each grower should propor-tionately sacrifice his/her maximum production. Constraints (5)and (6) guarantee that if a field is harvested, yijt = 1. Constraints(7) and (8) ensure that the harvesting operations in field j ofgrower i must be between the beginning period sijt and the

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Solve the optimization model

Set P = 1 or 100%

Set P = P2

Is the solution feasible?

Set P2 = P - 0.1

Yes

No

Set P = P2

Solve the optimization model

Is the solution feasible?

No

Yes

Define P1 = P2 + 0.1

Calculate 1 2

2m

P PP

+=

Set P = Pm

Solve the optimization model

Is the solution feasible?

No

Yes

Set P1 = Pm

Set P2 = Pm

Is P1 - P2 ≤ 0.01?No Yes

Obtain the best Pand the solution

Fig. 3. Flow chart of the solution procedure.

48 S. Thuankaewsing et al. / Computers and Electronics in Agriculture 110 (2015) 42–55

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S. Thuankaewsing et al. / Computers and Electronics in Agriculture 110 (2015) 42–55 49

completion period eijt. Constraints (9) and (10) ensure that thebeginning period and the ending period can occur only once; i.e.,once harvesting has started in any field, it must be completedbefore starting other fields. Constraint 11 prevents the harvestingof more than one field simultaneously, and when harvesting startsin any field and is not yet complete, no concurrent harvesting isallowed in the other cane fields. Constraint (12) ensures field-by-field operation and harvest sequencing. Constraint (13) enforcesthe requirement that a field must be harvested continuously onceharvesting begins. Thus, constraints (11)–(15) are used to preventthe undesirable harvest patterns shown in Fig. 2. Constraint (14)guarantees that xijt is non-negative. Finally, constraint (15) ensuresthat yijt, sijt, and eijt are binary variables.

3.2. Solution procedure

Because the value of P (the minimum yield proportion of caneproduction for all of the growers) must be specified in the optimi-zation model, in this section, a solution procedure is developed todetermine the best value of P and the optimal solution to the prob-lem. The binary search method has been applied to determine thebest value of P. The procedure starts with P = 1 or 100%, whichmeans that all of the growers can harvest their cane in the peakyield period. If a feasible solution can be obtained for the optimiza-tion model, then P = 1 and the harvest schedule obtained is theoptimal solution to the problem. If there is no feasible solution,then we find the range that includes the best feasible P (i.e., therange between P1 and P2, P1 > P2). Starting with P2 = 0.9, the modelis solved with the value of P = P2. If it does not yield a feasible solu-tion, then the value of P2 is decreased by a multiple of 0.1 (i.e.,P2 = 0.8, 0.7,. . .) until there is a value for P2 that provides a feasiblesolution. In this step, we have P1 = P2 + 0.1. Then, the binary searchis employed by calculating the middle point between P1 and P2

i:e:; Pm ¼ P1þP22

� �. If Pm yields a feasible solution, then P2 = Pm;

otherwise, P1 = Pm. The algorithm is iterated until the differencebetween P1 and P2 is not greater than 0.01. Then, the obtainedvalue of P2 is the best P of the model. This solution is optimal forthe problem. The steps of the solution procedure are shown inFig. 3.

4. Heuristic algorithm

4.1. Heuristic

Because the problem is formulated as a mixed integer program(MIP), the number of variables and constraints and the computa-tional time required for solving the problem increase exponentiallyas the size of the problem increases. Greater numbers of variablesand constraints are expected for a complex, industrial-scale prob-lem. Obtaining the optimal solution in a reasonable amount of timeis difficult, even with a high-performance computer. To solve prac-tical problems including those in the Thai sugar industry, a heuris-tic algorithm was developed. In this study, the heuristic isseparated into two parts. The first part is to obtain the initial solu-tion based on the cane yield, and then, the quality of the solution isimproved by the tabu search approach in the second part.

4.2. Part I: initial solution based on the yield trend

It should be noted that, in practice, growers prioritize fields tobe harvested based on their own estimation of the yield trends,which are mainly based on the crop age and variety. Hence, olderfields are prioritized over younger fields, and a crop variety thatcurrently has a higher sucrose content than others is prioritizedover other varieties.

The heuristic developed in this part determines the priority forharvesting each cane field during a specific period. The priority of afield is based on the prime harvest period for that field. In a specificperiod, the field that will lose the most yield if harvesting isdelayed until the next period is the most critical field, and this fieldis given the highest priority for harvesting. For a given period, theheuristic starts by dividing the cane fields into three sets. The firstset, Set A, contains the fields in which the yields are decreasing.The second set, Set B, contains the fields in which the yields areat their peak, and the third set, Set C, contains the fields in whichthe yields are increasing. The fields in Set A have the highest prior-ity for harvesting because the yields of these fields are decreasingwith time. If these fields are not harvested soon, their yields willdecrease. The fields in Set C have the lowest priority for harvestingbecause their yields will increase with time. The harvesting ofthese fields can be delayed until they have a higher cane yield. Ifthere is more than one cane field in the set, the cane fields in eachset must be prioritized.

Let Cijt be the field coefficient for field j of grower i in period t,and let Git be the grower coefficient of grower i in period t. The fieldcoefficient Cijt is the ratio of the estimated yield of field j of grower iin the period t to the maximum yield if the field could be harvestedin the best yield period, as shown in Eq. (26). The grower coeffi-cient Git is the total harvested cane yields from all of the fields ofgrower i in period t divided by the total maximum yield thatgrower i can obtain if all of his/her fields are harvested in theirhighest yield periods, as expressed in Eq. (27). The grower withthe lowest grower coefficient in the given period has the leastopportunity to harvest in the best yield period among the growersin the group.

In set A, fields with lower yield coefficients that belong to thegrower with a lower grower coefficient will have higher priorityto be harvested. For the fields in set B, the field owned by thegrower with the lower grower coefficient has higher priority, whilethe field in Set C with a higher field coefficient and higher growercoefficient will be primarily selected to be harvested.

Cijt ¼f ijt

Maxt2Tff ijtgð26Þ

Git0 ¼P8j2i

Pt0

t¼1xijt0aijf ijt0P8j2imij

ð27Þ

The steps of the heuristic algorithm are as follows:Step 0: Begin in harvest period 1, and set t0 = 1.Step 1: Set t ¼ bt0c, and divide all of the unharvested fields into

Set A, Set B, and Set C.Step 2: If Set A ¼ fØg, then go to Step 3; otherwise, prioritize

the fields in Set A.

Step 2-1: Prioritize the fields based on the yield coeffi-

cient Cijt. Select the field that has the lowestyield coefficient ði:e:; mini;j2 SetAfCijtgÞ to beharvested. If more than one field has thesame value for Cijt, then go to Step 2-2.

Step 2-2: Prioritize the fields based on the grower coef-ficient Git. Select the field that has the lowestgrower coefficient. If more than one field hasthe same value for Git, then go to Step 2-3.

Step 2-3: Prioritize the fields based on the field coeffi-cient of the next period, Cijt+1. Select the fieldthat has the lowest field coefficient in thenext period. If more than one field has thesame value for Cijt+1, then the fields are ran-domly selected.

Step 3: If Set B ¼ fØg, then go to Step 4; otherwise, prioritizethe fields in Set B.

Page 9

Table 5Data used in

a1 rai = 0.16 hbHT: number

50 S. Thuankaewsing et al. / Computers and Electronics in Agriculture 110 (2015) 42–55

Step 3-1: Prioritize the fields based on the grower coef-ficient Git. Select the field that has the lowestgrower coefficient. If more than one field hasthe same value of Git, then go to Step 3-2.

Step 3-2: Prioritize the fields based on the field coeffi-cient of the next period, Cijt+1. Select the fieldthat has the lowest field coefficient in thenext period. If more than one field has thesame value of Cijt+1, then the fields are ran-domly selected.

Step 4: If Set C ¼ fØg, then go to Step 6; otherwise, prioritizethe fields in Set C.

Step 4-1: Prioritize the fields based on the yield coeffi-

cient Cijt. Select the field that has the highestyield coefficient ði:e:; maxi;j2 Set CfCijtgÞ to beharvested. If more than one field has thesame value for Cijt, then go to Step 4-2.

Step 4-2: Prioritize the fields based on the grower coef-ficient Git. Select the field that has the highestgrower coefficient. If more than one field hasthe same value of Git, then go to Step 4-3.

Step 4-3: Prioritize the fields based on the field coeffi-cient of the next period, Cijt+1. Select the fieldthat has the highest field coefficient in thenext period. If more than one field has thesame value of Cijt+1, then the fields are ran-domly selected.

Step 5: Allocate the period(s) required for harvesting the entirearea of the selected field ði:e:; start in period bt0c andend in period dt0 þ rijteÞ. Then, update the periodt0 = t0 + rijt and go to Step 1.

Step 6: If all of the cane fields have been harvested, then stop.

To demonstrate the use of this part of the heuristic, consider acase of 2 growers in a group. Each grower owns 2 cane fields.The attributes of the fields for 6 harvest periods are shown inTable 5. A partial listing of the execution of the algorithmic stepsis as follows:

In period 1: Set A = {Ø}, Set B = {Ø}, Set C = {1(1), 1(2), 2(1), 2(2)}

Prioritize the fields in Set C based on Cijt (i.e., Step 4-1), giving{2(2), 1(2), 2(1), 1(1)}.Because C221 is the highest yield coefficient, choose field 2(2) forharvesting from period 1 to period 2.

In period 3: Set A = {Ø}, Set B = {1(2), 2(1)}, Set C = {1(1)}

Compute

G13 ¼ 0ð10Þð8:5Þþ0ð5Þð9Þþ0ð10Þð9Þþ0ð5Þð9:5Þþ0ð10Þð9:5Þþ0ð5Þð10Þ100þ50 ¼ 0 or 0%;

G23 ¼ 0ð5Þð9Þþ0:5ð10Þð9:5Þþ0ð5Þð9:5Þþ0:5ð10Þð10Þþ0ð5Þð10Þþ0ð10Þð9:5Þ50þ100 ¼ 0:65 or 65%:

heuristic illustration.

a.of periods required to harvest the entire field j of grower i if harvesting be

Therefore, based on Git (i.e., Step 3-1), field 1(2) is selected to beharvested.Harvest field 1(2) from period 3 to period 3.

In period 4: Set A = {2(1)}, Set B = {1(1)}, Set C = {Ø}

Harvest field 2(1) from period 4 to period 4.

In period 5: Set A = {1(1)}, Set B = {Ø}, Set C = {Ø}

Harvest field 1(1) from period 5 to period 6.

The solution given by the heuristic is to harvest field 2 of grower2 (i.e., field 2(2)) from periods 1 to 2. In period 3, all of the cane infield 2 of grower 1 (i.e., field 1(2)) is harvested. All of the cane infield 2(1) is scheduled to be harvested in period 4, and periods 5and 6 are allocated to harvest field 1(1)). Growers 1 and 2 havethe opportunity to harvest their cane at 95% and 97% (i.e.,G16 = 0.95, G26 = 0.97), respectively, of their expected maximumyields if they can harvest all of the cane in their best yieldperiods.

Even though the heuristic developed in this part is quite similarto what the growers would do in practice, the proposed model con-siders more of the comparative yield trends of the fields among thegrowers in the group and also focuses on having equal benefits forall of the growers in the group, which receives less consideration ingenuine practice.

4.3. Part II: Tabu search approach

The quality of the solution obtained from the initial solution,then, is improved by the tabu search (TS) approach (Glover,1989). The tabu search is a metaheuristic that has been widelyemployed in solving scheduling problems. The details of the tabusearch approach applied to this problem are described as follows:

Neighborhood: the swap move operation is used to structure theneighborhood of the search. This move is the interchange ofharvesting sequences between two fields.Tabu list: a tabu list with a fixed 3–5 iterations. In other words,the recent moves are stored in this list. The swap operationbetween two fields that have been recently swapped will beprohibited for the next 3–5 iterations.Termination criterion: the tabu search is stopped when there isnot any better solution than the current best solution for 5 con-secutive iterations. The current best solution is the solution ofthe heuristic.

The algorithm is to swap the harvesting sequence of two fieldsto find the better solution. To avoid becoming trapped in localoptima, the recently swapped pair of fields will be prohibited orstored in the tabu list with a fixed tenure of iterations. The

gins in period t.

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S. Thuankaewsing et al. / Computers and Electronics in Agriculture 110 (2015) 42–55 51

algorithm will be repeated until the termination criterion ismet. The additional notation and the pseudocode of the tabusearch algorithm developed for this harvesting problem aredescribed.

Additional notation

s[k]

StartSet TL

zBes

D

NS⁄ = S0

If

El

EnLoo

End

represents the field j of grower i on sequencing positionk {k = 1,2, . . .,K}.

s½k0 �

represents the field j0 of grower i0 on sequencingposition k0.

S

set of harvesting plan S = {s[1], s[2], . . ., s[K]}. S0 set of the best harvesting plan in the current search

iteration.

S⁄ set of the best harvesting plan of the previous iteration. SInit set of the initial harvesting plan obtained from the first

part of the heuristic.

SBest set of the best harvesting plan obtained from the tabu

search.

z the objective function value of the set S. z0 the objective function value of the set S0. z⁄ the objective function value of the set S*. zInit the objective function value of the set SInit. zBest the objective function value of the set SBest. V[+] set of a swapped pair of fields that provides the best

solution in the current iteration.

V[�] set of a pair of fields that exits from the tabu list. TL set of a pair of fields in the tabu list. d number of iterations with which the current best

solution has been found.

d⁄ maximum number of iterations allowed after the

current best solution has been found. This number is thetermination criterion.

Pseudocode of the tabu search algorithm

= /, d = 0, z⁄ = zInit, S⁄ = SInit, � Initializt = zInit, SBest = SInit

o while d < d⁄ � Check tz0 = 0, S0 = /, V[+] = / � InitializFor k = 1 to K

For k0 = k+1 to KS = S⁄If fs½k�; s½k0 �g R TL or fs½k0 �; s½k�g R TL then � Swap th

the besswap s½k� and s½k0 � by s½k� ¼ i0; j0; s½k0 � ¼ i; j

Calculate zIf z > z0 then

S0 ¼ S; z0 ¼ z;V ½þ� ¼ fs½k�; s½k0 �gEnd if

End ifNext k0

ext k, z⁄ = z0, TL = TL + V[+] � V[�] � Updatez⁄ > zBest then � Determ

SBest ¼ S�; zBest ¼ z�; d ¼ 0sed = d + 1d if

p � Go back

5. Results and discussion

5.1. Heuristic evaluation

In this section, 100 small-sized problems were generated tocompare the performance of the heuristic algorithm with that ofthe optimization model. The problems consisted of 2–8 growersin a group, 10–25 cane fields, 10 harvest periods and 600–2500tons for the transportation quota. The forecasted cane yield foreach cane field over the harvest season was predicted by theANN model, and these yields were used as inputs for the optimiza-tion model and the heuristic algorithm. For the optimizationmodel, the sample problems were solved with the mathematicalprogramming software LINGO 13 on a PC with an Intel(R) Cor-e(TM)2 Quad 2.66 GHz processor, to find the optimal harvestschedules. For the heuristic algorithm, these problems were solvedusing VBA in Microsoft Excel on the same PC. The average of thetotal harvested cane, the average of the yield proportion and theaverage computational times required for the two models are com-pared in Table 6. The results show that the solutions from the heu-ristic algorithm are similar to the optimal solutions. In addition,comparisons of the opportunities to harvest for growers in a groupin terms of the average maximum and minimum, the average andthe standard deviation of the grower coefficient are shown.

For example, in case (4,5,10) with a transportation quota of 600tons, there are 4 growers in a group, and each grower has 5 canefields. The problem assumes 10 harvest periods; in each period,only 60 tons of cane can be harvested and transported to the millby the group. In the optimal solution, the grower in a group whohas the highest opportunity to harvest (i.e., Max Git) obtains a har-vested yield of 99.60% of the maximum yield, whereas the growerwith the least opportunity (i.e., Min Git) to harvest their caneobtained 98.38% of the maximum yield, on average. The solutionsobtained using the heuristic averaged 99.22% and 97.20% for themaximum and minimum cases, respectively. On average, the

e the parameters to the initial solution

he termination criteria by continuing the search if d is less than d⁄

e z0 = 0, S0 = /, V[+] = / in each search iteration

e sequence of two fields that are not in the tabu list and selectt swapped pair that provides the best solution for this iteration

the obtained solution and the tabu listine and update the current best solution

to ‘‘Do While d < d⁄’’

Page 11

Table 6Result comparisons.

No. Problemparameters (i, j, t)

Transportationquota

Average of total harvestedcane (Tons)

% of harvestedcane deviation

Average of Max Git �Min Git (%) Average Git (%) % of Git

deviationStandard deviationof Git

Average of computationtime (sec)

Opt. Sol. Heu. Sol. Opt. Sol. Heu. Sol. Opt. Sol. Heu. Sol. Opt. Sol. Heu. Sol. Opt. Sol. Heu. Sol.

1 (2, 5, 10) 600 591.30 590.75 0.09 98.74–98.37 98.63–98.13 98.56 98.38 0.18 0.0026 0.0036 50.63 6.362 1800 1766.81 1766.19 0.04 98.78–97.73 98.75–97.71 98.26 98.23 0.03 0.0074 0.0074 51.91 8.213 2500 2455.49 2453.01 0.10 98.45–98.10 98.49–97.86 98.27 98.17 0.10 0.0025 0.0045 106.68 6.54

4 (3, 5, 10) 600 590.58 588.23 0.40 98.93–97.98 99.12–96.74 98.48 97.91 0.58 0.0049 0.0123 223.52 16.575 1800 1779.41 1775.54 0.22 99.30–98.51 99.15–98.11 98.83 98.65 0.19 0.0043 0.0054 124.46 18.796 2500 2466.13 2455.90 0.41 99.30–97.97 98.98–97.53 98.66 98.27 0.39 0.0068 0.0076 271.84 18.74

7 (4, 5, 10) 600 593.31 590.69 0.44 99.60–98.38 99.22–97.20 98.94 98.37 0.58 0.0056 0.0089 1701.27 43.918 1800 1781.83 1773.58 0.46 99.82–98.29 99.19–97.78 99.01 98.52 0.49 0.0067 0.0066 576.74 42.789 2500 2476.38 2469.11 0.29 99.53–98.77 99.28–97.89 99.09 98.77 0.32 0.0034 0.0063 1676.19 39.86

10 (5, 4, 10) 600 595.28 593.57 0.29 99.78–98.68 99.65–98.05 99.22 98.90 0.32 0.0048 0.0065 2498.07 41.8911 1800 1783.36 1777.84 0.31 99.75–98.41 99.52–97.98 99.13 98.77 0.36 0.0056 0.0061 1721.81 44.5012 2500 2472.98 2466.45 0.26 99.36–98.44 99.42–98.01 98.93 98.66 0.27 0.0039 0.0055 255.81 43.46

13 (6, 3, 10) 600 592.86 591.33 0.26 99.54–98.28 99.37–97.45 98.80 98.52 0.29 0.0052 0.0070 5027.13 26.2314 1800 1779.37 1772.74 0.37 99.73–98.25 99.74–97.22 98.89 98.57 0.32 0.0058 0.0101 1608.80 23.4715 2500 2467.16 2460.13 0.28 99.70–97.88 99.59–96.74 98.79 98.37 0.42 0.0077 0.0104 87788.42 33.70

16 (7, 3, 10) 600 594.30 592.59 0.29 99.71–98.32 99.64–97.27 99.06 98.71 0.35 0.0053 0.0086 1538.98 48.0217 1800 1780.96 1775.36 0.31 99.72–98.15 99.56–97.62 98.94 98.57 0.38 0.0063 0.0073 1320.36 43.2518 2500 2477.34 2473.65 0.15 99.76–98.45 99.74–97.73 99.15 98.95 0.21 0.0050 0.0067 2483.37 47.57

19 (8, 3, 10) 600 595.37 593.04 0.39 99.92–98.48 99.62–98.02 99.27 98.82 0.45 0.0050 0.0057 41513.94 64.2120 1800 1777.51 1772.49 0.28 99.75–98.12 99.82–96.56 98.74 98.37 0.38 0.0059 0.0117 19808.19 65.4821 2500 2476.04 2470.62 0.22 99.56–98.49 99.72–97.95 99.03 98.82 0.22 0.0037 0.0067 2526.46 62.08

52S.Thuankaew

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andElectronics

inA

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S. Thuankaewsing et al. / Computers and Electronics in Agriculture 110 (2015) 42–55 53

growers in a group can harvest 98.94% of their maximum caneyields (i.e., Avg. Git) if they follow the schedule given by the solu-tion of the optimization model, whereas they can harvest 98.37%using the schedule provided by the heuristic. The standard devia-tions of the opportunities of growers in a group (i.e., Std Git) are0.0056 and 0.0089 using the optimal schedule and the heuristicschedule, respectively. Moreover, the computational time withthe heuristic algorithm was significantly less than that of the opti-mization model, which indicates that the heuristic is practical forsolving large-scale problems.

5.2. Sensitivity analysis

In this section, the effect of the composition of the cane fields ina farm group (i.e., fields with various yield trends) is studied.Because fields have different yield trends, which is the result ofvarious cultivation factors, the composition of the fields in a groupcould affect the harvest schedule and the opportunity for growersto harvest in the best yield period. Generally, the fields can be sep-arated into 3 groups: group E contains fields in which the best yieldperiods are early in the harvest season, group M contains fields inwhich the best yields are obtained in the middle of the harvest sea-son, and group L contains fields that are best harvested late in theseason.

A problem with 5 growers, each owning 8 cane fields (i.e., atotal of 40 cane fields), 16 harvest periods and a transportationquota of 1800 tons, was analyzed. Group E consisted of the fields

Table 8Example of forecasted cane yields in the case study.

Grower Canefield

Area(rais)

Forecasted cane yield in each harvest round (tons/

1 2 3 4 5 6

1 1 2.00 10.60 11.02 11.43 11.61 11.79 11.892 2.41 14.53 14.74 14.96 15.05 15.13 15.02

2 1 2.79 13.33 14.03 14.74 15.13 15.52 15.772 2.71 13.90 14.54 15.18 15.98 16.79 16.913 3.05 16.80 17.03 17.26 17.57 17.87 17.90

3 1 2.75 15.99 16.08 16.16 16.52 16.89 17.102 3.14 17.49 17.94 18.38 18.81 19.23 19.363 2.21 13.34 13.48 13.63 13.65 13.68 13.694 2.67 14.57 14.81 15.05 15.30 15.54 15.855 2.86 17.15 17.42 17.68 17.77 17.86 17.896 2.74 13.08 13.78 14.47 14.85 15.23 15.477 2.51 15.19 15.41 15.64 15.73 15.82 15.708 2.48 12.75 13.14 13.54 13.90 14.27 14.44

..

. ... ..

. ... ..

. ... ..

. ... ..

.

8 1 2.64 14.67 15.45 16.24 16.43 16.62 16.272 2.29 10.80 11.42 12.05 12.79 13.53 13.773 2.77 14.07 15.65 17.23 17.32 17.41 17.20

Table 7Sensitivity analysis.

No. Field composition ratio %E:%M:%L Total harvested cane (tons)

1 100:0:0 (40:0:0) 1659.302 80:10:10 (32:4:4) 1730.823 70:15:15 (28:6:6) 1731.904 60:20:20 (24:8:8) 1745.965 40:30:30 (16:12:12) 1785.046 35:32.5:32.5 (14:13:13) 1786.467 20:40:40 (8:16:16) 1756.348 10:45:45 (4:18:18) 1746.759 0:50:50 (0:20:20) 1715.70

Note (E:M:L): number of fields in E, M and L groups, respectively.

where the best yield periods were between periods 1 and 5. GroupsM and L contained the fields whose best yield periods were fromperiods 6 to 11 and from periods 12 to 16, respectively. The sensi-tivity of the solutions, based on various compositions, is shown inTable 7. It is obvious that the cases where the field compositionshave more widely distributed yield trends (i.e., problems 5 and6) provide greater opportunities to harvest in the best yield periodsfor all of the growers (i.e., Git) than the cases in which the fieldshave the same yield trend (i.e., problem 1).

A noteworthy fact to the reader is that the proposed harvestrotation concept relies highly on the yield trends estimation. Dif-ferent yield trends would lead to different harvest scheduling.Hence, accurate estimation of the cane yield and its maximum con-tribute strongly to the effectiveness of the harvest schedule as wellas benefiting the growers.

5.3. Case study and implementation

The heuristic algorithm was employed to solve an industrial-scale problem as a case study. The data were collected from oneof the largest sugar mills in Thailand in the 2011/2012 harvest sea-son. The problem consisted of 8 growers, 44 cane fields, and16 weeks for harvesting, and a transportation quota of 1800 tons/week was scheduled based on the proposed approach. Severalexamples of the estimated yields and the harvest schedules areshown in Tables 8 and 9, respectively. In Table 8, each recordshows the information for each cane field of each grower and the

rai)

7 8 9 10 11 12 13 14 15 16

12.00 12.14 12.28 12.43 12.58 12.39 12.21 12.12 12.04 11.8614.91 14.82 14.72 14.68 14.65 14.34 14.03 13.90 13.77 13.67

16.02 16.36 16.70 16.97 17.24 17.41 17.58 17.55 17.52 17.4717.03 16.88 16.73 16.48 16.22 16.05 15.87 15.83 15.79 15.7317.92 18.25 18.58 18.89 19.20 18.99 18.78 18.34 17.89 17.54

17.31 17.15 16.99 16.52 16.05 15.87 15.68 15.57 15.46 15.2119.49 19.53 19.58 19.66 19.74 19.60 19.46 19.01 18.55 18.0513.71 13.82 13.93 13.92 13.92 13.90 13.88 13.87 13.86 13.8416.17 16.35 16.53 16.56 16.59 16.68 16.77 16.74 16.70 16.6417.92 17.95 17.97 17.91 17.84 17.79 17.74 17.65 17.57 17.5115.72 16.05 16.39 16.66 16.93 17.09 17.26 17.23 17.20 17.1515.59 15.49 15.39 15.35 15.31 14.99 14.67 14.54 14.40 14.2914.62 14.82 15.02 15.26 15.50 15.56 15.63 15.61 15.59 15.54

..

. ... ..

. ... ..

. ... ..

. ... ..

. ...

15.92 15.81 15.69 15.48 15.27 15.01 14.74 14.27 13.80 13.5514.01 14.21 14.41 14.34 14.26 14.18 14.11 13.82 13.52 13.3216.99 16.74 16.48 16.25 16.01 15.83 15.65 15.45 15.25 15.00

Max Git �Min Git (%) Average of Git (%) Standard deviation of Git

93.78–90.90 92.31 0.011296.76–95.64 96.14 0.005398.11–95.22 96.26 0.012997.71–96.17 96.95 0.006499.69–98.44 99.12 0.005299.59–99.08 99.25 0.002097.89–97.31 97.61 0.002697.36–96.70 97.03 0.003195.99–94.65 95.33 0.0050

Page 13

Table 10Yield proportions of all growers in the case study.

Grower Expected maximum yield(tons)

Total harvested cane(tons)

Git (%)

1 61.55 60.48 98.272 153.84 153.31 99.653 362.46 357.80 98.714 258.94 257.28 99.365 197.73 196.01 99.136 264.60 263.45 99.567 375.77 370.60 98.638 125.11 123.74 98.90

Max Git �Min Git (%) 99.65–98.27Average of Git (%) 99.03Standard deviation of Git 0.0049

54 S. Thuankaewsing et al. / Computers and Electronics in Agriculture 110 (2015) 42–55

estimated cane yield obtained from the ANN model. The problemcould not attain the optimal solution by the proposed optimizationmodel within 10 h of computation time, while the heuristic solu-tion consumed only 235.22 s. Table 9 shows the sequence of theharvest from the heuristic. The first harvested field was field 1 ofgrower 4, and the last harvested field was field 3 of grower 5.The harvested area of each cane field in each period is alsoreported. For example, in period 1, field 1 of grower 4, field 6 ofgrower 4, field 11 of grower 4, and field 2 of grower 7 were 100%harvested, and field 5 of grower 5 was harvested 32.90% of its totalarea. The opportunities to harvest for all of the growers are similar,as reported in Table 10. Therefore, this approach could provideequal opportunities to harvest among growers.

To implement the model, Higgins (1999) has suggested industryparticipation to ensure ownership of the model by industry. Theimplementation should involve grower workshops to ensure thesensibility of the results and satisfaction of the concept. Changemanagement workshops should be held to overcome implementa-tion barriers such as social issues. When delivering the concept togrowers and industry, the construction of general managementrules based on the proposed model is necessary in such a way thata general set of rules to organize their farms that is close to optimalis adopted. However, in the Thai case, the transition could takeyears due to the number of growers involved. A pilot group canbe set to quantify the actual outcomes that can be objectively con-veyed to the growers and industry. Then, diffusing the concept torapid adopters and later industry-wide can be accomplished. Asnoted, the estimation of the cane yield and trends play a crucial rolein the effectiveness of this harvest schedule. Hence, the construc-tion of a database and building a reliable field data collectionmethod are needed and are, in fact, crucial for implementation ofthe concept. Likewise, numerous uncertainties (e.g., unexpectedweather conditions, plant diseases, illegal fires in the crops) can alsoresult in deviations in the sugar cane yield. Hence, updating data ona timely basis and setting management rules to accommodate thoseuncertainties also contribute to industry adoption.

Table 9Some example of harvest schedules in the case study.

Grower Cane field The harvested area proportion in each harvest round (%)

1 2 3 4 5 6

4 1 100.004 6 100.004 11 100.007 2 100.005 5 32.90 67.101 2 100.003 7 100.004 7 100.003 5 8.65 91.354 2 100.008 3 100.003 3 9.50 90.507 3 100.008 1 100.004 4 36.63 63.374 3 100.005 6 100.002 2 52.34 47.3 1 100.6 3 100.7 1 40.6 1

..

. ... ..

. ... ..

. ... ..

. ...

3 66 45 3

6. Conclusions

In this paper, an optimization model and a heuristic algorithmwere developed to determine the most suitable sugar cane harvestschedule for a group of growers. Each grower owns a set of sugarcane fields that have different yield patterns depending on variouscultivation factors. The objective was to maximize sugar cane har-vest yields with equal returns for all growers in the group. Toemploy the developed harvest scheduling models, the yields ofeach field over the harvest season were estimated using an ANN.The proposed optimization model could be solved for only verylow-order problems, i.e., problems with fewer than 25 cane fieldsand 10 harvest periods. It is obvious that the optimization modelis not practical in actual industrial cases. The heuristic algorithmwas developed to solve an industrial-scale problem. It was foundthat the heuristic performed well relative to the optimizationmodel for very low-order problems, with less than a 2% deviationin both the harvested sugar cane yields and the average grower-coefficient Git, and the heuristic algorithm requires considerably

7 8 9 10 11 12 13 14 15 16

66000088 59.12

100.00

..

. ... ..

. ... ..

. ... ..

. ... ..

. ...

100.0018.22 81.78

100.00

Page 14

S. Thuankaewsing et al. / Computers and Electronics in Agriculture 110 (2015) 42–55 55

less computational time than was required by the optimizationmethod used. The heuristic algorithm can be successfully appliedto industrial-size problems. The algorithm was applied to an actualcase in the sugar industry in Thailand that consisted of eight grow-ers, 44 small sugar cane fields and 16 harvest periods. An accurateand practical solution was obtained.

A sensitivity analysis of the solutions showed that the farmgroups that consisted of fields that had widely distributed yieldtrends provided more opportunities to harvest cane in the bestyield period for all of the growers (i.e., Git) than the groups thatconsisted of fields that had the same yield trend. Therefore, toincrease the efficiency of the system, the optimum clustering offarms should be considered as well as the harvest schedule infuture research.

Acknowledgments

This research is supported by Mitr Phol Sugarcane ResearchCentre Co., Ltd., Supply Chain and Logistics System Research Unit,Khon Kaen University and the Food and Functional Food ResearchCluster of Khon Kaen University.

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