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Modeling within-season sugarcane growth for optimal harvest system selection
Agricultural Systems 73 (2002) 261–278 www.elsevier.com/locate/agsy
Modeling within-season sugarcane growth for optimal harvest system selection M.E. Salassi*, J.B. Breaux, C.J. Naquin Department of Agricultural Economics and Agribusiness, Louisiana State University Agricultural Center, 101 Agricultural Administration Building, Baton Rouge, LA 70803-5604, USA Received 26 September 2000; received in revised form 13 June 2001; accepted 15 June 2001
Abstract The recent switch from wholestalk to combine sugarcane harvesters has raised questions concerning which harvester is more profitable. Combine harvesters recovery more of the sugarcane in the field than wholestalk harvesters, but also have higher trash levels reducing sucrose recovery. The objective of the research presented in this article is to determine the optimal sugarcane harvest system selection for sugarcane production in Louisiana. Sugarcane stalk weight and sugar per stalk equations are estimated in order to predict tonnage and sugar yields throughout the harvest season. These predicted yields are then adjusted to reflect field tonnage and sugar recovery for the combine and wholestalk harvesting systems. A mixed integer mathematical programming model is then used to determine the optimal harvest system under alternative sugarcane variety combinations, wholestalk harvester field recovery rates, and combine harvester sugar recovery rates. Results identify field recovery and sucrose recovery conditions for which one type of harvest system would be preferred over the other. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Sugarcane; Yield growth; Optimal harvest system; Field recovery; Sucrose recovery
1. Introduction Sugarcane, a member of the grass family, is a perennial agricultural crop grown primarily for the juices expressed from its stalks. Raw sugar produced from these juices are later refined into white sugar. As a perennial crop, one planting of
* Corresponding author. Tel.: +1-225-388-2713; fax: +1-225-388-2716. E-mail address: [email protected] (M.E. Salassi). 0308-521X/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0308-521X(01)00081-6
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sugarcane will generally allow for three to six or more annual harvests before replanting is necessary. Sugarcane crops are generally classified based on its current year or stage of the crop cycle. From the planting through the first harvest, a sugarcane crop is referred to as a plantcane crop. After the first harvest succeeding crops are referred to as stubble crops. First stubble, for example, would refer to a sugarcane crop in its first year of stubble or regrowth after the first harvest. Production of sugarcane occurs in warm, humid climates throughout the world. In the United States, sugarcane production is concentrated primarily in the states of Louisiana and Florida, with some production also located in Texas, Hawaii, and Puerto Rico. In the 1999/2000 crop year, 400,316 ha of sugarcane were harvested in the United States (USDA, 2000). Approximately 379,000 of these hectares were harvested for sugar with the remainder used for seed. Louisiana harvested 188,179 ha and Florida harvested 186,156 ha. Average yields per harvested acre for Louisiana and Florida were 29.6 and 31.7 metric tons of sugarcane per acre, respectively. Sugarcane is planted vegetatively in late summer or early fall by placing stalks of sugarcane in open furrows. At each plant node, these stalks have buds or ‘‘eyes’’ from which new plants develop. As a sugarcane plant matures throughout the growing season, the amount of sucrose in the cane increases. Most of this sucrose production occurs when the plant is fully mature and begins to ripen (Alexander, 1973). Sugarcane harvest in the United States begins in the fall of the year. The oldest sugarcane crops are usually harvested first (second stubble and older crops), followed by newer crops (first stubble and finally plantcane). In Florida, the sugarcane harvest season runs from October through to March or April. However, in Louisiana, the harvest season begins in late September and concludes at the end of December or early January. The reason for this restricted harvest season is due to the limited cold tolerance of sugarcane varieties and the risk of freezing temperatures in Louisiana towards the end of the harvest season. Exposure to cold weather requires that cold tolerance be an important characteristic of commercial varieties of sugarcane grown in these regions (Tai and Miller, 1993). In recent years, two simultaneous changes have occurred in the sugarcane industry in Louisiana, both of which have had a dramatic impact on the economics of sugarcane production in the state. In 1993, the variety LCP 85-384 was released. This variety is a high yielding, excellent stubbling variety (Louisiana State University Agricultural Center, 1999). The excellent stubbling ability of this variety implies that the yields of succeeding crops, after the first harvest (plantcane), are higher than those for comparable varieties. It is slow to emerge after planting, produces a large number of small stalks and exceeds most other varieties in sugar per acre. However, this variety frequently lodges, is brittle, and difficult to harvest when lodged. Studies conducted with the previously predominant wholestalk harvesting system found that LCP 85-384 had the highest percent of scrap (unharvested plant material) left in the field and the highest percent of stalks damaged by wholestalk harvesters (Dufrene et al., 1996). At the same time, Louisiana sugarcane producers switched from the traditional wholestalk harvesters to the combine harvesters similar to the types used in Florida and other sugarcane producing regions. In the 1950s, sugarcane producers in
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Australia began experimenting with combine sugarcane harvesters (Churchward and Belcher, 1972). These harvesters would cut sugarcane stalks into 12–14 inch billets, remove extraneous matter, and deposit the billets into wagons running beside the harvester. The original harvesters were designed to cut burned sugarcane, as were the wholestalk harvesters. In the 1970s, considerable attention in Australia was being focused on developing a combine harvester which would harvest green sugarcane (Churchward and Poulsen, 1988). A primary advantage of harvesting green sugarcane is that the harvester deposits extraneous organic matter in a layer on the field, promoting moisture conservation, weed control, and cost savings in cultivation. The main disadvantage of harvesting green sugarcane is the potential to deliver more extraneous plant material to the mill, reducing sugar recovery. The combine harvesters being used in Louisiana were better able to harvest sugarcane fields with high tonnage yields compared with wholestalk harvesters. However, it was still necessary to burn the sugarcane to remove extraneous leaf and other plant material prior to delivering to the mill. With wholestalk harvesting, stalks of sugarcane would be piled into rows after harvest and then burned to remove leaf trash. The adoption of combine harvesters required the standing stalks of sugarcane in the field to be burned prior to harvest. Although the field recovery rates of sugarcane tonnage for these harvesters were higher, they also tended to deliver more leaf and other plant material trash after burning to the mill, due to the different harvest method of chopping the sugarcane stalk into small pieces and dumping into wagons. This generally resulted in lower commercially recoverable sugar measures per ton of sugarcane harvested for the combine harvester as compared with the more traditional wholestalk harvesters. Although combine harvesting systems can recover a higher percentage of sugarcane in the field than the wholestalk harvesters, they also have higher investment and operating costs. As a result, it is not clear which type of harvesting system would be more economical under alternative possible yield scenarios. The decision of selecting the optimal (most profitable) sugarcane harvesting system is therefore dependent upon the relative recoverable yield and quality of the sugarcane harvested as well as the investment and operating costs of the two respective systems. This article develops two models which are jointly used to evaluate sugarcane harvesting system selection under alternative sugarcane yield and quality scenarios. The first model is a sugarcane growth model consisting of two equations which predict sugarcane tonnage and sucrose levels throughout the harvest system. Estimates from this model provide yield and sucrose predictions which are then incorporated into a mixed integer mathematical programming model which determines the optimal harvest system selection within a whole-farm context. Several studies have developed models to predict the sucrose level in sugarcane. Alvarez et al. (1982), developed sugarcane yield prediction models as a function of several agronomic and climatic factors. Crane et al. (1982) used these yield predictions to develop a sugarcane stubble replacement decision model. They reported that sugar accumulation is a function of both sucrose accumulation and vegetative growth. Chang (1995), in research on Taiwanese sugarcane cultivars, suggested that individual cultivars have distinct sucrose maturation curves with different peak levels.
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Applications of crop harvest scheduling models, utilizing some type of operations research procedure, are most common in the timber industry. Most of these applications involve the use of either linear programming or simulation models. Recent studies have investigated the use of Monte Carlo integer programming (Nelson et al., 1991; Daust and Nelson, 1993), bayesian concepts (Van Deusen, 1996), and tabu search procedures (Brumelle et al., 1998). Crop growth models have provided useful tools for several crop management activities such as pesticide and irrigation timing (Mishoe et al., 1984). Several studies have developed crop growth models to predict the harvest date of agricultural crops (Wolf, 1986; Lass et al., 1993; Malezieux, 1994). However, most of these studies utilize optimal harvest decision rules based upon agronomic characteristics of the crop rather than economic principles. Several studies have addressed various aspects of sugarcane productivity and harvest operations. Millhollon and Legendre (1996) studied the use of glyphosate, an artificial crop ripener used in sugarcane production, on sugarcane yield. Two studies have evaluated the economics of sugarcane stubble crop replacement in Florida (Crane et al., 1982) and Louisiana (Salassi and Milligan, 1997). These studies evaluated the optimal crop cycle length by comparing annualized future net returns from replanting to estimated returns from extending the current crop cycle for another year. Semenzato (1995) developed a simulation algorithm for scheduling sugarcane harvest operations at the individual farm level in such a way that the lapse of time between the end of burning and processing is minimized. A recent study in Australia did determine optimal sugarcane harvest schedules which maximized net returns using mathematical programming procedures (Higgins et al., 1998; Muchow et al., 1998). However, the modeling framework in this study encompassed many farms within a production region over a multi-year harvest period.
2. Model formulation 2.1. The sugar yield prediction models The amount of raw sugar in a field of sugarcane is a function of several variables. Two important measures of sugarcane yield include metric tons of sugarcane per hectare and kilograms of raw sugar produced per hectare. The relationship between sugar per hectare and factors which influence it can be stated simply as follows: SH ¼ TRS TONS ¼ TRS POP STWT
ð1Þ
where SH is total kilograms of raw sugar per hectare, TRS is theoretical recoverable sugar in kilograms of sugar per metric ton of cane, TONS is the metric tons of sugarcane produced per hectare, POP is the per hectare population of sugarcane stalks in the field, and STWT is the stalk weight in kilograms per stalk. Although the population of sugarcane stalks within a field can be assumed to be constant throughout the harvest season, the same assumption cannot be made for the other
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factors in the relationship. Theoretical recoverable sugar and stalk weight both increase as the harvest season progresses. In order to incorporate this yield increase within a whole-farm mathematical programming harvest scheduling model, estimates must be obtained for the predicted levels of each of these factors for each variety of sugarcane produced on the farm for every day of the harvest season. Sucrose maturity data developed at the ARS, USDA Sugar Cane Research Unit in Houma, Louisiana, were used in the analysis. Stalk weight and sugar content of the commercial sugarcane cultivars grown in Louisiana were sampled at intervals during the harvest season from 1981 to 1996. The data included measurements of theoretical recoverable sugar, sugar per stalk and stalk weight by julian date for 3– 16 years, depending upon variety. The harvest season for sugarcane in Louisiana has historically run from the first of October through to the end of December. Observations for each commercial cultivar ranged from julian date 255 to 346 or approximately the middle of September through to the middle of December. The age of the crop (plantcane or stubble) was also included. Models were estimated for stalk weight and sugar per stalk for major sugarcane cultivars produced in Louisiana in order to predict the amount of sugarcane and raw sugar in the field for each day of the harvest season. Previous research suggests that a quadratic model can be used to model sugar accumulation (Crane et al., 1982). Graphical analysis of both the stalk weight as well as the sugar per stalk data suggested that these variables could be estimated using a semi-log functional form. Biological response functions of stalk weight and sugar per stalk were estimated for each cultivar as follows: STWTct ¼ 0 þ 1 LNJD þ 2 CROP þ
y X i YEARi þ "
ð2Þ
i¼x
SPSct ¼ 0 þ 1 LNJD þ 2 CROP þ
y X i YEARi þ "
ð3Þ
i¼x
where STWTct represents stalk weight in kilograms per stalk of cultivar c on day t, SPSct represents sugar per stalk in kilograms of cultivar c on day t, LNJD is the natural log of julian date (numeric day of the year), CROP is a (0,1) indicator variable representing crop age as either plantcane or stubble crop, and YEARi represents discrete indicator variables for different years. Only two categories of the indicator variable CROP were included in the model as stubble crops for a given variety generally have similar sucrose accumulation levels regardless of crop age. These stubble crop sucrose levels, however, are significantly different than plant cane sucrose levels. The annual indicator variables for year were included to capture the relationship that sugarcane cultivars have distinct sugar accumulation curves which shift vertically from year to year depending upon weather and other factors. The base year for comparison in this estimation was 1996 and the indicator variables serve the purpose of adjusting the sugar accumulation curve to factors in a given year by shifting the intercept of the prediction equation. All models were estimated
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using SAS (SAS Institute, version 6.12). The estimates of stalk weight and sugar per stalk were combined with stalk populations to estimate sugar cane and sugar yield for each field. Estimated models of stalk weight and sugar per stalk for two major sugarcane cultivars, CP70-321 and LCP85-384, are shown in Eqs. (4)–(7). Julian date (LNJD) and crop age (CROP) were found to be highly significant in the stalk weight prediction models (Eqs. (4) and (5)). Positive signs on the julian date variable indicate that stalk weight increases throughout the harvest season. The signs on the significant crop age variables were negative, as expected, indicating that stalk weight tends to be greater for plantcane crops than for older stubble crops. Coefficients of determination for specific variety models ranged from 0.36 to 0.80. Similar results were found for the sugar per stalk prediction models (Eqs. (6) and (7)). Julian date was highly significant with positive coefficients indicating sugar accumulation increases during the harvest season. Crop age was found to be significant in one of the two equations estimated. Coefficients of determination were very high in the sugar per stalk models, with and estimated value of 0.89 for both variety models. Durbin-Watson tests for autocorrelation either failed to reject the hypothesis of no autocorrelation or were inconclusive, indicating that the error terms from the model predictions were not serially correlated. The White test for heteroscedasticity (White) failed to reject the hypothesis of homoscedasticity for each cultivar tested, indicating that error terms from the model predictions have a constant variance. The absence autocorrelation and heteroscedasticity indicated that the estimated parameters in the prediction models were efficient (minimum variance) estimators. STWT321;t ¼ 3:022 ð6:92Þ Adj: R2 ¼ 0:80
þ0:748 LNJD ð9:82Þ Durbin-Watson ¼ 1:94
0:149 CROP ð10:27Þ White prob: ¼ 0:41
STWT384;t ¼ 4:163 ð3:53Þ Adj: R2 ¼ 0:36
þ0:901 LNJD ð4:35Þ Durbin-Watson ¼ 2:42
0:071 CROP ð1:88Þ White prob: ¼ 0:36
SPS321;t ¼ 1:571 ð25:99Þ Adj: R2 ¼ 0:89
þ0:300 LNJD 0:013 CROP ð28:49Þ ð6:54Þ Durbin-Watson ¼ 1:99 White prob: ¼ 0:20
SPS384;t ¼ 1:848 ð15:74Þ Adj: R2 ¼ 0:89
þ0:343 LNJD þ0:002 CROP ð16:64Þ ð0:43Þ Durbin-Watson ¼ 2:74 White prob: ¼ 0:14
ð4Þ
ð5Þ
ð6Þ
ð7Þ
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2.2. Farm-level sugar yield predictions Estimated stalk weight, estimated number of stalks per hectare and estimated sugar per stalk were used to predict yield throughout the harvest season for a representative farm. Estimated metric tons of sugarcane per hectare, theoretical recoverable sugar (TRS) and kilograms of raw sugar per hectare were calculated as follows: TONSft ¼ POPf STWTct =2000
ð8Þ
TRSft ¼ POPf SPSct =TONSft
ð9Þ
SUGARft ¼ TONSft TRSft
ð10Þ
where TONSft is the estimated metric tons of sugarcane per hectare in field f on julian date t, POPf is the estimated stalk population per hectare in field f, STWTct is the estimated stalk weight in kilograms per stalk for cultivar c on julian date t, TRSft is the estimated kilograms of raw sugar per metric ton of sugarcane in field f on julian date t (also referred to as TRS), SPSct is the estimated raw sugar per stalk in kilograms for cultivar c on julian date t, and SUGARft is the estimated kilograms of raw sugar per hectare in the field available for harvest. Since POPf, STWTct and SPSct are predicted values with associated variances, direct multiplication would cause the estimated variances of predicted cane and sugar yield estimates to be very large, making the confidence intervals for predicted values considerably wider (Griffiths et al., 1993). As a result, the relationships in Eqs. (8) and (9) were converted to natural log form for calculation. Estimated recoverable yields per field were then adjusted for harvesting parameters associated with each type of harvesting system (field recovery and trash content) and mill efficiency (differences between theoretical recoverable sugar and commercial recoverable sugar) using the following relationships: RTONSfth ¼ TONSft 1 þ TRASHfh FLDRECfh ð11Þ CRSfth ¼ TRSft 0:8345 SFACTORh
ð12Þ
RSUGARfth ¼ RTONSfth CRSfth
ð13Þ
RTONSfth represents the actual metric tons of sugarcane per hectare recovered from field f on day t by harvest system h. TRASHfh is a percentage estimate of the additional leaf matter and other trash in the sugarcane harvested by harvest system h, and FLDRECfh is a percentage estimate of metric tons of sugarcane in field f actually recovered by harvest system h. CRSfth represents the actual kilograms of raw sugar per metric ton of sugarcane recovered from the processed cane. The estimated
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sugar yield is multiplied by a standard factor (0.8345) to convert theoretical recoverable sugar into commercially recoverable sugar. This standard is used by sugar mills to estimate recovery since the actual liquidation factor will not be known until the end of season. Accounting for differences from the laboratory analysis to the fields, the estimated sugar per field is reduced by a scale factor, SFACTORh. The assumed scaler factor varies by type of harvest system used as well as field harvest conditions. In this analysis it was used to adjust sugar recovery by type of harvest system. 2.3. The mixed integer programming model A mixed integer mathematical programming model was developed to determine the most economical harvest system selection for a representative farm. The representative farm was assumed to be 404 ha in total land area with 80.8 ha of land in each phase of the sugarcane crop cycle through harvest of third stubble (fallow, plantcane, first stubble, second stubble, and third stubble). With approximately 20% of harvested plantcane acreage used for seed, the representative farm was assumed to have approximately 307 ha of millable sugarcane. The objective of the mixed integer programming model was to select the harvest system, either wholestalk or combine, which would maximize total farm net returns. In the mixed integer programming harvest system selection model, the harvest season was divided into 2-week periods. The harvest of sugarcane in Louisiana begins with the oldest stubble crops (second stubble and older), followed by first stubble crops, and concluding with plantcane crops. For the representative sugarcane farm modeled in this analysis, each sugarcane crop on the farm was assigned to three possible harvest periods. Second stubble and older crops were assigned to the first and second 2-week periods in October and the first 2week period in November. First stubble crops were assigned for possible harvest in the second 2-week period in October and the two periods in November. Plantcane was assigned to the second 2-week period in November and the two periods in December. The stalk weight and sugar per stalk models presented above were used to predict sugarcane tonnage and raw sugar yields for a date in the middle of each 2-week harvest period. Predicted yields on these dates were used to simulate yields harvested within each 2-week harvest period. The specific dates used in the analysis were: 11 and 25 October, 8 and 22 November, and 6 and 20 December. The mixed integer programming model used in this study was designed as a net revenue maximizing model. Preharvest and harvest field operations for each land area on the farm are specified and the model determines the equipment required to perform these operations. The number of implements and tractors required to perform preharvest operations are determined as integer values by the model. Equipment costs are based on annual fixed costs per equipment item and variable costs per hour of use. For harvest operations, the model is allowed to choose which harvest system, wholestalk or combine, would result in higher net returns. The model maximizes net revenues over total farm cost (Z):
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Maximize Z ¼ Ps TQs þ Pm TQm Ps MQs Pm MQm Ps LQs Pm LQm
n 2 u X X X Cp Ap Wa Sa wHt p¼1
t¼1
g d X n X u X X
c¼1
c¼1 p¼1 t¼1 f¼1
TFCc TRc
TVCc THcptf
g b b X n X u X X X EFCe EQe EVCe EHeptf e¼1
a
d X
e¼1 p¼1 t¼1 f¼1
2 X
q 2 X n X u X X HVCj HVHjptk
j¼1
j¼1 p¼1 t¼1 k¼1
HFCj HVj
ð14Þ
where Ps is the price per kilogram of raw sugar; TQs is the total quantity of raw sugar produced (kg); Pm is the price per liter of molasses; TQm is the total quantity of molasses produced (l); MQs is the processing mill’s share of raw sugar production; MQm is the processing mill’s share of molasses production; LQs is the landlord’s share of raw sugar production; LQm is the landlord’s share of molasses production; Cp is the input variable cost per hectare for crop production phase p; Ap is the number of farm hectares in crop production phase p; Wa is the annual salary for full-time class a workers; Sa is the number of class a full-time workers; w is the hourly part-time wage rate; Ht is the hours of part-time labor hired in time period t; TFCc is the annual fixed cost of tractor type c; TRc is the number of type c tractors used; TVCc is the variable cost per hour of operation for tractor type c; THcptf is the hours of operation for tractor type c on crop production phase p in time period t for field operation f; EFCe is the annual fixed cost of implement type e; EQe is the number of type e implements used; EVCe is the variable cost per hour of operation for implement type e; EHeptf is the hours of operation for implement type e on crop production phase p in time period t for field operation f; HFCj is the annual fixed cost of harvester type j; HVj is the number of type j harvesters used; HVCj is the variable cost per hour of operation for harvester type j; and HVHjptk is the hours of operation for harvester type j on crop production phase p in time period t for harvest land tract k.
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The mixed integer programming model consists of more than one thousand functional constraints. These functional constraints include farm income accounting equations, land allocation equations, and yield equations, as well as constraints for labor availability and time available for field work. Predicted values of sugarcane tonnage and sugar content, described in the previous section, were incorporated into the model through a series of constraints which related area harvested by harvest system type to predicted values for sugar yield. Area harvested by system type as well as tonnage of sugarcane recovered were related to area available for harvest by the following two general sets of equations: 2 X u X AHkjt Ak ¼ 0 for k ¼ 1 . . . q
ð15Þ
j¼1 t¼r
where AHkjt is the area of land tract k harvested (ha) by harvest system j in time period t, and Ak is the area of land tract k (ha) available for harvest. 2 X u X RTONSkjt AHkjt TONSkjt ¼ 0 for k ¼ 1 . . . q
ð16Þ
j¼1 t¼r
where RTONSkjt is the predicted value of recoverable metric tons of sugarcane on land tract k by harvest system j in time period t, and TONSkjt is the total quantity of sugarcane harvested (metric tons) on land tract k by harvest system j in time period t. Total raw sugar produced on the representative farm was estimated by the equation which incorporated predicted values of sugar per ton of sugarcane described in the previous section: q X 2 X u X CRSkjt TONSkjt TQs ¼ 0
ð17Þ
k¼1 j¼1 t¼r
where CRSkjt is the predicted value of raw sugar per ton of sugarcane (kilograms per metric ton) on land tract k for harvest system j in time period t, and TQs is the total quantity of raw sugar produced (kilograms).
3. Results and discussion Results of this analysis is presented in three sections. The first section presents predicted values of sugarcane stalk weight and sugar per stalk for two major sugarcane varieties grown in Louisiana. These estimates are converted to metric tons per hectare and sugar per metric ton values for alternative dates throughout the harvest season. The second section presents results from the mixed integer programming model analyzing the impact of field recovery on optimal harvest system selection,
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while the final section presents results from the analysis of the impact of sucrose recovery on system selection. 3.1. Predicted sugarcane tonnage and sucrose level Predicted sugarcane stalk weight for the two major varieties of sugarcane produced in Louisiana are presented in Table 1. The six dates listed represent the midpoints of each 2-week harvest period. Stalk weight values were estimated to increase at a diminishing rate throughout the harvest season and were higher for plantcane than for stubble crops for both varieties. Estimated stalk weight values for the variety LCP 85-384 were slightly less than those of CP 70-321. Predicted LCP 85-384 stalk weights ranged from 0.924 to 1.123 kg for plantcane and 0.852 to 1.051 kg for stubble crops. Stalk weights for CP 70-321 were estimated to range from 1.205 to 1.368 kg for plantcane and 1.055 to 1.219 kg for stubble crops. The heavier tonnage yields produced by LCP 85-384 compared with other varieties is due primarily to the substantially higher population of stalks per acre. Estimates of predicted sugar per stalk for the two varieties are presented in Table 2. Similar to the estimation of stalk weight, sugar per stalk was modeled to increase at a diminishing rate throughout the harvest season. Although sugar per stalk would eventually reach a maximum and then start to decline, the restricted Table 1 Predicted sugarcane stalk weight by variety Date
Oct. 11 Oct. 25 Nov. 8 Nov. 22 Dec. 6 Dec. 20
Julian date
285 299 313 327 341 355
CP 70-321 (kg per stalk)
LCP 85-384 (kg per stalk)
Plantcane crop
Stubble cane crops
Plantcane crop
Stubble cane crops
1.205 1.241 1.277 1.309 1.341 1.368
1.055 1.092 1.128 1.160 1.191 1.219
0.924 0.969 1.010 1.046 1.087 1.123
0.852 0.897 0.938 0.978 1.015 1.051
Table 2 Predicted sugar per stalk by variety Date
Oct. 11 Oct. 25 Nov. 8 Nov. 22 Dec. 6 Dec. 20
Julian date
285 299 313 327 341 355
CP 70-321 (kg per stalk)
LCP 85-384 (kg per stalk)
Plantcane crop
Stubble cane crops
Plantcane crop
Stubble cane crops
0.125 0.140 0.154 0.167 0.179 0.192
0.112 0.127 0.140 0.154 0.166 0.178
0.089 0.106 0.121 0.137 0.151 0.165
0.091 0.108 0.123 0.139 0.153 0.167
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harvest season in Louisiana practically eliminates harvest during sugarcane maturity stages of decreasing sugar per stalk. Predicted values for CP 70-321 were slightly higher compared with values for LCP 85-384. Plantcane sucrose levels ranged from 0.125 to 0.192 kg of sugar per stalk for CP 70-321 compared with a range of 0.089 to 0.165 kg per stalk for LCP 85-384. Sucrose levels for stubble crops for each variety throughout the harvest season ranged from 0.112 to 0.179 and 0.091 to 0.167 kg per stalk, respectively. Predicted values of sugarcane stalk weight and sugar per stalk were used to estimate the tonnage and sucrose level of sugarcane in the field as well as the amount recovered by each harvest system. These estimates for the sugarcane varieties LCP 85-384 and CP 70-321 are presented in Tables 3 and 4. Stalk weight and sugar per Table 3 Comparison of predicted recoverable sugar per acre by harvest system for variety LCP 85-384 Harvest datea
Predicted sugar in the fieldb (kg/ha)
Wholestalk harvest system
Combine harvest system
Tonnage recoveredc (t/ha)
CRSd (kg/t)
9798 10,826 11,815
77.1 79.7 82.4
103 110 116
7945 8780 9582
84.0 86.9 89.8
98 104 110
8208 9070 9899
First stubble Oct. 25 9378 Nov. 8 10,741 Nov. 22 12,045
80.0 83.6 87.1
95 104 112
7606 8712 9769
87.1 91.2 95.0
90 99 106
7857 9000 10,092
Second stubble Oct. 11 9188 Oct. 25 10,840 Nov. 8 12,416
87.8 92.3 96.5
85 95 104
7452 8791 10,070
95.9 100.6 105.3
80 90 99
7698 9081 10,402
Third stubble Oct. 11 8909 Oct. 25 10,511 Nov. 8 12,039
85.1 89.6 93.6
85 95 104
7225 8524 9763
93.0 97.7 102.1
80 90 99
7464 8806 10,085
Plantcane Nov. 22 Dec. 6 Dec. 20
a
Total sugare (kg/ha)
Tonnage recoveredc (t/ha)
CRSd (kg/t)
Total sugare (kg/ha)
Harvest date is the midpoint of each 2-week harvest period. Predicted sugar in the field is the product of predicted tons of sugarcane and the theoretical recoverable sugar (TRS). Tonnage based on stalk populations of 71,615, 86,898, 100,444, and 97,389 stalks per hectare for plantcane, first stubble, second stubble and third stubble, respectively. c Tonnage in the field recovered by the harvester. Tons recovered by the wholestalk system based on a 93% field recovery rate and a 10% trash content. Tons recovered by the combine system based on a 97% field recovery rate and a 15% trash content. d Commercially recoverable sugar (CRS) is the sugar actually recovered from the cane by the mill and represents the TRS value adjusted by a scale factor. Scale factors for the wholestalk and combine systems are 95 and 90%, respectively. e Total sugar is the product of tonnage delivered and the CRS value. b
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M.E. Salassi et al. / Agricultural Systems 73 (2002) 261–278 Table 4 Comparison of predicted recoverable sugar per acre by harvest system for variety CP 70-321 Harvest datea
Predicted sugar in the fieldb (kg/ha)
Wholestalk harvest system
Combine harvest system
Tonnage recoveredc (t/ha)
CRSd (kg/t)
Total sugare (kg/ha)
Tonnage recoveredc (t/ha)
CRSd (kg/t)
Total sugare (kg/ha)
8972 9648 10,297
72.1 73.7 75.5
101 106 111
7276 7824 8350
78.6 80.4 82.2
95 100 105
7517 8083 8627
7253 8040 8790
64.1 65.9 67.9
92 99 105
5884 6520 7129
69.7 71.9 73.9
87 93 99
6078 6736 7364
Second stubble Oct. 11 6726 Oct. 25 7586 Nov. 8 8408
64.7 67.0 69.0
84 92 99
5455 6153 6818
70.6 73.0 75.3
80 87 93
5635 6356 7043
Third stubble Oct. 11 6587 Oct. 25 7429 Nov. 8 8233
63.4 65.4 67.6
84 92 99
5342 6026 6677
69.0 71.5 73.7
80 87 93
5518 6225 6898
Plantcane Nov. 22 Dec. 6 Dec. 20 First stubble Oct. 25 Nov. 8 Nov. 22
a
Harvest date is the midpoint of each 2-week harvest period. Predicted sugar in the field is the product of predicted tons of sugarcane and the theoretical recoverable sugar (TRS). Tonnage based on stalk populations of 53,710, 57,117, 59,726, and 58,491 stalks per hectare for plantcane, first stubble, second stubble and third stubble, respectively. c Tonnage in the field recovered by the harvester. Tons recovered by the wholestalk system based on a 93% field recovery rate and a 10% trash content. Tons recovered by the combine system based on a 97% field recovery rate and a 15% trash content. d Commercially recoverable sugar (CRS) is the sugar actually recovered from the cane by the mill and represents the TRS value adjusted by a scale factor. Scale factors for the wholestalk and combine systems are 95 and 90%, respectively. e Total sugar is the product of tonnage delivered and the CRS value. b
stalk estimates were converted to predicted values of sugar in the field, before harvest, as defined in Eqs. (8)–(10). Stalk population counts for each of the four crops of the two varieties are taken from field plot study results (Louisiana State University Agricultural Center, 1999). Metric tons of sugarcane and pounds of sugar actually recovered by the wholestalk and combine harvest systems were estimated using Eqs. (11)–(13). The predicted values of sugar per hectare recovered by the two harvest systems represent reflect typical harvest conditions. Combine harvesters have a higher field recovery rate than wholestalk harvesters, resulting in a greater percentage of the sugarcane in the field actually recovered by the harvesting system. Combine harvesters also tend to deliver harvested sugarcane to the mill with a
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higher trash content. This higher trash content causes the sugar recovery to be less efficient. This is reflected in the lower estimates of commercially recoverable sugar (CRS) for the combine system compared with the wholestalk system. Estimated yield values for both varieties in Tables 3 and 4 show slightly higher sugar per hectare yields for the combine system compared with the wholestalk system. However, due to the higher investment and operating costs of the combine system, it is not clear as to which type of harvesting system is more economical. To address this question, alternative yield scenarios were simulated within the mixed integer programming harvest system selection model to identify specific field recovery and sucrose recovery levels at which the most profitable harvesting system changes. 3.2. Impact of field recovery One variable factor which can influence the relative profitability of one sugarcane harvest system over another is related to the field recovery of the wholestalk systems. Field recovery is the percentage of sugarcane tons existing in the field prior to harvest which the harvest system is able to recover and deliver to the mill. Field recovery rates for the combine system are relatively high and consistent, averaging above 95%. However, field recovery rates for the wholestalk system are much more variable and are affected by harvesting conditions as well as the condition of the sugarcane. To analyze the impact of this field recovery variability, the mixed integer programming model was used to determine the most profitable harvesting system under alternative wholestalk field recovery rates. Three combination of the two sugarcane varieties were analyzed at three different wholestalk field recovery rates. The three variety combinations analyzed included low yield (CP 70-321)/high yield (LCP 85-384) variety mixes of 25/75%, 50/50%, and 75/25% of total farm acreage. The three wholestalk harvesting system field recovery rates analyzed were 85, 90, and 95%. Results of this analysis are presented in the Table 5. At a field recovery rate of 85% for the wholestalk system, the combine system was found to be more profitable at all three variety combinations (Table 5). Although the combine system had a lower sugar recovery per metric ton of sugarcane harvested than the wholestalk system, the ability to recover higher field tonnages resulted in greater net returns for the combine system. Total sugar yield ranged from 9200 kg/ha for the variety combination with 75% high yield variety to 7909 kg/ha for the variety combination with 75% low yield variety. Total tons harvested ranged from 92.6 t/ha to 81.3 t/ha, which were higher than recoverable yields from the wholestalk system. With a wholestalk field recovery rate of 90%, the wholestalk harvesting system was identified as the most profitable system. This system recovered less sugar and tonnage per hectare than the combine system, however lower fixed and operating costs resulted in higher net returns than the combine system. 3.3. Impact of sucrose recovery A second factor which can influence the relative profitability of one sugarcane harvest system over another concerns the sugar recovery of the combine system. The
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Low yield/high yield variety percentage 25/75
50/50
75/25
85% Field recovery System chosen Total sugara (kg/ha) Total tonsa (t/ha) Harvest costsa ($/ha) Net incomeb,c ($/total farm ha)
Combine 9200 92.6 149.54 399.14
Combine 8548 87.0 149.54 301.66
Combine 7909 81.3 149.54 205.88
90% Field recovery System chosen Total sugara (kg/ha) Total tonsa (t/ha) Harvest costsa ($/ha) Net incomeb,c ($/total farm ha)
Wholestalk 8677 82.2 90.66 434.01
Wholestalk 8058 77.3 90.66 341.07
Wholestalk 7451 72.4 90.66 250.29
95% Field recovery System chosen Total sugara (kg/ha) Total tonsa (t/ha) Harvest costsa ($/ha) Net incomeb,c ($/total farm ha)
Wholestalk 9161 87.0 90.66 506.18
Wholestalk 8506 81.6 90.66 408.06
Wholestalk 7865 76.4 90.66 312.11
a
Harvested area includes 307 ha of the total farm area of 404 ha. Total farm area includes 404 ha. c Net income represents net returns above variable and fixed production and harvesting expenses. General farm overhead and family living expenses were not included in the calculation of net returns. b
increased level of leaf trash included with combine-harvested sugarcane delivered to mills results in a lower CRS value compared with sugarcane harvested by wholestalk systems. To analyze the impact of varying levels of sucrose recovery, the mixed integer programming model was solved using different scale factor measures for the combine system. Scale factors of 85, 90, and 95% were simulated, representing increasing levels of sucrose recovery from combine-harvested sugarcane. These scale factors resulted in average CRS values for combine-harvested sugarcane of approximately 92–95, 97–100, and 102–105 kg of sugar per metric ton of cane, respectively. The wholestalk system was found to be most profitable at a combine scale factor of 85%. This scenario simulates the situation where the trash levels in the combine-harvested sugarcane are at such high levels than the sugar per ton of cane is low enough to offset the higher tonnage recovered, resulting in the combine system yielding lower net returns than the wholestalk system. Estimates of average CRS values for the wholestalk system were in the 103–105 range, dividing total kilograms of sugar per hectare by metric tons of sugarcane per hectare. As the scale factor was raised to 90%, the combine system became the most profitable system at all variety combinations except the 75% low yield/25% high yield case. At a scale
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factor of 95%, the combine system was found to be the most profitable system at all variety combinations (Table 6).
4. Conclusions This study combined within season crop yield models and a mixed integer mathematical programming model to evaluate the impact of alternative sugarcane yield and quality scenarios on the optimal harvest system selection. Sugar yield prediction models were estimated for two major sugarcane varieties produced in Louisiana. The estimated models were used to predict stalk weight and sugar per stalk at various points in time throughout the harvest season. Results indicated that predicted values of stalk weight increase 10–20% throughout the harvest season, while sugar per stalk increases by more than 50% throughout the season. These values were then converted to estimates of metric tons of sugarcane per hectare and kilograms of sugar per ton of sugarcane, with adjustments for harvest system specific field and sucrose recovery.
Table 6 Impact of combine system sugar recovery on optimal harvest system selection Combine scale factor (%)
Low yield/high yield variety percentage 25/75
50/50
75/25
85% Scale factor System chosen Total sugara (kg/ha) Total tonsa (t/ha) Harvest costsa ($/ha) Net incomeb,c ($/total farm ha)
Wholestalk 8286 79.1 90.66 375.22
Wholestalk 7789 74.8 90.66 300.87
Wholestalk 7203 69.9 90.66 387.40
90% Scale factor System chosen Total sugara (kg/ha) Total tonsa (t/ha) Harvest costsa ($/ha) Net incomeb,c ($/total farm ha)
Combine 9200 92.6 149.54 399.14
Combine 8547 87.0 149.54 301.49
Wholestalk 7203 69.9 90.66 213.07
95% Scale factor System chosen Total sugara (kg/ha) Total tonsa (t/ha) Harvest costsa ($/ha) Net incomeb,c ($/total farm ha)
Combine 9712 92.6 149.54 475.79
Combine 9022 87.0 149.54 372.48
Combine 8348 81.3 149.54 271.6
a
Harvested area includes 307 ha of the total farm area of 404 ha. Total farm area includes 404 ha. c Net income represents net returns above variable and fixed production and harvesting expenses. General farm overhead and family living expenses were not included in the calculation of net returns. b
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Predicted sugarcane crop yield values were incorporated into a mixed integer mathematical programming model which maximized whole farm net returns. The model incorporated preharvest and harvest field operations and selected the equipment complement necessary to perform these operations. Two sugarcane harvest systems were included in the model: wholestalk sugarcane harvesters and combine sugarcane harvesters. The primary objective of the study was to evaluate how predicted sugar yields, specifically the impact of varying levels of sugarcane recovery (field recovery) and sucrose recovery, affected the most economical harvest system selection. Results from the mixed integer harvest system selection model verified that the optimal selection of a sugarcane harvest system is dependent on several factors including yield of the specific variety, field recovery of the harvest system, and the impact of leaf trash and other extraneous plant material on the recovery of sucrose from the cane stalks. Field recovery is the percentage of sugarcane tons existing in the field prior to harvest which a particular harvest system is able to recover and deliver to the mill for processing. The breakeven point in terms of field recovery was found to be somewhere between 85 and 90% for the wholestalk harvest system. The combine harvest system was found to generate higher net returns than the wholestalk harvest system when the field recovery rate of the wholestalk system was 85%. Although the sucrose recovery was lower for the combine system, the ability to recovery and deliver more metric tons per hectare resulted in greater net returns. With a field recovery rate of 90%, the wholestalk system resulted in whole farm net returns which were greater than the combine system. Sucrose recovery concerns the kilograms of sugar recovered per metric ton of cane processed. Results indicated that increased trash levels in combine harvested sugarcane significantly reduced the profitability of that system, compared with the wholestalk system, when sucrose recovery levels were 90% or less of that for wholestalk harvesters. The basic modeling approach utilized in this study can be easily adapted for economic analysis of mechanized sugarcane harvesting in other regions of the world. The primary adjustments which would have to be made to the model would be to expand the number of sugarcane stubble crops modeled and to predict yield values for these stubble crops throughout the harvest season. Economic analysis of machinery selection in annual crop production, for such crops as wheat, corn, or soybeans for example, could also be conducted with the basic model structure by defining several time periods within the corresponding harvest seasons of these crops and incorporating predicted yield values for each time period. References Alexander, A.G., 1973. Chapter 11—Maturation and Natural Ripening in Sugarcane Physiology. A Comprehensive Study of the Saccharum Source-to-Sink System. Elsevier. Alvarez, J., Crane, D.R., Spreen, T.H., Kidder, G., 1982. A yield prediction model for Florida sugarcane. Agricultural Systems 9, 161–179. Brumelle, S., Granot, D., Halme, M., Vertinsky, I., 1998. A tabu search algorithm for finding good forest harvest schedules satisfying green-up constraints. European Journal of Operational Research 106, 408–424.
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Chang, Y.S., 1995. The trend of sucrose accumulation during maturation of sugarcane with special reference to the maturity of sugarcane cultivars. Report of the Taiwan Sugar Research Institute 148, 1–9. Churchward, E.H., Belcher, R.M., 1972. Some economic aspects of mechanical cane harvesting in Queensland. Proceedings of the Queensland Society of Sugar Cane Technologists Thirty-Ninth Conference. Watson Ferguson and Co., Brisbane, Queensland, pp. 31–38. Churchward, E.H., Poulsen, N.J., 1988. A review of harvesting developments. Proceedings of the 1988 Conference of the Australian Society of Sugar Cane Technologists. Watson Ferguson and Co., Brisbane, Queensland, pp. 1–6. Crane, D.R., Spreen, T.H., Alvarez, J., Kidder, G., 1982. An Analysis of the Stubble Replacement Decision for Florida Sugarcane Growers (Bulletin 822). Agricultural Experiment Station, Institute of Food and Agricultural Sciences, University of Florida. Daust, D.K., Nelson, J.D., 1993. Spatial reduction factors for strata-based harvest schedules. Forest Science 39, 152–165. Dufrene, E.O., Garrison, D.D., Legendre, B.L., 1996. Harvestability of recently released Louisiana sugarcane cultivars: LHo 83-153, LCP 85-384, and HoCP 85-845. Journal of the American Society of Sugar Cane Technologists 16, 115. Griffiths, W.E., Hill, R.C., Judge, G.G., 1993. Learning and Practicing Econometrics, Wiley, New York. Higgins, A.J., Muchow, R.C., Rudd, A.V., Ford, A.W., 1998. Optimising harvest date in sugar production: a case study for the Mossman Mill region in Australia—I. Development of operations research model and solution. Field Crops Research 57, 153–162. Lass, L.W., Callihan, R.H., Everson, D.O., 1993. Forecasting the harvest date and yield of sweet corn by complex regression models. Journal of the American Society for Horticultural Science 118, 450–455. Louisiana State University Agricultural Center, 1999. Sugarcane: planting recommendations & suggestions for Louisiana sugarcane producers. Cooperative Extension Service. Malezieux, E., 1994. Predicting pineapple harvest date in different environments, using a computer simulation model. Agronomy Journal 86, 609–617. Millhollon, R.W., Legendre, B.L., 1996. Sugarcane yield as affected by annual glyphosate ripener treatments. American Society of Sugar Cane Technologists Journal 16, 7–12. Mishoe, J.W., Jones, J.W., Swaney, D.P., Wilkerson, G.G., 1984. Using crop and pest models for management applications. Agricultural Systems 15, 153–170. Muchow, R.C., Higgins, A.J., Rudd, A.V., Ford, A.W., 1998. Optimising harvest date in sugar production: a case study for the Mossman Mill region in Australia—I. Sensitivity to crop age and crop class distribution. Field Crops Research 57, 243–251. Nelson, J.J., Brodie, D., Sessions, J., 1991. Integrating short-term, area-based logging plans with longterm harvest schedules. Forest Science 37, 101–122. Salassi, M.E., Milligan, S.B., 1997. Economic analysis of sugarcane variety selection, crop yield patterns, and ratoon crop plow out decisions. Journal of Production Agriculture 10, 539–545. Semenzato, R., 1995. A simulation study of sugar cane harvesting. Agricultural Systems 47, 427–437. Statistical Analysis System (SAS), Version 6.12. SAS Institute Inc., Cary, NC, USA. Tai, P.Y.P, Miller, J.D., 1993. Recurrent selection for cold tolerance of sugarcane. Journal of the American Society of Sugar Cane Technologists 13, 40–45. United States Department of Agriculture, 2000. Sugar and Sweetener Situation and Outlook Yearbook (SSS-228). Economic Research Service, pp. 57–58. Van Deusen, P.C., 1996. Habitat and harvest scheduling using Bayesian statistical concepts. Canadian Journal of Forest Research 26, 1375–1383. Wolf, S., 1986. Predicting harvesting date of processing tomatoes by a simulation model. Journal of the American Society for Horticultural Science 111, 11–16.
Modeling within-season sugarcane growth for optimal harvest system selection M.E. Salassi*, J.B. Breaux, C.J. Naquin Department of Agricultural Economics and Agribusiness, Louisiana State University Agricultural Center, 101 Agricultural Administration Building, Baton Rouge, LA 70803-5604, USA Received 26 September 2000; received in revised form 13 June 2001; accepted 15 June 2001
Abstract The recent switch from wholestalk to combine sugarcane harvesters has raised questions concerning which harvester is more profitable. Combine harvesters recovery more of the sugarcane in the field than wholestalk harvesters, but also have higher trash levels reducing sucrose recovery. The objective of the research presented in this article is to determine the optimal sugarcane harvest system selection for sugarcane production in Louisiana. Sugarcane stalk weight and sugar per stalk equations are estimated in order to predict tonnage and sugar yields throughout the harvest season. These predicted yields are then adjusted to reflect field tonnage and sugar recovery for the combine and wholestalk harvesting systems. A mixed integer mathematical programming model is then used to determine the optimal harvest system under alternative sugarcane variety combinations, wholestalk harvester field recovery rates, and combine harvester sugar recovery rates. Results identify field recovery and sucrose recovery conditions for which one type of harvest system would be preferred over the other. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Sugarcane; Yield growth; Optimal harvest system; Field recovery; Sucrose recovery
1. Introduction Sugarcane, a member of the grass family, is a perennial agricultural crop grown primarily for the juices expressed from its stalks. Raw sugar produced from these juices are later refined into white sugar. As a perennial crop, one planting of
* Corresponding author. Tel.: +1-225-388-2713; fax: +1-225-388-2716. E-mail address: [email protected] (M.E. Salassi). 0308-521X/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0308-521X(01)00081-6
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sugarcane will generally allow for three to six or more annual harvests before replanting is necessary. Sugarcane crops are generally classified based on its current year or stage of the crop cycle. From the planting through the first harvest, a sugarcane crop is referred to as a plantcane crop. After the first harvest succeeding crops are referred to as stubble crops. First stubble, for example, would refer to a sugarcane crop in its first year of stubble or regrowth after the first harvest. Production of sugarcane occurs in warm, humid climates throughout the world. In the United States, sugarcane production is concentrated primarily in the states of Louisiana and Florida, with some production also located in Texas, Hawaii, and Puerto Rico. In the 1999/2000 crop year, 400,316 ha of sugarcane were harvested in the United States (USDA, 2000). Approximately 379,000 of these hectares were harvested for sugar with the remainder used for seed. Louisiana harvested 188,179 ha and Florida harvested 186,156 ha. Average yields per harvested acre for Louisiana and Florida were 29.6 and 31.7 metric tons of sugarcane per acre, respectively. Sugarcane is planted vegetatively in late summer or early fall by placing stalks of sugarcane in open furrows. At each plant node, these stalks have buds or ‘‘eyes’’ from which new plants develop. As a sugarcane plant matures throughout the growing season, the amount of sucrose in the cane increases. Most of this sucrose production occurs when the plant is fully mature and begins to ripen (Alexander, 1973). Sugarcane harvest in the United States begins in the fall of the year. The oldest sugarcane crops are usually harvested first (second stubble and older crops), followed by newer crops (first stubble and finally plantcane). In Florida, the sugarcane harvest season runs from October through to March or April. However, in Louisiana, the harvest season begins in late September and concludes at the end of December or early January. The reason for this restricted harvest season is due to the limited cold tolerance of sugarcane varieties and the risk of freezing temperatures in Louisiana towards the end of the harvest season. Exposure to cold weather requires that cold tolerance be an important characteristic of commercial varieties of sugarcane grown in these regions (Tai and Miller, 1993). In recent years, two simultaneous changes have occurred in the sugarcane industry in Louisiana, both of which have had a dramatic impact on the economics of sugarcane production in the state. In 1993, the variety LCP 85-384 was released. This variety is a high yielding, excellent stubbling variety (Louisiana State University Agricultural Center, 1999). The excellent stubbling ability of this variety implies that the yields of succeeding crops, after the first harvest (plantcane), are higher than those for comparable varieties. It is slow to emerge after planting, produces a large number of small stalks and exceeds most other varieties in sugar per acre. However, this variety frequently lodges, is brittle, and difficult to harvest when lodged. Studies conducted with the previously predominant wholestalk harvesting system found that LCP 85-384 had the highest percent of scrap (unharvested plant material) left in the field and the highest percent of stalks damaged by wholestalk harvesters (Dufrene et al., 1996). At the same time, Louisiana sugarcane producers switched from the traditional wholestalk harvesters to the combine harvesters similar to the types used in Florida and other sugarcane producing regions. In the 1950s, sugarcane producers in
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Australia began experimenting with combine sugarcane harvesters (Churchward and Belcher, 1972). These harvesters would cut sugarcane stalks into 12–14 inch billets, remove extraneous matter, and deposit the billets into wagons running beside the harvester. The original harvesters were designed to cut burned sugarcane, as were the wholestalk harvesters. In the 1970s, considerable attention in Australia was being focused on developing a combine harvester which would harvest green sugarcane (Churchward and Poulsen, 1988). A primary advantage of harvesting green sugarcane is that the harvester deposits extraneous organic matter in a layer on the field, promoting moisture conservation, weed control, and cost savings in cultivation. The main disadvantage of harvesting green sugarcane is the potential to deliver more extraneous plant material to the mill, reducing sugar recovery. The combine harvesters being used in Louisiana were better able to harvest sugarcane fields with high tonnage yields compared with wholestalk harvesters. However, it was still necessary to burn the sugarcane to remove extraneous leaf and other plant material prior to delivering to the mill. With wholestalk harvesting, stalks of sugarcane would be piled into rows after harvest and then burned to remove leaf trash. The adoption of combine harvesters required the standing stalks of sugarcane in the field to be burned prior to harvest. Although the field recovery rates of sugarcane tonnage for these harvesters were higher, they also tended to deliver more leaf and other plant material trash after burning to the mill, due to the different harvest method of chopping the sugarcane stalk into small pieces and dumping into wagons. This generally resulted in lower commercially recoverable sugar measures per ton of sugarcane harvested for the combine harvester as compared with the more traditional wholestalk harvesters. Although combine harvesting systems can recover a higher percentage of sugarcane in the field than the wholestalk harvesters, they also have higher investment and operating costs. As a result, it is not clear which type of harvesting system would be more economical under alternative possible yield scenarios. The decision of selecting the optimal (most profitable) sugarcane harvesting system is therefore dependent upon the relative recoverable yield and quality of the sugarcane harvested as well as the investment and operating costs of the two respective systems. This article develops two models which are jointly used to evaluate sugarcane harvesting system selection under alternative sugarcane yield and quality scenarios. The first model is a sugarcane growth model consisting of two equations which predict sugarcane tonnage and sucrose levels throughout the harvest system. Estimates from this model provide yield and sucrose predictions which are then incorporated into a mixed integer mathematical programming model which determines the optimal harvest system selection within a whole-farm context. Several studies have developed models to predict the sucrose level in sugarcane. Alvarez et al. (1982), developed sugarcane yield prediction models as a function of several agronomic and climatic factors. Crane et al. (1982) used these yield predictions to develop a sugarcane stubble replacement decision model. They reported that sugar accumulation is a function of both sucrose accumulation and vegetative growth. Chang (1995), in research on Taiwanese sugarcane cultivars, suggested that individual cultivars have distinct sucrose maturation curves with different peak levels.
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Applications of crop harvest scheduling models, utilizing some type of operations research procedure, are most common in the timber industry. Most of these applications involve the use of either linear programming or simulation models. Recent studies have investigated the use of Monte Carlo integer programming (Nelson et al., 1991; Daust and Nelson, 1993), bayesian concepts (Van Deusen, 1996), and tabu search procedures (Brumelle et al., 1998). Crop growth models have provided useful tools for several crop management activities such as pesticide and irrigation timing (Mishoe et al., 1984). Several studies have developed crop growth models to predict the harvest date of agricultural crops (Wolf, 1986; Lass et al., 1993; Malezieux, 1994). However, most of these studies utilize optimal harvest decision rules based upon agronomic characteristics of the crop rather than economic principles. Several studies have addressed various aspects of sugarcane productivity and harvest operations. Millhollon and Legendre (1996) studied the use of glyphosate, an artificial crop ripener used in sugarcane production, on sugarcane yield. Two studies have evaluated the economics of sugarcane stubble crop replacement in Florida (Crane et al., 1982) and Louisiana (Salassi and Milligan, 1997). These studies evaluated the optimal crop cycle length by comparing annualized future net returns from replanting to estimated returns from extending the current crop cycle for another year. Semenzato (1995) developed a simulation algorithm for scheduling sugarcane harvest operations at the individual farm level in such a way that the lapse of time between the end of burning and processing is minimized. A recent study in Australia did determine optimal sugarcane harvest schedules which maximized net returns using mathematical programming procedures (Higgins et al., 1998; Muchow et al., 1998). However, the modeling framework in this study encompassed many farms within a production region over a multi-year harvest period.
2. Model formulation 2.1. The sugar yield prediction models The amount of raw sugar in a field of sugarcane is a function of several variables. Two important measures of sugarcane yield include metric tons of sugarcane per hectare and kilograms of raw sugar produced per hectare. The relationship between sugar per hectare and factors which influence it can be stated simply as follows: SH ¼ TRS TONS ¼ TRS POP STWT
ð1Þ
where SH is total kilograms of raw sugar per hectare, TRS is theoretical recoverable sugar in kilograms of sugar per metric ton of cane, TONS is the metric tons of sugarcane produced per hectare, POP is the per hectare population of sugarcane stalks in the field, and STWT is the stalk weight in kilograms per stalk. Although the population of sugarcane stalks within a field can be assumed to be constant throughout the harvest season, the same assumption cannot be made for the other
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factors in the relationship. Theoretical recoverable sugar and stalk weight both increase as the harvest season progresses. In order to incorporate this yield increase within a whole-farm mathematical programming harvest scheduling model, estimates must be obtained for the predicted levels of each of these factors for each variety of sugarcane produced on the farm for every day of the harvest season. Sucrose maturity data developed at the ARS, USDA Sugar Cane Research Unit in Houma, Louisiana, were used in the analysis. Stalk weight and sugar content of the commercial sugarcane cultivars grown in Louisiana were sampled at intervals during the harvest season from 1981 to 1996. The data included measurements of theoretical recoverable sugar, sugar per stalk and stalk weight by julian date for 3– 16 years, depending upon variety. The harvest season for sugarcane in Louisiana has historically run from the first of October through to the end of December. Observations for each commercial cultivar ranged from julian date 255 to 346 or approximately the middle of September through to the middle of December. The age of the crop (plantcane or stubble) was also included. Models were estimated for stalk weight and sugar per stalk for major sugarcane cultivars produced in Louisiana in order to predict the amount of sugarcane and raw sugar in the field for each day of the harvest season. Previous research suggests that a quadratic model can be used to model sugar accumulation (Crane et al., 1982). Graphical analysis of both the stalk weight as well as the sugar per stalk data suggested that these variables could be estimated using a semi-log functional form. Biological response functions of stalk weight and sugar per stalk were estimated for each cultivar as follows: STWTct ¼ 0 þ 1 LNJD þ 2 CROP þ
y X i YEARi þ "
ð2Þ
i¼x
SPSct ¼ 0 þ 1 LNJD þ 2 CROP þ
y X i YEARi þ "
ð3Þ
i¼x
where STWTct represents stalk weight in kilograms per stalk of cultivar c on day t, SPSct represents sugar per stalk in kilograms of cultivar c on day t, LNJD is the natural log of julian date (numeric day of the year), CROP is a (0,1) indicator variable representing crop age as either plantcane or stubble crop, and YEARi represents discrete indicator variables for different years. Only two categories of the indicator variable CROP were included in the model as stubble crops for a given variety generally have similar sucrose accumulation levels regardless of crop age. These stubble crop sucrose levels, however, are significantly different than plant cane sucrose levels. The annual indicator variables for year were included to capture the relationship that sugarcane cultivars have distinct sugar accumulation curves which shift vertically from year to year depending upon weather and other factors. The base year for comparison in this estimation was 1996 and the indicator variables serve the purpose of adjusting the sugar accumulation curve to factors in a given year by shifting the intercept of the prediction equation. All models were estimated
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using SAS (SAS Institute, version 6.12). The estimates of stalk weight and sugar per stalk were combined with stalk populations to estimate sugar cane and sugar yield for each field. Estimated models of stalk weight and sugar per stalk for two major sugarcane cultivars, CP70-321 and LCP85-384, are shown in Eqs. (4)–(7). Julian date (LNJD) and crop age (CROP) were found to be highly significant in the stalk weight prediction models (Eqs. (4) and (5)). Positive signs on the julian date variable indicate that stalk weight increases throughout the harvest season. The signs on the significant crop age variables were negative, as expected, indicating that stalk weight tends to be greater for plantcane crops than for older stubble crops. Coefficients of determination for specific variety models ranged from 0.36 to 0.80. Similar results were found for the sugar per stalk prediction models (Eqs. (6) and (7)). Julian date was highly significant with positive coefficients indicating sugar accumulation increases during the harvest season. Crop age was found to be significant in one of the two equations estimated. Coefficients of determination were very high in the sugar per stalk models, with and estimated value of 0.89 for both variety models. Durbin-Watson tests for autocorrelation either failed to reject the hypothesis of no autocorrelation or were inconclusive, indicating that the error terms from the model predictions were not serially correlated. The White test for heteroscedasticity (White) failed to reject the hypothesis of homoscedasticity for each cultivar tested, indicating that error terms from the model predictions have a constant variance. The absence autocorrelation and heteroscedasticity indicated that the estimated parameters in the prediction models were efficient (minimum variance) estimators. STWT321;t ¼ 3:022 ð6:92Þ Adj: R2 ¼ 0:80
þ0:748 LNJD ð9:82Þ Durbin-Watson ¼ 1:94
0:149 CROP ð10:27Þ White prob: ¼ 0:41
STWT384;t ¼ 4:163 ð3:53Þ Adj: R2 ¼ 0:36
þ0:901 LNJD ð4:35Þ Durbin-Watson ¼ 2:42
0:071 CROP ð1:88Þ White prob: ¼ 0:36
SPS321;t ¼ 1:571 ð25:99Þ Adj: R2 ¼ 0:89
þ0:300 LNJD 0:013 CROP ð28:49Þ ð6:54Þ Durbin-Watson ¼ 1:99 White prob: ¼ 0:20
SPS384;t ¼ 1:848 ð15:74Þ Adj: R2 ¼ 0:89
þ0:343 LNJD þ0:002 CROP ð16:64Þ ð0:43Þ Durbin-Watson ¼ 2:74 White prob: ¼ 0:14
ð4Þ
ð5Þ
ð6Þ
ð7Þ
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2.2. Farm-level sugar yield predictions Estimated stalk weight, estimated number of stalks per hectare and estimated sugar per stalk were used to predict yield throughout the harvest season for a representative farm. Estimated metric tons of sugarcane per hectare, theoretical recoverable sugar (TRS) and kilograms of raw sugar per hectare were calculated as follows: TONSft ¼ POPf STWTct =2000
ð8Þ
TRSft ¼ POPf SPSct =TONSft
ð9Þ
SUGARft ¼ TONSft TRSft
ð10Þ
where TONSft is the estimated metric tons of sugarcane per hectare in field f on julian date t, POPf is the estimated stalk population per hectare in field f, STWTct is the estimated stalk weight in kilograms per stalk for cultivar c on julian date t, TRSft is the estimated kilograms of raw sugar per metric ton of sugarcane in field f on julian date t (also referred to as TRS), SPSct is the estimated raw sugar per stalk in kilograms for cultivar c on julian date t, and SUGARft is the estimated kilograms of raw sugar per hectare in the field available for harvest. Since POPf, STWTct and SPSct are predicted values with associated variances, direct multiplication would cause the estimated variances of predicted cane and sugar yield estimates to be very large, making the confidence intervals for predicted values considerably wider (Griffiths et al., 1993). As a result, the relationships in Eqs. (8) and (9) were converted to natural log form for calculation. Estimated recoverable yields per field were then adjusted for harvesting parameters associated with each type of harvesting system (field recovery and trash content) and mill efficiency (differences between theoretical recoverable sugar and commercial recoverable sugar) using the following relationships: RTONSfth ¼ TONSft 1 þ TRASHfh FLDRECfh ð11Þ CRSfth ¼ TRSft 0:8345 SFACTORh
ð12Þ
RSUGARfth ¼ RTONSfth CRSfth
ð13Þ
RTONSfth represents the actual metric tons of sugarcane per hectare recovered from field f on day t by harvest system h. TRASHfh is a percentage estimate of the additional leaf matter and other trash in the sugarcane harvested by harvest system h, and FLDRECfh is a percentage estimate of metric tons of sugarcane in field f actually recovered by harvest system h. CRSfth represents the actual kilograms of raw sugar per metric ton of sugarcane recovered from the processed cane. The estimated
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sugar yield is multiplied by a standard factor (0.8345) to convert theoretical recoverable sugar into commercially recoverable sugar. This standard is used by sugar mills to estimate recovery since the actual liquidation factor will not be known until the end of season. Accounting for differences from the laboratory analysis to the fields, the estimated sugar per field is reduced by a scale factor, SFACTORh. The assumed scaler factor varies by type of harvest system used as well as field harvest conditions. In this analysis it was used to adjust sugar recovery by type of harvest system. 2.3. The mixed integer programming model A mixed integer mathematical programming model was developed to determine the most economical harvest system selection for a representative farm. The representative farm was assumed to be 404 ha in total land area with 80.8 ha of land in each phase of the sugarcane crop cycle through harvest of third stubble (fallow, plantcane, first stubble, second stubble, and third stubble). With approximately 20% of harvested plantcane acreage used for seed, the representative farm was assumed to have approximately 307 ha of millable sugarcane. The objective of the mixed integer programming model was to select the harvest system, either wholestalk or combine, which would maximize total farm net returns. In the mixed integer programming harvest system selection model, the harvest season was divided into 2-week periods. The harvest of sugarcane in Louisiana begins with the oldest stubble crops (second stubble and older), followed by first stubble crops, and concluding with plantcane crops. For the representative sugarcane farm modeled in this analysis, each sugarcane crop on the farm was assigned to three possible harvest periods. Second stubble and older crops were assigned to the first and second 2-week periods in October and the first 2week period in November. First stubble crops were assigned for possible harvest in the second 2-week period in October and the two periods in November. Plantcane was assigned to the second 2-week period in November and the two periods in December. The stalk weight and sugar per stalk models presented above were used to predict sugarcane tonnage and raw sugar yields for a date in the middle of each 2-week harvest period. Predicted yields on these dates were used to simulate yields harvested within each 2-week harvest period. The specific dates used in the analysis were: 11 and 25 October, 8 and 22 November, and 6 and 20 December. The mixed integer programming model used in this study was designed as a net revenue maximizing model. Preharvest and harvest field operations for each land area on the farm are specified and the model determines the equipment required to perform these operations. The number of implements and tractors required to perform preharvest operations are determined as integer values by the model. Equipment costs are based on annual fixed costs per equipment item and variable costs per hour of use. For harvest operations, the model is allowed to choose which harvest system, wholestalk or combine, would result in higher net returns. The model maximizes net revenues over total farm cost (Z):
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Maximize Z ¼ Ps TQs þ Pm TQm Ps MQs Pm MQm Ps LQs Pm LQm
n 2 u X X X Cp Ap Wa Sa wHt p¼1
t¼1
g d X n X u X X
c¼1
c¼1 p¼1 t¼1 f¼1
TFCc TRc
TVCc THcptf
g b b X n X u X X X EFCe EQe EVCe EHeptf e¼1
a
d X
e¼1 p¼1 t¼1 f¼1
2 X
q 2 X n X u X X HVCj HVHjptk
j¼1
j¼1 p¼1 t¼1 k¼1
HFCj HVj
ð14Þ
where Ps is the price per kilogram of raw sugar; TQs is the total quantity of raw sugar produced (kg); Pm is the price per liter of molasses; TQm is the total quantity of molasses produced (l); MQs is the processing mill’s share of raw sugar production; MQm is the processing mill’s share of molasses production; LQs is the landlord’s share of raw sugar production; LQm is the landlord’s share of molasses production; Cp is the input variable cost per hectare for crop production phase p; Ap is the number of farm hectares in crop production phase p; Wa is the annual salary for full-time class a workers; Sa is the number of class a full-time workers; w is the hourly part-time wage rate; Ht is the hours of part-time labor hired in time period t; TFCc is the annual fixed cost of tractor type c; TRc is the number of type c tractors used; TVCc is the variable cost per hour of operation for tractor type c; THcptf is the hours of operation for tractor type c on crop production phase p in time period t for field operation f; EFCe is the annual fixed cost of implement type e; EQe is the number of type e implements used; EVCe is the variable cost per hour of operation for implement type e; EHeptf is the hours of operation for implement type e on crop production phase p in time period t for field operation f; HFCj is the annual fixed cost of harvester type j; HVj is the number of type j harvesters used; HVCj is the variable cost per hour of operation for harvester type j; and HVHjptk is the hours of operation for harvester type j on crop production phase p in time period t for harvest land tract k.
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The mixed integer programming model consists of more than one thousand functional constraints. These functional constraints include farm income accounting equations, land allocation equations, and yield equations, as well as constraints for labor availability and time available for field work. Predicted values of sugarcane tonnage and sugar content, described in the previous section, were incorporated into the model through a series of constraints which related area harvested by harvest system type to predicted values for sugar yield. Area harvested by system type as well as tonnage of sugarcane recovered were related to area available for harvest by the following two general sets of equations: 2 X u X AHkjt Ak ¼ 0 for k ¼ 1 . . . q
ð15Þ
j¼1 t¼r
where AHkjt is the area of land tract k harvested (ha) by harvest system j in time period t, and Ak is the area of land tract k (ha) available for harvest. 2 X u X RTONSkjt AHkjt TONSkjt ¼ 0 for k ¼ 1 . . . q
ð16Þ
j¼1 t¼r
where RTONSkjt is the predicted value of recoverable metric tons of sugarcane on land tract k by harvest system j in time period t, and TONSkjt is the total quantity of sugarcane harvested (metric tons) on land tract k by harvest system j in time period t. Total raw sugar produced on the representative farm was estimated by the equation which incorporated predicted values of sugar per ton of sugarcane described in the previous section: q X 2 X u X CRSkjt TONSkjt TQs ¼ 0
ð17Þ
k¼1 j¼1 t¼r
where CRSkjt is the predicted value of raw sugar per ton of sugarcane (kilograms per metric ton) on land tract k for harvest system j in time period t, and TQs is the total quantity of raw sugar produced (kilograms).
3. Results and discussion Results of this analysis is presented in three sections. The first section presents predicted values of sugarcane stalk weight and sugar per stalk for two major sugarcane varieties grown in Louisiana. These estimates are converted to metric tons per hectare and sugar per metric ton values for alternative dates throughout the harvest season. The second section presents results from the mixed integer programming model analyzing the impact of field recovery on optimal harvest system selection,
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while the final section presents results from the analysis of the impact of sucrose recovery on system selection. 3.1. Predicted sugarcane tonnage and sucrose level Predicted sugarcane stalk weight for the two major varieties of sugarcane produced in Louisiana are presented in Table 1. The six dates listed represent the midpoints of each 2-week harvest period. Stalk weight values were estimated to increase at a diminishing rate throughout the harvest season and were higher for plantcane than for stubble crops for both varieties. Estimated stalk weight values for the variety LCP 85-384 were slightly less than those of CP 70-321. Predicted LCP 85-384 stalk weights ranged from 0.924 to 1.123 kg for plantcane and 0.852 to 1.051 kg for stubble crops. Stalk weights for CP 70-321 were estimated to range from 1.205 to 1.368 kg for plantcane and 1.055 to 1.219 kg for stubble crops. The heavier tonnage yields produced by LCP 85-384 compared with other varieties is due primarily to the substantially higher population of stalks per acre. Estimates of predicted sugar per stalk for the two varieties are presented in Table 2. Similar to the estimation of stalk weight, sugar per stalk was modeled to increase at a diminishing rate throughout the harvest season. Although sugar per stalk would eventually reach a maximum and then start to decline, the restricted Table 1 Predicted sugarcane stalk weight by variety Date
Oct. 11 Oct. 25 Nov. 8 Nov. 22 Dec. 6 Dec. 20
Julian date
285 299 313 327 341 355
CP 70-321 (kg per stalk)
LCP 85-384 (kg per stalk)
Plantcane crop
Stubble cane crops
Plantcane crop
Stubble cane crops
1.205 1.241 1.277 1.309 1.341 1.368
1.055 1.092 1.128 1.160 1.191 1.219
0.924 0.969 1.010 1.046 1.087 1.123
0.852 0.897 0.938 0.978 1.015 1.051
Table 2 Predicted sugar per stalk by variety Date
Oct. 11 Oct. 25 Nov. 8 Nov. 22 Dec. 6 Dec. 20
Julian date
285 299 313 327 341 355
CP 70-321 (kg per stalk)
LCP 85-384 (kg per stalk)
Plantcane crop
Stubble cane crops
Plantcane crop
Stubble cane crops
0.125 0.140 0.154 0.167 0.179 0.192
0.112 0.127 0.140 0.154 0.166 0.178
0.089 0.106 0.121 0.137 0.151 0.165
0.091 0.108 0.123 0.139 0.153 0.167
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harvest season in Louisiana practically eliminates harvest during sugarcane maturity stages of decreasing sugar per stalk. Predicted values for CP 70-321 were slightly higher compared with values for LCP 85-384. Plantcane sucrose levels ranged from 0.125 to 0.192 kg of sugar per stalk for CP 70-321 compared with a range of 0.089 to 0.165 kg per stalk for LCP 85-384. Sucrose levels for stubble crops for each variety throughout the harvest season ranged from 0.112 to 0.179 and 0.091 to 0.167 kg per stalk, respectively. Predicted values of sugarcane stalk weight and sugar per stalk were used to estimate the tonnage and sucrose level of sugarcane in the field as well as the amount recovered by each harvest system. These estimates for the sugarcane varieties LCP 85-384 and CP 70-321 are presented in Tables 3 and 4. Stalk weight and sugar per Table 3 Comparison of predicted recoverable sugar per acre by harvest system for variety LCP 85-384 Harvest datea
Predicted sugar in the fieldb (kg/ha)
Wholestalk harvest system
Combine harvest system
Tonnage recoveredc (t/ha)
CRSd (kg/t)
9798 10,826 11,815
77.1 79.7 82.4
103 110 116
7945 8780 9582
84.0 86.9 89.8
98 104 110
8208 9070 9899
First stubble Oct. 25 9378 Nov. 8 10,741 Nov. 22 12,045
80.0 83.6 87.1
95 104 112
7606 8712 9769
87.1 91.2 95.0
90 99 106
7857 9000 10,092
Second stubble Oct. 11 9188 Oct. 25 10,840 Nov. 8 12,416
87.8 92.3 96.5
85 95 104
7452 8791 10,070
95.9 100.6 105.3
80 90 99
7698 9081 10,402
Third stubble Oct. 11 8909 Oct. 25 10,511 Nov. 8 12,039
85.1 89.6 93.6
85 95 104
7225 8524 9763
93.0 97.7 102.1
80 90 99
7464 8806 10,085
Plantcane Nov. 22 Dec. 6 Dec. 20
a
Total sugare (kg/ha)
Tonnage recoveredc (t/ha)
CRSd (kg/t)
Total sugare (kg/ha)
Harvest date is the midpoint of each 2-week harvest period. Predicted sugar in the field is the product of predicted tons of sugarcane and the theoretical recoverable sugar (TRS). Tonnage based on stalk populations of 71,615, 86,898, 100,444, and 97,389 stalks per hectare for plantcane, first stubble, second stubble and third stubble, respectively. c Tonnage in the field recovered by the harvester. Tons recovered by the wholestalk system based on a 93% field recovery rate and a 10% trash content. Tons recovered by the combine system based on a 97% field recovery rate and a 15% trash content. d Commercially recoverable sugar (CRS) is the sugar actually recovered from the cane by the mill and represents the TRS value adjusted by a scale factor. Scale factors for the wholestalk and combine systems are 95 and 90%, respectively. e Total sugar is the product of tonnage delivered and the CRS value. b
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M.E. Salassi et al. / Agricultural Systems 73 (2002) 261–278 Table 4 Comparison of predicted recoverable sugar per acre by harvest system for variety CP 70-321 Harvest datea
Predicted sugar in the fieldb (kg/ha)
Wholestalk harvest system
Combine harvest system
Tonnage recoveredc (t/ha)
CRSd (kg/t)
Total sugare (kg/ha)
Tonnage recoveredc (t/ha)
CRSd (kg/t)
Total sugare (kg/ha)
8972 9648 10,297
72.1 73.7 75.5
101 106 111
7276 7824 8350
78.6 80.4 82.2
95 100 105
7517 8083 8627
7253 8040 8790
64.1 65.9 67.9
92 99 105
5884 6520 7129
69.7 71.9 73.9
87 93 99
6078 6736 7364
Second stubble Oct. 11 6726 Oct. 25 7586 Nov. 8 8408
64.7 67.0 69.0
84 92 99
5455 6153 6818
70.6 73.0 75.3
80 87 93
5635 6356 7043
Third stubble Oct. 11 6587 Oct. 25 7429 Nov. 8 8233
63.4 65.4 67.6
84 92 99
5342 6026 6677
69.0 71.5 73.7
80 87 93
5518 6225 6898
Plantcane Nov. 22 Dec. 6 Dec. 20 First stubble Oct. 25 Nov. 8 Nov. 22
a
Harvest date is the midpoint of each 2-week harvest period. Predicted sugar in the field is the product of predicted tons of sugarcane and the theoretical recoverable sugar (TRS). Tonnage based on stalk populations of 53,710, 57,117, 59,726, and 58,491 stalks per hectare for plantcane, first stubble, second stubble and third stubble, respectively. c Tonnage in the field recovered by the harvester. Tons recovered by the wholestalk system based on a 93% field recovery rate and a 10% trash content. Tons recovered by the combine system based on a 97% field recovery rate and a 15% trash content. d Commercially recoverable sugar (CRS) is the sugar actually recovered from the cane by the mill and represents the TRS value adjusted by a scale factor. Scale factors for the wholestalk and combine systems are 95 and 90%, respectively. e Total sugar is the product of tonnage delivered and the CRS value. b
stalk estimates were converted to predicted values of sugar in the field, before harvest, as defined in Eqs. (8)–(10). Stalk population counts for each of the four crops of the two varieties are taken from field plot study results (Louisiana State University Agricultural Center, 1999). Metric tons of sugarcane and pounds of sugar actually recovered by the wholestalk and combine harvest systems were estimated using Eqs. (11)–(13). The predicted values of sugar per hectare recovered by the two harvest systems represent reflect typical harvest conditions. Combine harvesters have a higher field recovery rate than wholestalk harvesters, resulting in a greater percentage of the sugarcane in the field actually recovered by the harvesting system. Combine harvesters also tend to deliver harvested sugarcane to the mill with a
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higher trash content. This higher trash content causes the sugar recovery to be less efficient. This is reflected in the lower estimates of commercially recoverable sugar (CRS) for the combine system compared with the wholestalk system. Estimated yield values for both varieties in Tables 3 and 4 show slightly higher sugar per hectare yields for the combine system compared with the wholestalk system. However, due to the higher investment and operating costs of the combine system, it is not clear as to which type of harvesting system is more economical. To address this question, alternative yield scenarios were simulated within the mixed integer programming harvest system selection model to identify specific field recovery and sucrose recovery levels at which the most profitable harvesting system changes. 3.2. Impact of field recovery One variable factor which can influence the relative profitability of one sugarcane harvest system over another is related to the field recovery of the wholestalk systems. Field recovery is the percentage of sugarcane tons existing in the field prior to harvest which the harvest system is able to recover and deliver to the mill. Field recovery rates for the combine system are relatively high and consistent, averaging above 95%. However, field recovery rates for the wholestalk system are much more variable and are affected by harvesting conditions as well as the condition of the sugarcane. To analyze the impact of this field recovery variability, the mixed integer programming model was used to determine the most profitable harvesting system under alternative wholestalk field recovery rates. Three combination of the two sugarcane varieties were analyzed at three different wholestalk field recovery rates. The three variety combinations analyzed included low yield (CP 70-321)/high yield (LCP 85-384) variety mixes of 25/75%, 50/50%, and 75/25% of total farm acreage. The three wholestalk harvesting system field recovery rates analyzed were 85, 90, and 95%. Results of this analysis are presented in the Table 5. At a field recovery rate of 85% for the wholestalk system, the combine system was found to be more profitable at all three variety combinations (Table 5). Although the combine system had a lower sugar recovery per metric ton of sugarcane harvested than the wholestalk system, the ability to recover higher field tonnages resulted in greater net returns for the combine system. Total sugar yield ranged from 9200 kg/ha for the variety combination with 75% high yield variety to 7909 kg/ha for the variety combination with 75% low yield variety. Total tons harvested ranged from 92.6 t/ha to 81.3 t/ha, which were higher than recoverable yields from the wholestalk system. With a wholestalk field recovery rate of 90%, the wholestalk harvesting system was identified as the most profitable system. This system recovered less sugar and tonnage per hectare than the combine system, however lower fixed and operating costs resulted in higher net returns than the combine system. 3.3. Impact of sucrose recovery A second factor which can influence the relative profitability of one sugarcane harvest system over another concerns the sugar recovery of the combine system. The
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M.E. Salassi et al. / Agricultural Systems 73 (2002) 261–278 Table 5 Impact of wholestalk system field recovery on optimal harvest system selection Wholestalk recovery (%)
Low yield/high yield variety percentage 25/75
50/50
75/25
85% Field recovery System chosen Total sugara (kg/ha) Total tonsa (t/ha) Harvest costsa ($/ha) Net incomeb,c ($/total farm ha)
Combine 9200 92.6 149.54 399.14
Combine 8548 87.0 149.54 301.66
Combine 7909 81.3 149.54 205.88
90% Field recovery System chosen Total sugara (kg/ha) Total tonsa (t/ha) Harvest costsa ($/ha) Net incomeb,c ($/total farm ha)
Wholestalk 8677 82.2 90.66 434.01
Wholestalk 8058 77.3 90.66 341.07
Wholestalk 7451 72.4 90.66 250.29
95% Field recovery System chosen Total sugara (kg/ha) Total tonsa (t/ha) Harvest costsa ($/ha) Net incomeb,c ($/total farm ha)
Wholestalk 9161 87.0 90.66 506.18
Wholestalk 8506 81.6 90.66 408.06
Wholestalk 7865 76.4 90.66 312.11
a
Harvested area includes 307 ha of the total farm area of 404 ha. Total farm area includes 404 ha. c Net income represents net returns above variable and fixed production and harvesting expenses. General farm overhead and family living expenses were not included in the calculation of net returns. b
increased level of leaf trash included with combine-harvested sugarcane delivered to mills results in a lower CRS value compared with sugarcane harvested by wholestalk systems. To analyze the impact of varying levels of sucrose recovery, the mixed integer programming model was solved using different scale factor measures for the combine system. Scale factors of 85, 90, and 95% were simulated, representing increasing levels of sucrose recovery from combine-harvested sugarcane. These scale factors resulted in average CRS values for combine-harvested sugarcane of approximately 92–95, 97–100, and 102–105 kg of sugar per metric ton of cane, respectively. The wholestalk system was found to be most profitable at a combine scale factor of 85%. This scenario simulates the situation where the trash levels in the combine-harvested sugarcane are at such high levels than the sugar per ton of cane is low enough to offset the higher tonnage recovered, resulting in the combine system yielding lower net returns than the wholestalk system. Estimates of average CRS values for the wholestalk system were in the 103–105 range, dividing total kilograms of sugar per hectare by metric tons of sugarcane per hectare. As the scale factor was raised to 90%, the combine system became the most profitable system at all variety combinations except the 75% low yield/25% high yield case. At a scale
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factor of 95%, the combine system was found to be the most profitable system at all variety combinations (Table 6).
4. Conclusions This study combined within season crop yield models and a mixed integer mathematical programming model to evaluate the impact of alternative sugarcane yield and quality scenarios on the optimal harvest system selection. Sugar yield prediction models were estimated for two major sugarcane varieties produced in Louisiana. The estimated models were used to predict stalk weight and sugar per stalk at various points in time throughout the harvest season. Results indicated that predicted values of stalk weight increase 10–20% throughout the harvest season, while sugar per stalk increases by more than 50% throughout the season. These values were then converted to estimates of metric tons of sugarcane per hectare and kilograms of sugar per ton of sugarcane, with adjustments for harvest system specific field and sucrose recovery.
Table 6 Impact of combine system sugar recovery on optimal harvest system selection Combine scale factor (%)
Low yield/high yield variety percentage 25/75
50/50
75/25
85% Scale factor System chosen Total sugara (kg/ha) Total tonsa (t/ha) Harvest costsa ($/ha) Net incomeb,c ($/total farm ha)
Wholestalk 8286 79.1 90.66 375.22
Wholestalk 7789 74.8 90.66 300.87
Wholestalk 7203 69.9 90.66 387.40
90% Scale factor System chosen Total sugara (kg/ha) Total tonsa (t/ha) Harvest costsa ($/ha) Net incomeb,c ($/total farm ha)
Combine 9200 92.6 149.54 399.14
Combine 8547 87.0 149.54 301.49
Wholestalk 7203 69.9 90.66 213.07
95% Scale factor System chosen Total sugara (kg/ha) Total tonsa (t/ha) Harvest costsa ($/ha) Net incomeb,c ($/total farm ha)
Combine 9712 92.6 149.54 475.79
Combine 9022 87.0 149.54 372.48
Combine 8348 81.3 149.54 271.6
a
Harvested area includes 307 ha of the total farm area of 404 ha. Total farm area includes 404 ha. c Net income represents net returns above variable and fixed production and harvesting expenses. General farm overhead and family living expenses were not included in the calculation of net returns. b
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Predicted sugarcane crop yield values were incorporated into a mixed integer mathematical programming model which maximized whole farm net returns. The model incorporated preharvest and harvest field operations and selected the equipment complement necessary to perform these operations. Two sugarcane harvest systems were included in the model: wholestalk sugarcane harvesters and combine sugarcane harvesters. The primary objective of the study was to evaluate how predicted sugar yields, specifically the impact of varying levels of sugarcane recovery (field recovery) and sucrose recovery, affected the most economical harvest system selection. Results from the mixed integer harvest system selection model verified that the optimal selection of a sugarcane harvest system is dependent on several factors including yield of the specific variety, field recovery of the harvest system, and the impact of leaf trash and other extraneous plant material on the recovery of sucrose from the cane stalks. Field recovery is the percentage of sugarcane tons existing in the field prior to harvest which a particular harvest system is able to recover and deliver to the mill for processing. The breakeven point in terms of field recovery was found to be somewhere between 85 and 90% for the wholestalk harvest system. The combine harvest system was found to generate higher net returns than the wholestalk harvest system when the field recovery rate of the wholestalk system was 85%. Although the sucrose recovery was lower for the combine system, the ability to recovery and deliver more metric tons per hectare resulted in greater net returns. With a field recovery rate of 90%, the wholestalk system resulted in whole farm net returns which were greater than the combine system. Sucrose recovery concerns the kilograms of sugar recovered per metric ton of cane processed. Results indicated that increased trash levels in combine harvested sugarcane significantly reduced the profitability of that system, compared with the wholestalk system, when sucrose recovery levels were 90% or less of that for wholestalk harvesters. The basic modeling approach utilized in this study can be easily adapted for economic analysis of mechanized sugarcane harvesting in other regions of the world. The primary adjustments which would have to be made to the model would be to expand the number of sugarcane stubble crops modeled and to predict yield values for these stubble crops throughout the harvest season. Economic analysis of machinery selection in annual crop production, for such crops as wheat, corn, or soybeans for example, could also be conducted with the basic model structure by defining several time periods within the corresponding harvest seasons of these crops and incorporating predicted yield values for each time period. References Alexander, A.G., 1973. Chapter 11—Maturation and Natural Ripening in Sugarcane Physiology. A Comprehensive Study of the Saccharum Source-to-Sink System. Elsevier. Alvarez, J., Crane, D.R., Spreen, T.H., Kidder, G., 1982. A yield prediction model for Florida sugarcane. Agricultural Systems 9, 161–179. Brumelle, S., Granot, D., Halme, M., Vertinsky, I., 1998. A tabu search algorithm for finding good forest harvest schedules satisfying green-up constraints. European Journal of Operational Research 106, 408–424.
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