Modelling corn silage harvest logistics for a cost optimization approach

Modelling corn silage harvest logistics for a cost optimization approach

Computers and Electronics in Agriculture 118 (2015) 56–65 Contents lists available at ScienceDirect Computers and Electronics in Agriculture journal...

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Computers and Electronics in Agriculture 118 (2015) 56–65

Contents lists available at ScienceDirect

Computers and Electronics in Agriculture journal homepage: www.elsevier.com/locate/compag

Modelling corn silage harvest logistics for a cost optimization approach Carlos Amiama ⇑, José M. Pereira, Angel Castro, Javier Bueno Department of Agroforestry Engineering, University of Santiago de Compostela, Higher Polytechnic School, Campus Universitario, 27002 Lugo, Spain

a r t i c l e

i n f o

Article history: Received 26 August 2014 Received in revised form 5 August 2015 Accepted 21 August 2015

Keywords: Fleet management Corn silage harvest cycle Harvest cost Biomass transportation simulation

a b s t r a c t Harvesting corn silage requires balancing the capacities for harvest, transport, and storage operations to eliminate bottlenecks. The overall goal of this paper is to simulate the silage harvest system in order to provide the technicians with a decision support tool. This tool will be useful when performing both the strategic planning at the beginning of the harvest season, and in daily decision making, in order to determine the right combination of resources according to fields to harvest. A model was constructed to evaluate the handling system comprising the harvest, transport and packing of forage intended for corn silage. In order to provide a real example of the usefulness for strategic planning by the tool developed, the harvesting of 590 fields of corn silage in a region of NW Spain was simulated. The model obtained provided a value of 27 trucks to obtain lower harvesting costs if 6-row SPFH were used and 33 trucks with 8-row SPFH. The proper packer capacity at the silo was 3.35 t min1. The impact that the matching of equipment has on the costs and on the length of the harvest season for each of the harvesters analyzed was more significant with 8-row SPFH. If the number of trucks is less than 30, a 6-row SPFH is more cost efficient than an 8-row SPFH. On the other hand if the number is greater, then the use of the 8-row SPFH would incur lower costs. The harvesting process is more sensitive to changes in the packing capacity than to the number of trucks used relative to the optimum value determined. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction In the harvesting process of corn silage, once the proper maturity and moisture content has been reached, the primary management concerns are to harvest the crop as quickly as possible, avoid runoff and store and treat the corn silage in a manner that eliminates and excludes as much oxygen as possible. These steps will ensure a fast and efficient fermentation with minimum losses during ensiling, storage and feed-out. Research at the USDA Forage Research Center supports mechanical processing in corn silage management as it improves feed efficiency and milk production (Shinners et al., 2007). However, the equipment is expensive and may not be economically viable in smaller operations. Small farms are not able to capitalize on new technology because of the high cost of purchasing large equipment. Consequently, in recent years, in milk producing areas of Western Europe, forage processing plants have been created and operate cooperatively. With this procedure, farmers transfer their field forage (corn silage) to a forage

⇑ Corresponding author at: Escuela Politécnica Superior, Campus Universitario, 27002 Lugo, Spain. Tel.: +34 982 25 22 31; fax: +34 982 28 59 26. E-mail address: [email protected] (C. Amiama). http://dx.doi.org/10.1016/j.compag.2015.08.024 0168-1699/Ó 2015 Elsevier B.V. All rights reserved.

processing plant that manages the corn silage process (including harvesting and storing). The logistic process includes multiple harvest, transport, and storage operations. The harvest operation involves self-propelled forage harvesters (SPFH), trucks for transport, and machinery for silage packing. All of these need to be co-ordinated, and the number of equipment components needs to be adjusted according to the field’s capacity – all under a tight schedule, with a large number of fields to harvest. Bottlenecks within transport or unloading operations can reduce the capacity of harvest operations (Buckmaster, 2006). For this reason, many researchers have used simulation models to analyze and optimize these complex systems. Several authors have successfully applied these models to commodities (Berruto and Busato, 2008; De Toro et al., 2012; Higgins and Davies, 2005; Ravula et al., 2008). The simulation demonstrated the usefulness of systems analysis in predicting the amount and cost of biomass supply in appropriate resource allocation to minimize bottlenecks. The overall goal of this paper is to simulate the silage harvest system in order to provide a decision support tool for technicians that manage this process. This tool will be useful when performing both the strategic planning at the beginning of the harvest season and the daily decision making, in order to determine the suitable

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combination of resources according to the fields to harvest. The specific objectives of this paper are:  To develop a model to quantify resource allocations for biomass supply and transport operations.  To provide an example of the usefulness of the decision support tool for strategic planning:  Comparing the performance of the system with different SPFH header widths.  Evaluating different resource combinations, in order to minimize the total system costs.  Determining which elements have a greater impact on the behaviour of the system via a sensitivity analysis. 2. Materials and method

Table 1 Number of fields and farmers involved.

SPFH1 SPFH2 SPFH3 SPFH4

Fields

Farmers

Area (ha)

Harvest season (days)

181 161 158 90

27 38 45 22

215.5 221.2 265.3 128.3

33 37 40 23

being 1 and 10 km away. Fig. 1 shows the spatial distribution of these fields. 2.2. Modelling of the corn silage harvest system The development of the process model has been carried out primarily to reflect the reality of working conditions.

2.1. Description of the corn silage process In northern Spain corn silage is usually harvested with SPFHs. This process involves SPFHs and dump trucks for transport to bunker silos at the forage processing plant, which may be several kilometres from where the corn was harvested. The cycle includes three parallel machinery operations: harvesting, transporting and packing at the silo. SPFH travel between farms should also be considered. The extended use of SPFHs, with a hopper for on-board storage, has been encouraged in recent years in our latitudes due to small, irregularly shaped fields. Forage is unloaded into dump trucks when the hopper is full. To do this, the hopper needs to be held over the truck. The loading capacity of the trucks is equivalent to, or slightly larger than, the capacity of the on-board storage of the SPFH. Tractors and loading shovels carry out the packing at the silo. Typically, farmers estimate when corn forage has reached the suitable moisture content to be harvested, subsequently notifying the processing plant and request its harvest. The processing plant schedules the overall silage process (harvest, transport and packing) for each week. All partners’ requests are harvested on a firstin, first-out (FIFO) basis. A farmer’s entire fields have to be harvested before starting on the next farmer’s fields. This is because farmers want all their fields to be harvested consecutively. Fields are assigned to SPFH by a proximity criteria (SPFH have a reduced travel speed), and trucks are assigned trying to minimize SPFH waiting times. An average corn silage harvest season in northwest Spain ranges from 35 to 40 days, typically from 20th September to 30th October. Before the start of the harvesting season, the technician that manages the harvest should perform a preliminary scheduling. Their objective is to estimate the combination of resources needed to harvest the fields in the available time with minimum cost. Obviously this schedule must be checked daily according to the weather and crop conditions. Nonetheless, the changes in planning generally involve varying the workday, while trying to keep the harvesting resources as constant as possible. This case study was conducted at a forage processing plant (CAVI) located in Ribadeo, Galicia (Spain). The harvesting process of corn silage during the 2011 harvest season was simulated. Four SPFH of the same brand and model (New Holland FX58 with a Racine 2025 bunker) were considered. The allocation of SPFHs to the fields, the order of harvesting and the original routes were maintained, because our objective was to predict the performance of the system using different resource allocations and not route management. Table 1 reflects the fields harvested by the four SPFH considered. The fields for harvesting are found at a maximum distance of 30 km from the CAVI, the majority of which are being situated

2.2.1. Harvester performance The throughput (material capacity) of the forage harvester was obtained by the expression (1), according to ASABE EP 496.3 (ASABE Standards, 2011).

Cm ¼ Ca  Y

ð1Þ

where Cm, throughput (t h1). Ca, effective field capacity (ha h1). Y, crop yield (t ha1). Data for the harvester activity during the 2011 corn silage harvesting season were recorded by means of a telemetric system (Amiama et al., 2008). The SPFH considered can be equipped with different headers, with 8 rows which have a 6.0 m working width, or 6 rows which have a 4.5 m working width. When a SPFH ends its activity in a field it moves to the next field to harvest. Travelling times between fields have been registered. Table 2 shows the values used to simulate the harvesting system. 2.2.2. Truck cycle The cycle time for the transport without idle time, CTt (h cycle1), was obtained from the time between two successive unloading operations for each of the transports in the cycle, according to the expression (2).

CTt ¼ Ttu; a þ Tt þ Tht; t

ð2Þ

where Ttu,a: Alignment and unloading time for the truck at the silo, (h unload1). This time comprises the period from arrival of the transport at the silo until the transport finishes unloading and starts to make its way back to the field. An average value of 0.074 h was obtained from 30 unloading times. Tht,t: Time for harvest/transport interaction and transfer, (h unload1). This time comprises operations for unloading forage into the transport vehicle. The value of Tht,t (comprised in the effective field capacity of the harvester) was determined recording 156 unloads, with an average value of 0.033 h being obtained. Tt: Transport travel time (h). Time required for round trip (fieldsilo-field). The loading capacity of the trucks is equivalent to, or slightly larger than, the capacity of the on-board storage of the SPFH. In order to determine the travel speed of the transporter, GPS data loggers were attached to the trucks, and signals were analyzed. A

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Fig. 1. Spatial distribution of fields to harvest.

Table 2 Data used for the simulation. General input

Units

Value

Effective field capacity, Ca (6 rows) Effective field capacity, Ca (8 rows) Crop yield, Y Loading capacity of trucks Alignment and unloading time for the transport in the silo Time for harvest/transport interaction and transfer Packing capacity of a loading shovel (green fodder) Packing capacity of a tractor (green fodder) Length of workday

ha h1 ha h1 t ha1 t h h t h1 t h1 h

1.14 1.39 42.31 8 0.074 0.033 81 39 8

2.2.3. Packing activity Tractors and loading shovels carry out the packing at the silo. Their capacity is a function of their weight. As a general rule a tractor can pack about twice its weight in silage (DM) per hour (Tyson et al., 1996), and this was adopted in our simulation. The transport unloading operation at the plant can be done simultaneously with the packing operation. The wide bunker entrance allows the continuous operation of the packer. In our simulation at CAVI two types of packers were considered: the one in most commonly used, a loading shovel with a weight of 13.5 t, and tractors with an average weight of 6.5 t. Performances obtained for packing forage were 81.0 t h1 and 39.0 t h1, respectively, considering a DM value of 33% (this value can vary between 32% and 35%).

software application in Visual Basic was developed to process data gathered by the GPS providing distances between the field and CAVI and the time spent in travelling. With this data average speeds were obtained. Full and empty truck speeds were differentiated. The truck speed adopted for the simulation was calculated by a linear regression (Harrigan, 2003). Statistical analyses were performed using the SPSS statistical software package (SPSS, Inc., Chicago, Ill.) Regression parameters are shown in Table 3. According to the field trials, the maximum distance was 30 km, and this is the maximum value allowed by the model. Tt has been determined specifically for each field, taking into account the average speed (determined by linear regression) and the distance between the field and silo. As said original routes (recorded by GPS data loggers) were maintained.

2.2.4. Determination of the allocation of trucks to harvester Some authors establish the number of transport vehicles needed to keep the forage harvester working at full capacity (Harrigan, 2003; Buckmaster and Hilton, 2005). This is not always the best way to minimize costs. It can be better to keep the harvester waiting for a while than to add an extra transporter that will be predominantly inactive. The mathematical solution that provides the SPFH utilization factor (Uh) with the lowest total costs (transport costs + harvest costs) requires a comparison of the costs associated with the use of the SPFH together with 1 transporter, and the costs associated with the use of the SPFH in conjunction with two trucks, three trucks, etc. Costs are determined by means of the expression (3):

Table 3 Regression coefficients for truck speed.

Nt  C þ C  C 0 =C ðNt  C þ C 0 Þ=Uh ¼ Ce  Uh Ce

Transport

Constant

Empty 28.417 Full 22.176 Dependent variable: S (km h1) D: distance (km).

D (km)

Significance level

Partial correlation

0.864 0.898

1% 1%

0.65 0.66

where Nt: Number of trucks involved in transportation. C: Cost of the truck (€ h1). C0 : Cost of the SPFH (€ h1). Ce: Effective field capacity of the SPFH (ha h1).

ð3Þ

C. Amiama et al. / Computers and Electronics in Agriculture 118 (2015) 56–65

Uh: Utilization of the SPFH, (busy h h1). The objective is to calculate the Uh that makes it profitable to move from 1 truck to 2 trucks, from 2 to 3 trucks, and so on.The minimum cost per ha (Uh = 1) with n + 1 trucks is:

ðNt þ 1Þ  C þ C 0 Ce

ð4Þ

The intersection of the 2 curves is at:

Uh ¼

Nt þ C 0 =C Nt þ 1 þ C 0 =C

ð5Þ

In our case we want to determine the number of trucks needed to keep the SPFH busy for Uh minutes each cycle. From expression (6) we can obtain the number of trucks (Nto) required to provide an appropriate utilization of the SPFH:

Uh  Nto2 þ ðUh þ Uh  C 0 =C  1Þ  Nto  C 0 =C ¼ 0

ð6Þ

59

 If the hopper is less than 1/2 full (harvest field is finished), and the next field belongs to the same farmer, the ‘‘fieldx” event will be run. At this event the travelling time between fields is added, and the process starts again.  If there are trucks waiting and the hopper is over 1/2 full, the ‘‘startux” event will be run to start the forage transfer to the truck.  If there are no trucks waiting at the field and the hopper is over 1/2 full, or if the hopper is less than 1/2 full but the next field belongs to a different farmer, the ‘‘waittrx” event will be run. At this point the activity status of the SPFH changes (waiting), making a distinction between when the trucks are waiting at the silo, event ‘‘twsx” and when there are no trucks waiting, event ‘‘tnwsx”. This distinction is useful, because it enables us to discern when the increase in trucks results in lower SPFH waiting times. With data recorded in ‘‘meterxA” and ‘‘meterxB” events, waiting times of each SPFH will be calculated. When the ‘‘endux” event is reached the time for harvest/transport interaction and transfer (0.033 h) is computed. At this event we must choose some of these options:

2.3. Machinery costs Cost values have been based on information from the forage processing plant according to the real cost of hiring harvesting operations. Table 4 shows the hourly cost of the different equipment considered. All times, including waiting times, were computed for the cost calculations, as in real life. 2.4. Simulation Event graph modelling software based on discrete-event simulation, SIGMA (www.sigmawiki.com) was used to run the model. Fig. 2 shows the model used to simulate the corn silage process. Different shapes were assigned to each type of equipment: circles for the SPFH cycle, squares for the truck activity and octagons for the packer’s activity. As said previously, 4 SPFH were considered. 2.4.1. State variables setup The ‘‘runx” events (diamonds) include information about the state variables shown in Table 2. The events initialize several variables needed to determine the ID of the harvested field, the farmer ID, the number of trucks waiting with each harvester, the number of tonnes unloaded at the silo, the number of tonnes packed and several intermediate counters to obtain the activity state of harvesters, trucks and packers. 2.4.2. Harvesters’ cycle Fig. 3 shows the flow of SPFH activity. Firstly the farmer is assigned to the harvester x (‘‘farmerx” event) and the field to harvest is selected (‘‘fieldx” event), as per the real allocation in the 2011 harvesting season. The fill level of the hopper is determined at the ‘‘r0cx” event (SPFH can carry forage from another field) and at the ‘‘starthx” event, the harvesting starts. At the ‘‘endhx” event, the remaining forage and the time spent harvesting are determined. Several scenarios were considered: Table 4 Estimated machine operating cost for harvesting corn silage. Operation

Hourly cost rate (€ h1)

Harvesting (6 rows) Harvesting (8 rows) Transporting (truck) Packing (tractor) Packing (loading shovel)

265 305 40 50 60

 If the harvest of the last field has not finished the ‘‘starthx” event will be run.  If the field harvest has finished but the farmer has more fields, the SPFH will move to the next field (‘‘fieldx” event) adding the travelling time between fields.  If the farmer has no more fields ‘‘farmerx” event will be run. At this point the system checks how many farmers have not been covered. If there are none remaining, the ‘‘stophx” event will be run. 2.4.3. Trucks’ cycle Trucks involved in the forage transport are defined in the ‘‘run” events. In the ‘‘trucks” event (see Fig. 4) trucks are assigned to the SPFH with a smaller Uh, according to the value of the expression (6). In the ‘‘truckhx” event a counter determines the number of trucks assigned to a SPFH at each moment. When the ‘‘waittx” event is reached it simulates the truck arriving at the field, and the time to move from the silo to the field is computed. If the SPFH is in ‘‘harvest” state, the truck is in the ‘‘waiting” state. Otherwise the ‘‘startux” event is run (see Section 2.4.2). Waiting times of the truck are determined by the ‘‘metertx” event. When the truck reaches the ‘‘truckhx” event, travelling times between the field and silo are computed. The maximum amount of unspread forage in the silo, prior to the completion of a new unload was estimated at 16 t (truck capacity ⁄ 2). This reflects the real situation, because if more trucks are unloaded, the activity of packers can be interrupted. When the truck arrives at the ‘‘silo” event, two possibilities were considered:  If there are more than 16 t not spread, the trucks enter the ‘‘waiting” state and the forage is not unloaded, recording this data at the ‘‘twsilo” event. Waiting times for the truck at the silo are recorded at the ‘‘waitts” event. For this purpose twodimensional array were used.  When the amount of unspread forage is lower than 16 t a new truck unloads (‘‘starttu” event). This process needs 0.074 h (alignment and unloading time for the transporter in the silo) and will run the ‘‘endtu” vertex, ending the unloading and assigning the truck to another SPFH (‘‘trucks” event). 2.4.4. Packing cycle Once the first truck unloads the forage at the silo, spreading and packing operations begin (‘‘packing” event). The performance

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Fig. 2. Activity distribution in model (green border state variables, red border SPFH, yellow border packers and without border forage transport).

depends on the number and type of equipment involved (see Section 2.2.3). Fig. 5 shows a flow chart of the silo activity. When all forage has been spread, packers stop (‘‘stopp” event). At the ‘‘waitp” and ‘‘meterp” events, packers’ wait times are computed. 2.5. Simulation scenarios For each SPFH considered (6 rows and 8 rows) we analyzed the equipment setup that provides a less expensive solution, by successive approximations. Firstly the right number of trucks involved is calculated (trucks are the most easily varied component in the

system), considering that there are no limitations from packing at the silo. With this value, the packing performance that provides minimum costs is determined. The right number of trucks is subsequently adjusted again. We calculated the impact of the number of trucks over the length of the harvesting season. In this work timeliness was not considered as a cost, due to the difficulty of determining the appropriate day in relation to the value of the harvest. Furthermore, there was little variation between the actual date of the harvest (rather than that which could be considered as the appropriate date) and the date provided by the model, except when considering a very low number of trucks.

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meterxA

meterxB

state variables

endux

startux

farmerx

fieldx

r0cx

twsx

starthx

endhx

endhx

wairx

tnwsx

stophx

Fig. 3. Simulation of SPFH activity with a flow chart.

state variables

truckhx

endtu

waittx

metertx

trucks

starttu

silo

waitts

twsilo

truckhx

endux

startux

packing

Fig. 4. Simulation of truck activity with a flow chart.

In addition, the distributions of waiting and activity times for SPFH were analyzed, verifying whether the waiting times are caused by the inability of trucks to transport the forage or whether packer capacity has been exceeded. A sensitivity analysis of the key parameters in the harvesting process was carried out. This model has been applied for a particular region. However this model and analysis methodology can easily be extended to handle similar problems in other areas.

3. Results and discussion 3.1. Equipment setup To determine the combination of equipment that provides a minimum cost, firstly we started the simulations establishing a packing capacity of 16 t min1. Our objective was to determine the number of trucks that provide the best Uh for each SPFH,

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state variables

endtu

packing

stopp

waitp

meterp

Fig. 5. Simulation of packer’s activity with a flow chart.

13,00,000.00

As can be observed in the case of the 6-row SPFH the minimum cost is obtained using 27 trucks, rising to €592,130. In the case of the 8-row SPFHs the minimum cost can be obtained with 33 trucks, rising to €588,150. Data fits very well with polynomial regression models, so the harvest cost can be predicted with great accuracy, when the number of trucks are altered. This fit was not observed when the size of the truck fleet was fixed and the packing capacity was variable, as can be observed in Fig. 8.

9,00,000

y = -11.23x3 + 1613.87x2 - 69848.74x + 1540864 R² = 0.999

8,50,000 8,00,000

Harvest costs (€)

avoiding waiting times of trucks at the silo. Fig. 6 shows the results obtained. When evaluating the 6-row SPFH, lowest costs are obtained with 30 trucks and when evaluating the 8-row SPFH, the lowest costs are obtained with 34 trucks. The combination of trucks and packers which provide the lowest harvest cost has been established by decreasing the packing capacity. As can be seen in Table 5, a lower cost is obtained with a packing capacity of 3.35 t min1 with 6-row SPFHs; the same as with 8-row SPFHs. The packing capacity corresponds to two loading shovels and a tractor, a combination which is in frequent use in our region. The right number of trucks when evaluating a packing capacity of 3.35 t min1, can differ slightly from that obtained in Fig. 6, due to an increase in the waiting times of the trucks at the silo. To determine the proper number of trucks needed, the cost analysis has been repeated, establishing a packing activity of 3.35 t min1. The results obtained are shown in Fig. 7.

y = -17.00x3 + 2157.57x2 - 81662.69x + 1562095 R² = 0.994

7,50,000 7,00,000 6,50,000 6,00,000

Harvest cost (€)

12,00,000.00

5,50,000 5,00,000

11,00,000.00

12

16

20

24

28

32

36

40

44

48

Trucks 10,00,000.00

6-row SPFH

8-row SPFH

Fig. 7. Harvesting costs simulation with 3.35 t min1 of packing capacity.

9,00,000.00

7,50,000

8,00,000.00

6-row SPFH

7,30,000 7,00,000.00 12

16

20

24

28

32

36

40

44

8-row SPFH

Fig. 6. Harvest cost simulation with 16 t min1 of packing capacity. Table 5 Predicted cost (thousands of €) for corn harvesting season with different packing capacities. Packing capacity (t min1)

6-row SPFH (30 trucks)

8-row SPFH (34 trucks)

16.00 8.00 6.00 5.35 4.00 3.35 2.00

810.01 676.55 643.13 624.60 610.01 594.96 658.52

767.70 654.75 624.67 610.07 596.04 589.82 736.44

Harvest costs (€)

Trucks 6-row SPFH

8-row SPFH

7,10,000

48

6,90,000 6,70,000 6,50,000 6,30,000 6,10,000 5,90,000 5,70,000 5,50,000 0

1

2

3

4

5

6

7

8

9

Packing capacity (t.min-1) Fig. 8. Harvest cost simulation with 6-rows SPFH/30 trucks and 8-rows SPFH/34 trucks.

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The intersection of cost curves for both is produced with 29.8 trucks, which signifies that if the number of trucks available is less than 30 it is more cost efficient to use the 6-row SPFH. On the other hand if the number is greater, then the use of the 8-row SPFH would incur lower costs. 3.2. Cost analysis In Table 6 a breakdown of the costs of the equipment used in the harvest system can be observed based on minimum cost. It is assumed that transport is the element with the greatest cost within the system, derived from the high number of trucks required. The packers are the element assumed to incur the least cost. Fig. 9 shows the developments of costs as the number of trucks are altered, taking into account a packing capacity of 3.35 t min1. It can be observed that the costs of the SPFH are more responsive to an insufficient truck fleet size than the packers. 3.3. Harvest season length

tion of suitable costs and use of the 6-row SPFH the duration of the harvest season reaches 39.6 days. This value can be seen to reduce to 33.6 days when the 8-row SPFH is used. Although, as can be observed in Table 6, the use of a 6-row or 8-row SPFH does not imply a significant economic saving, however, a considerable reduction in time is obtained considering the short season that exists for carrying out this operation. Fig. 10 shows the variation in the duration of the harvest season in relation to the number of trucks and a packing capacity at the silo of 3.35 t min1. In general an increase in the number of trucks with respect to the optimum calculated has a much lesser impact on the duration of the process than the reduction. In the case of the 6-row SPFH an increase of 9 trucks with respect to the optimum assumes a curtailment of 3 days and a reduction of 7 trucks implies an increase of 9.5 days in the length of the harvest season. This tendency is maintained in the 8-row SPFH, since an increase of 7 trucks implies a shortening in the harvest season by 2.5 days and a decrease of 9 trucks incurs an increase of 7.5 days. 3.4. Analysis of SPFH occupation

The impact of efficient management of the trucks over the duration of the harvest season has been determined. With a combina-

Fig. 11 shows the percentage distribution of the average time employed by each of the combine harvesters analyzed. In both

Table 6 Minimum predicted cost (thousands of €) for corn harvesting season. SPFH costs

%

Trucks costs

%

Packers costs

%

Harvest costs

6-rows 8-rows

266.50 260.40

45.0 44.3

271.50 282.30

45.9 48.0

53.65 45.45

9.1 7.7

592.13 588.15

9,00,000 8,00,000 7,00,000 6,00,000

Cost (€)

70

Harvest season (days)

SPFH type

65

6-row SPFH

60

8-row SPFH

55 50 45 40

5,00,000

35

4,00,000

30 0

3,00,000

10

20

30

40

50

60

Trucks

2,00,000 Fig. 10. Duration of harvest season with 6-row SPFH and 8-row SPFH, with a 3.35 t min1 of packing capacity.

1,00,000 0 10

15

20

25

30

35

40

45

50

Trucks Packers cost

Trucks cost

120% SPFHs cost

Total cost

100%

9,00,000 8,00,000 7,00,000

80%

Travelling times

Cost (€)

6,00,000 Harvesting times

5,00,000

60%

4,00,000

Waiting times with trucks at silo

3,00,000

Waiting times without trucks at silo

40%

2,00,000 1,00,000

20%

0 10

15

20

25

30

35

40

45

50

Trucks Packers cost

Trucks cost

SPFHs cost

Total cost

0% 8-rows SPFH

Fig. 9. Cost analysis of harvesting season with 6-row SPFH (top) and 8-row SPFH (bottom), with 3.35 t min1 of packing capacity.

6-rows SPFH

Fig. 11. Average time percentage for each SPFH considered.

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cases harvesting times were high, at approximately 87.5%. Travelling times were approximately 4.0%, which indicates adequate management of the routes. The waiting times for each truck were higher for the 6-row SPFH (9.00% as opposed to 8.16%), owing to the greater value of C0 /C (see Section 2.2.4). While the SPFH are waiting, the trucks are mostly travelling indicating that delays are rarely caused by packer bottlenecks. 3.5. Sensitivity analysis The purpose of this analysis is to determine whether the process is more receptive to a variation in the number of trucks involved or to a variation in the number of packers. Starting at a base of minimal cost with each combine harvester, the packing capacity has been increased by 0.65 t min1 (taking into consideration an additional tractor) or it has been reduced by 1.35 t min1 (decreasing a loading shovel), which increases the hourly cost of the system by 50 € h1 or reduces it by 60 € h1, respectively (as can be seen in Table 4). The variations in the total costs of the harvest have varied between 3.07% and 7.28% in the case of the 6-row SPFH and 1.53% and 23.32% in the case of the 8-row SPFH. Based on the same principal of minimal cost, the fleet of transport vehicles has been modified by adding or decreasing two

6-row SPFH

0

20000

40000

60000

80000

100000 120000 140000 160000

Harvest cost variation (€) Packing capacity reduction

Packing capacity increase

2 trucks reduction

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trucks, which implies an increase or decrease in hourly costs of 80 € h1, slightly higher than the packers. In Fig. 12 it can be observed how the variation in total costs are inferior to those obtained previously, by changing the packing capacity, varying between 0.26% and 2.18% in the case of the 6-row SPFH and 0.59% and 0.61% in the case of the 8-row SPFH. Consequently, it can be concluded that, in our conditions, the system is more sensitive to a correct adjustment of the packing capacity than a suitable number of trucks involved in the process. 4. Conclusions With the results obtained from this work it can be concluded that discrete event model simulation is a useful decision support tool for corn silage harvest simulation. The equipment setup that provides lower costs varies depending on the SPFH considered. For our conditions, in the case of the 6-row SPFH right performance was reached with 27 trucks and with the 8-row SPFH right performance was obtained with 33 trucks. The intersection of the cost curves of both harvesters was produced with 30 trucks. In both scenarios 3.35 t min1 was determined as the optimum packer capacity at the silo. Harvest season costs were similar with the use of 6-row and 8-row SPFH, when trucks and packers are optimized. Nevertheless, if we consider the 8-row SPFH, the harvest season length is reduced by more than 6 days, which is an important aspect considering the reduced time available for carrying out this operation. The use of a lower number of trucks than the optimum will have a greater impact on the length of the harvest than expanding the fleet of trucks. As was to be expected, in the cases of minimum cost, the periods of inactivity caused by waiting times for the trucks are higher for the 6-row than the 8-row SPFH, originating from the higher hourly cost of the latter. Bottlenecks at the silo do not occur frequently if appropriate packer capacity is considered. The analysis of sensitivity demonstrates that for both of the harvesters considered, the harvesting process is more sensitive to changes in the packing capacity than to the number of trucks used in relation to the suitable value determined. Consequently greater attention should be paid to the sizing of equipment for spreading and packing than to the number of trucks involved. These conclusions have been obtained for a particular region. However this model and analysis methodology can easily be extended to handle similar problems in other areas. Further research can be carried out such as to determine the penalty cost for imposing the constraint that all fields owned by a particular farmer must be harvested sequentially. References

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Fig. 12. Harvest cost variation to the increase or reduction in the number of trucks or in the packing capacity, in relation to the minimal cost setting.

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