=Paper=
{{Paper
|id=Vol-1152/paper27
|storemode=property
|title=Simulation of Bin Loading Process During Manual Harvest of Specialty Crops Using the Machine Repair Model
|pdfUrl=https://ceur-ws.org/Vol-1152/paper27.pdf
|volume=Vol-1152
|dblpUrl=https://dblp.org/rec/conf/haicta/AmpatzidisVW11
}}
==Simulation of Bin Loading Process During Manual Harvest of Specialty Crops Using the Machine Repair Model==
<pdf width="1500px">https://ceur-ws.org/Vol-1152/paper27.pdf</pdf>
<pre>
    Simulation of Bin Loading Process During Manual
   Harvest of Specialty Crops Using the Machine Repair
                          Model

             Yiannis Ampatzidis1, Stavros Vougioukas2 and Matthew Whiting3
    1
     Center for Precision and Automated Agricultural Systems, Washington State University,
               99350 Prosser, WA, USA, e-mail: yiannis.ampatzidis@wsu.edu
     2
        Department of Agricultural Engineering, Aristotle University of Thessaloniki, 54124
                      Thessaloniki, Greece, e-mail: bougis@agro.auth.gr
     3
       Department of Horticulture and Landscape Architecture, Washington State University,
                   99350 Prosser, WA, USA, email: mdwhiting@wsu.edu



        Abstract. Machine repair models play an important role in many
        applications including computer systems, maintenance operations, and
        manufacturing systems. In this paper the machine repair model was
        adapted to describe, analyze, and simulate an agricultural application:
        the bin loading process during manual harvest of two specialty crops –
        grapes in Greece and sweet cherries in USA. In addition, a
        management tool was developed in Matlab®, based on the proposed
        algorithm, to evaluate the performance of the system and find the
        optimal combination of bin “carriers” and “service stations”. The use
        of repair models for agricultural operations shows promise for
        developing seasonable solutions for similar applications in other
        specialty crops (e.g. peach and apples).

        Keywords: queueing systems, modeling, simulation, specialty crop harvest,
        machine repair model, finite source model.




1 Introduction

   Specialty crops compete on most farms for limited capital, land, labor and
management resources. These crops are characterized generally by high costs of
production, heavy dependence upon manual labor, and high crop value. Harvest costs
are often the single greatest expense for specialty crop producers. Harvest costs for
sweet cherries (Prunus avium L.), for example, account for approximately 60% of
total cost of production (Seavert et al., 2002, 2008). Fruit crops are also highly
perishable and inefficiency in the harvest and handling process can have detrimental
effects on product quality and storability. Proper management and optimization of
________________________________
Copyright ©by the paper’s authors. Copying permitted only for private and academic purposes.
In: M. Salampasis, A. Matopoulos (eds.): Proceedings of the International Conference on Information
and Communication Technologies
for Sustainable Agri-production and Environment (HAICTA 2011), Skiathos, 8-11 September, 2011.



                                                 309
harvest operations is essential for reducing costs and maintaining fruit quality. The
window for harvesting fruit crops at optimum maturity varies by species but is
generally considered to be a matter of days. Harvesting sweet cherries prematurely or
beyond optimal timing affects consumer satisfaction with the fruit (Chauvin et al.,
2009).
   To optimize harvest efficiency the number of the machines and workers necessary
for harvesting, handling, and transport, as well as the execution of field operations
need to be planned. Recently, optimization algorithms for dynamic optimal planning
of harvesting operations for agronomic crops (e.g. wheat, corn, and cotton) was
introduced (Bochtis et al., 2006, 2007). The optimization criterion for planning the
cooperation of a fleet of combines supported by a fleet of transport carts is the
minimization of the total traveled length. Other optimization criteria include the
minimization of the non-productive time, fuel consumption, in-field travel distance,
and soil compaction in the field (Sørensena and Bochtis, 2010; Bochtis and
Vougioukas, 2009; Bocthis et al., 2007b).
   For specialty crops however, few simulation tools have been adopted successfully
to improve work methods. Bechar et al. (2007) applied industrial engineering
techniques to improve horticultural production in greenhouse tomato. They used two
simulation models (Arena tool and an algorithm in Visual Basic) to compare
alternative working methods in the trellising and harvesting stages and documented
potential savings of up to 32% of manual labor. Guan et al. (2006, 2008) designed
and formulated the farm work planning problem for geographically dispersed farms,
based on the hybrid Petri nets, but they did not develop an optimization algorithm to
improve farming process (farm work flow). Ampatzidis (2010) developed a
simulation tool in Matlab, based in UML and hybrid Petri nets analysis, to calculate
harvest efficiency during manual harvest of tree fruit in Greece. This algorithm does
not optimize the harvest process but, an optimal solution can be achieved simulating
a number of scenarios.
   In this paper the bin loading process during manual harvest of specialty crop is
modeled adopting a modified machine repair model (machine interference problem),
from the operations research area. An algorithm was developed in Matlab®, based on
the above model, in order to estimate the performance of the system (waiting time,
expected number of worker/machines at the loading unit etc.) and improve
confidence in sizing the fleet (workers and machines). Two different case studies are
modeled using this algorithm: i) manual table grape harvest in Greece, and ii) sweet
cherry harvest in Washington State, USA. First, the two different harvesting
procedures are described. Then the machine repair model is formulated to model the
harvest process. Finally, the bin loading process during grape harvest, in Greece, is
simulated, as an example, and results are presented.


2 Harvesting Procedure

   In this section, a brief description of the bin loading processes during manual
harvest of grapes in Greece and sweet cherries in US are presented. Generally, the
harvest process can be split into two discrete parts !"#!$%&'%()!*+,%-!%(-.!/%(0 (pick);



                                          310
1#! &.223&-ing the full fruit bins from the orchard (load) (Ampatzidis, 2010). The
4%0&+3-3! $5+-! 6"#! %0! 373&,-34! 528.0-! %(! -93! 0583! :5;! *.+! /.-9! &.,(-+%30; only the
capacity of the bins differs – 10 or 20 kg in Greece vs. ca. 170 kg in US. The
procedure for loading differs however: in Greece, workers collect bins full of grapes
using small hand-pushed carts whereas in USA, small tractors push a bin trailer able
to collect up to 4 bins.


2.1 Manual Grape Harvest in Greece

   Typically in Greece, manual grape harvesting is carried out with crews of 30 to 50
persons per field. There are typically two kinds of workers (Ampatzidis et al., 2008):
the fruit pickers who harvest fruit from the vine, and the carriers who load filled bins
onto small two-wheeled carts (Fig. 1) and manually transport them to a central
collection point where the bins are loaded in trucks. The process is the following:
grapes are harvested manually by fruit pickers and placed in vented plastic bins
whose capacity is ca. 10 kg. Once filled, the bins are left on the ground next to the
vine that was harvested. Next, the bins are loaded by the carriers into small carts (5-8
bins) which are transferred to a central location and loaded on a truck. After
harvesting a field, the workers and their equipment are transported to another field
which may or may not belong to the same farmer. When a truck is filled with bins it
returns to the packinghouse; otherwise the truck’s remaining free space is filled with
bins from the next field.




 Fig. 1. The “fruit pickers”, who collect the grapes and the “carrier”, who load bins into small
                                       hand-pushed cart.


2.2 Manual Sweet Cherries Harvest in WA

   The general harvest process for sweet cherry fruit has not evolved in over a
century. Pickers carry and place their ladder (2.75 to 4.5 m tall), climb to access fruit,



                                              311
place fruit into a metal bucket, whose capacity is limited by human carrying
capability (7 kg), secured over their shoulders with straps. Fruit are harvested by
grabbing pedicels and twisting, releasing them from the spur tissue. If the picking
bucket is full, or all reachable fruit are harvested, pickers then climb down and dump
fruit into a larger plastic or wood bin (capacity ca. 170 kg; 1.2 x 1.2 x 0.6 m), or
continue to harvest until the bucket is filled. Next, the bins are collected, by a fleet of
small tractors pushing hydraulic bin trailers that collect and transport up to 4 bins
(referred to as “carriers”, Fig. 2). Full bins are transferred to a central location and
loaded on refrigerated trucks by forklift. Finally, they are delivered to local packing
sheds for cooling, sorting, cleaning and packaging.




          Fig. 2. Tractor pushes a bin trailer (“carriers”) able to collect up to 4 bin.



3 Review of the Machine Repair Model

   The machine repair (or machine interference, or finite-population, or machine-
servicing etc.) model (MRM) is a finite source model, in which arrivals (or
customers) are drawn from a small (finite) population (Winston, 2004). These
systems consist of K machines subject to periodical breakdowns, and S repair
persons. When a machine breaks down it is repaired by a crew of repair persons who
therefore unavailable for repair other broken machines at the same time (Chen,
2006). Thus, the system performance (e.g. the expected number of broken machines,
the expected time a machine spends waiting for repair, the time a particular repair
person is idle) can be derived if key parameters of the system could be estimated,
such as the breakdown and service rate. Also, the cost and profit analysis of the
machine repair problem could be investigated (Ke and Wang, 1999; Armstrong,
2002; Schultz, 2004).
   In a queuing system (A/B/C):(D/E/F), A denotes the arrival rate, B the service rate,
C represents the number of the service stations, D states some general queue
disciplines regarding the priority of serving (e.g. first-come, first-served, FCFS; last-
come, first-served, LCFS; service in random order, SIRO), E denotes the maximum




                                               312
number of the customers allowed in the queuing system, and F states the size of the
population that the customers are drawn. The finite model (M/M/S):(GD/K/K)
denotes that the incoming traffic is modeled via a Poisson distribution (e.g. the
machine breakdown rate ( , inter-arrival rate) and service rate (!) follow an
exponential distribution (M)). The number of the machines is finite K, which can be
repaired by a number of repair persons S<K. The queue discipline is first-come, first-
served (FCFS). In this system arrivals are drawn from a small (finite) population K.


3.1 Adapting Machine Repair Model to Describe the Bin Loading
Process

    In this study the MRM was modified to model the bin loading process during
manual harvest of two specialty crops (grape and sweet cherry). The “carriers” are
treated as machine breakdowns and the trucks (or general the unloading points) are
servers (repair persons) in the system. For example, in manual grape harvesting the
“carriers” collect the bins (machine breakdowns) and move to the “unloading point”,
where some other workers (one per truck - repair person), placed on the truck, unload
and stack the bins into the truck.
    Consider a MRM that consists of K “carriers” and S servers (unloading points),
which work parallel and independent from each other. It is supposed the arrival rate
( ) of the “carriers” follows an exponential distribution (M). At any instant in time, a
particular “carrier” either collects a bin in the orchard (outside the system), or
unloads bins into the truck (waiting in queue or being served). When a “carrier”
collects the bins (machine breaks down) and all the unloading station-servers are
busy, it has to wait (Fig. 3). The first-come, first-served scheduling discipline is
followed by the system, and hence when a server will be available, it will serve the
first “carrier” in the line. Once a “carrier” is served (machine is repaired), it returns
back to collect more bin (machine returns to good condition).




               Fig. 3. A finite-source queuing model (machine repair model).




                                           313
   Further, the standard equations of the above queuing system are analyzed, using
the theory of the birth-death processes and the limit theorems of probability theory
(Sztrik and Bunday, 1993; Shashiashvili, 2007).
   The steady state probability that there are n carriers (customers) in the queueing
system will be given by equation:

            &' K ( n
            ,- . ) " ) P0             0*n+S
            ,/ n 0                                                                   (1)
            ,,' K ( n ! " n                             'K(      K!              #
       Pn 1 2- . ) n % S ) P0         S * n * K , where - . 1                ,"1
             ,/ n 0 S ! S                                n
                                                        / 0   K % n ! !) n !     $
             ,0                           n3K
             ,
             ,4


  The probability of having zero carriers in the system P 0 is calculated by applying
                                K
Little’s queuing formulae     5 P 1 1 , where:
                                      n
                               n 10


                                                       %1
            6 S %1 ' K (     K
                                  ' K ( n !) " n 7
       P0 1 9 5 - . ) " n 8 5 - . )            n%S :
                                                                                     (2)
            ; n 10 / n 0    n 1 S / n 0 S !) S     <

   The expected average number of carrier waiting for service L q (number of carries
in the queue, queue length), the expected (average or mean) number of carries in the
queuing system L (queue and service), and the expected (average or mean) number of
carries receiving service L s , when the system is in the steady state, can be calculated
by equations:

             K                          S %1
                                                    'K(
       Lq 1 5 n % S ! Pn 1 L % S 8 P0 ) 5 S % n ! ) - . ) " n                        (3)
            n1S                         n 10        /n0

and

            K         6 S %1 ' K (   1 K ' K ( n!       7
       L 1 5 nPn 1 P0 9 5 n - . " n 8 5 n - . n % S " n :                            (4)
           n 10       ; n 10 / n 0   S ! n1S / n 0 S    <

       LS 1 L % Lq                                                                   (5)

   The average time a carrier spends in the queue Wq is calculated by:

                  Lq                                                                 (6)
       Wq 1
              # ) K % L!




                                                  314
   The expected average waiting time in the system:

                L                                                                (7)
       W1
            # ) K % L!

   Let E be the percentage of time that a carrier spends working outside the queuing
system (carriers collect bins):

                 1#                                                              (8)
       E1
            1 # 8 Wq 8 1 $

   Also, if A is the average number of carries working outside the queuing system
(collecting bins):

                           1#                                                    (9)
       A1 K )E 1 K
                      1 # 8 Wq 8 1 $

   Finally, a management tool was created, utilizing the above equations, in Matlab
R2009a, in order to estimate the performance of the system.
   Below, the performance of a bin loading system was evaluated (number of
carriers-servers, waiting time etc.), using the proposed algorithm, during the yield
measurement and identification of grapes in a small vineyard in Greece.


3.2 Experimental Design

   In this paper, bin loading systems are simulated, based on real measurements in
the field, using a standard number of carriers and different number of service station
(trucks). The performance of each system is evaluated.
   At any instant in time, a particular carrier is in either “collecting bin from the
field” or “unloading bins onto the trucks” condition. When a carrier arrives at a
moment that all service stations are busy, it has to wait the carriers being served.
Once a carrier is served, it returns to collect more bins. Hence, the parameters: arrival
rate , and service rate !, must be calculated, as they are used as “inputs” in the
algorithm. Also, it must be investigated if these parameters follow an exponential
(Poisson) distribution or some other distribution.
   The arrival and service rates were calculated during loading and reckoning of the
bin weight and ID in a small vineyard (size ~500 m2), located at Folia Kavalas, in
Northern Greece (Ampatzidis et al., 2008). In this experiment, a portable
identification and weighing unit (PIWU, Fig. 4a) was mounted on the truck and
hence each bin was identified and weighed as it entered the truck (Fig. 4b). In this
queuing system the PIWU (and the trunk) treated as the servers and the carriers as the
customers. Then, a number of carrier K=10 was selected and the system performance




                                          315
was evaluated under different number of the service stations (trunks with PIWU)
S=1-4.




                    a                                                  b
Fig. 4. a) A portable identification and weighing unit (PIWU), with barcode reader and digital
scale, b) Each bin can be identified and weighed as it enters the truck (Ampatzidis et al.,
2008).



4 Results and Discussion
  The carriers’ arrival rate, as well as the service rate, followed a Poisson
distribution, applying the Pearson's chi-square test (<2, test of goodness of fit, which
establishes whether or not an observed frequency distribution differs from a normal
distribution). Further, the average se+=%&3! +5-3! :50! &52&,25-34! 50! >?@AB! &5++%3+0C8%(!
5(4! -93! &5++%3+0! 5++%=52! +5-3! 50! D?EA@F! &5++%3+0C8%(A! G20.H! /3&5,03! -93! +5-%.!
 " 1 # / $ 1 0.1125 + 1 the system is in equilibrium, has the Markov property and is
ergodic, so that it has a unique equilibrium status and the equations 1-9 can be used.
Using the proposed algorithm the manager of the farm can know the expected
number of carriers in the queuing system, the expected number of carriers waiting for
service, the expected average time a carrier spends in the queue or in the system etc.
  Table 1 presents the system performance under different number of service stations
(1 to 4), using the equations (and the algorithm) 1-9. It is observed, that using two
service stations (trucks) the characteristics of system are improved satisfactorily and
hence, two service stations (trucks) can be chosen for this system (ten carriers).




                                             316
     Table 1: Queuing systems characteristics. The service stations vary between 1 to 4.
              Service
             Station #
                              S=1,             S=2,             S=3,            S=4,
                              K=10             K=10             K=10            K=10
    System
    Characteristics
            P"                  0.171             0.330           0.349          0.351
           P(1)                 0.189             0.364           0.385          0.387
           P(2)                 0.187             0.181           0.191          0.192
           P(3)                 0.165             0.080           0.056          0.056
           P(4)                 0.127             0.031           0.014          0.011
      L q (carriers)            1.654             0.187           0.023          0.002
       L (carriers)             2.482             1.161           1.014          0.995
        W q (min)               1.247             0.120           0.015          0.002
         W (min)                1.872             0.745           0.640          0.627
            E                   0.752             0.884           0.899          0.901
       A (carriers)             7.518             8.893            8.99          9.005


5 Conclusion
A paradigm for the planning and evaluation of a bin loading operation executed by
bin carriers and transport trucks was presented in this paper. In this paradigm a
mathematical modeling and optimization tool, from operation research, was adapted
to model a common agricultural process for specialty crops. Further, a management
tool was developed to evaluate this procedure. Using the proposed method and
software, farm managers could investigate the performance of a bin loading system
(e.g. the time a carrier or a service station –truck- is idle etc.) and choose the
appropriate number of worker and machines for each orchard. Differenced harvest
process for two specialty crops, grapes in Greece and sweet cherries in USA, can
efficiently planning using the above model.
   This algorithm could be used as a part of a general simulation tool which utilizes
operation research techniques and optimization algorithms in order to model and
improve the total harvest process and minimize the probability a worker or machine
will be idle for a long period of time. Overall, the execution of harvest operations
with a crew of workers and a fleet of machines must careful planned in order to
collect, pack and distribute for sale, fruit with optimal quality and in the proper time.


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   T^"V>Q[RY! [TSV[`"Y! "WVU1T`"Y! W"U! U<JPD"ZU>]MPM"Y! 6a.432%()! 5(4! 323&-+.(%&!




                                            317
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