Journal of Applied Engineering Science
doi:10.5937/jaes16-17696 Paper number: 16(2018)4, 561, 523 - 537
DESIGN OF AN INVENTORY MANAGEMENT SYSTEM IN
AN AGRICULTURAL SUPPLY CHAIN CONSIDERING THE
DETERIORATION OF THE PRODUCT: THE CASE OF SMALL
CITRUS PRODUCERS IN A DEVELOPING COUNTRY
Cristhian Guillermo Acosta Imbachi1*, Andrés Felipe Cano Larrahondo1, Diego León Peña Orozco2,
Leonardo Rivera Cadavid1, Juan José Bravo Bastidas1
1Department of Industrial Engineering, Universidad del Valle, Colombia
2University Corporation Minuto de Dios, Department of engineering, Industrial Engineering, Colombia
Inventory management along the agrifood supply chain is a subject of great interest due to the constraints related
with the perishable condition of product. Signifi cant problems like demand forecasting, inventory management and
transportation was evidenced within the supply chain studied. Additionally, the management of perishables and their
lifecycle are the most frequently issue in this kind of supply chain.An inventory management policy is defi ned taking
in consideration the optimal quantity for an order and the time for ordering so as to ward off costs related with un-
derstock or overstock. This paper presents a mathematical model for inventory management in agricultural supply
chains considering perishability. The supply chain studied involves a retailer, a producer and a supplier. The advan-
tages of integrating inventory management along the supply chain are discussed and fi nally some recommendations
and research opportunities set forth.
Key words: Inventory management; Perishable product; Fruit supply chain; Integration in supply chain
INTRODUCTION
Around 2,500 million people work part-time or full-time
in 500 million small farms around the world. However,
although the land is occupied by these producers, it only
represents 12% of all agricultural land covering more
than 80% of the worldwide food demand [01]. The contri-
bution by family farmers and small farmers to the millen-
nium goal related to food security, poverty reduction and
sustainable development recognized by the General As-
sembly of the United Nations. For this reason, the need
to count with new methodologies that enable greater ef-
fi ciency and competitiveness in the supply chain of small
agricultural producers looms up.
Agricultural supply chains are a subject of great interest,
where an effort in the coordination of the actors, activ-
ities and resources is required in order to meet the re-
quirements of thecustomers [02], in this sense [03] affi rm
that in order to improve the customer satisfaction and
reduce the cost, the cooperative relationship between
the companies must be built, especially in perishables
supply chain. However, due to the conditions in which
these chains operate, different problems come into view.
Among the most important issueslie demand forecast-
ing, inventory management and transport [04]. There
are other factors such as margins of intermediation, in-
frastructure and geographical conditions that can have
serious repercussions in terms of post-harvest losses,
which affect the economy of the members of the chain.
Literature related to the performance of fruit supply
chains confi rms that inventory management is a topic
of increasing interest because of the restriction that the
perishable condition of the product implies. Considering
this constraint, it is important to determine the inventory’s
frequency of revision so that the product’s deterioration
cycle is lower than the revision cycle, with the purpose
of avoiding product losses caused by an inadequate in-
ventory policy. This policy must also consider the opti-
mal quantity of orders and the time products should be
ordered to prevent costs due to “understock” or “over-
stocking” [05, 06, 07]. In this sense [08] developed a mul-
ti-echelon inventory model for a deteriorating item from
an integrated perspective and determine the optimal de-
livery quantities for each echelon. On the other hand, au-
thors such as [09] have shown the benefi ts of integration
in the supply chain thanks to the sharing of information,
which enables coordinated decisionmaking therein.
In this regard, [10] defi ne four supply chain archetypes
described as the traditional supply chain, shared-infor-
mation supply chain, supplier supply chain (managed by
the supplier) and synchronized supply. The latter repre-
sents a scenario where information is transmitted in real
time among the members of the chain, such as their lev-
els of inventory, product in transit and sales, achieving
the best management amongst the archetypes present-
ed. In this case, the structure of the chain is centralized
and its performance signifi cantly improved thanks to in-
formation sharing. Nevertheless, not all chains are cen-
tralized, so it is necessary to create collaboration mech-
anisms in decentralized chains to achieve some level of
integration. Authors such [11] have defi ned integration as
a necessary strategy for getting into new markets. In this
respect[12]validate the importance of information in de-
cisionmaking in the chain by putting forward a classifi ca
523
* Cl. 13 #100-00, Cali, Valle del Cauca, Colombia, cristhian.acosta@correounivalle.edu.co
Journal of Applied Engineering Science Vol. 16, No. 4, 2018
ISSN 1451-4117
tion of integration mechanisms in decentralized chains
where they include information technologies, shared in-
formation, joint decision making and contract models.
This paper aims to approach the management of inven-
tories in the framework of an agricultural supply chain
through a mathematical model that considers the dete-
rioration of the product over time and demonstrates the
advantages of integrating of its echelons. The character-
istics of the chain under study are presented, then the
mathematical model used to determine the inventory
policy is described, subsequently the results are laid out
and a sensitivity analysis is carried out by varying some
parameters. Finally,conclusions, recommendations and
opportunities for new studies are developed.
PROBLEM STATEMENT
As described above, the study of agricultural supply
chains is of great interest mainly due to coordination
problems in the chain that affect, among other aspects,
the fi nancial results that refl ect in the form of low income-
for the case of small farmers. There are some determin-
ing factors for the appropriate performance of the chain
set forth by [13], such as the variability of demand and
prices; the availability of workers; the yield of the crop;
labor costs and those associated with the recollection
of products; the use of means of transportation that bal-
ance out the time it takes to reach the market and the
cost; post-harvest management of crops; the degree
of maturity of the product; the maximum time for deliv-
ery; the availability of products; transportation time and
delivery costs. Other authors such as [14], assure that
the handling of perishable products and their life cycle
are the most differentiating factors of this type of chain.
On the other hand, authors how [15], present fruits and
vegetables as products that have features of freshness,
perishability [16], timeliness, logistics performance [17].
This makes agrifood supply chains constantly-varying
complex systems that involve several echelons such as
suppliers, distributors, marketers, wholesalers and retail-
ers, among others, which makes it behave as a multi-
disciplinary system that attempts to satisfy the demands
of the fi nal customer through effective coordination of
information fl ows, products and fi nancial resources [18].
A problem of great interest, identifi ed in the literature re-
lated to the performance of agricultural supply chains,
especially fruit chains, is the management of invento-
ries along the chain, due to the restriction involved in
the product’s lifecycle. Due to the aforementioned rea-
sons, inventory management becomes a critical issue
when dealing with perishable products such as fruits,
which require compliance with strict quality requisites.
These demands cannot be satisfi ed only with the desire
of small producers to do it, it is also necessary to syn-
chronize from suppliers’ supply times, to producers and
intermediaries, and from intermediaries to retailers, in or-
der to achieve an adequate estimation of amounts, con-
sumption times in each echelon and eventually the best
performance in the chain. The model presented below
seeks to represent the behavior of these relationships in
a decentralized fruit supply chain, assuming a scenario
where information is shared for decision making regard-
ing the inventory along the chain.
MATERIALS AND METHODS
Development of mathematical model
a. Interaction between supply chain echelons
under study
The chain under study consists of three echelons, name-
ly: a single supplier, a producer and a retailer, as shown
in Figure 1. The supplier is responsible for starting the
fl ow of the product to the other echelons, below. The
next member of the chain is the producer, who has a
warehouse for raw materials and another warehouse to
store the fi nished product. Finally, facing the consumer is
the retail echelon, in charge of directly satisfying his de-
mand; the former is also the one that initiates the fl ow of
information, sharing the expected demand with the other
actors in the supply chain. The interaction in the supply
chain begins at the time the retailer makes an order that
attempts to satisfy the demand during a planning period
T. This information about the demand is shared with the
other echelons and sent to the next supply chain actor
(the producer) through an order. The latter must satis-
fy this order by means of deliveries, at fi xed intervals of
time, placed in retailer warehouse. Upon receipt of the
order, the producer initiates a value-adding process on
the raw material in order to generate the fi nishedproduct
Figure 1: Supply Chain Inventory Management for each echelon
Cristhian Guillermo Acosta Imbachi et al. - Design of an inventory management system in an agricultural supply chain considering
the deterioration of the product: the case of small citrus producers in a developing country
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for the agrifood supply chain under study.
As shown in Figure 1, there is an inversely proportion-
al relationship between the inventories held by the pro-
ducer, since the raw material inventory is reduced over
time when the value-adding process starts, while that of
fi nished product increases. Since the production rate is
higher than the demand’s, the producer accumulates the
inventory of fi nished product for deliveries carried out in
a period after the time of production. In this case, it is as-
sumed that the accumulated inventory is enough to meet
the number of remaining deliveries taking into consid-
eration the amount of product that suffers deterioration.
To start off his productive process, the producer requires
raw material, which is provided by the supplier. This ech-
elon must perform the supplying of inputs from an exter-
nal supplier (not considered in this case study), with the
objective of maintaining good quality raw material for the
producer. The supplier is responsible for providing the
raw material required by the producer for itsprocessing.
This is achieved by delivering equal quantities at fi xed
time intervals.
b. Assumptions
• Mathematical inventory model for a single perisha-
ble product in an integrated supply chain.
• The aim is to determine the optimal number of deliv-
eries and lot sizes that minimize the total cost of the
supply chain.
• Demand and constant production over time.
• The demand rate is lower than the production rate.
• The planning period is known.
• The Lead Time is zero, shortage is not allowed.
• One item is only considered.
• The parameters that represents the deterioration
rates are constant and deterministic.
• An order is satisfi ed through multiple deliveries.
• The supplier delivers the same amount of raw mate-
rial to the producer.
c. Variables and parameters
SYMBOL DESCRIPTION
T Planning time
T1Production time used by the producer T1= npt+t3
T2Cycle time used by the provider T2=(np+1)t
N Number of deliveries received by the retailer from the producer for each planning time T
npNumber of deliveries received by the retailer from the producer during T1
t3Production time from the point np to the end of production
qBLot-size per delivery from the producer to retailer of fi nished goods
QBTotal order quantity of fi nished goods for retailer per planning time T.
qpFinished goods quantity produced in time t.
qPW Quantity of raw material per delivery received in the producer’s warehouse from the supplier.
qnPW Quantity of raw material delivery received in the producer’s warehouse from supplier in last delivery.
QSSupplier’s total order quantity of raw materials for period T2
QPW Quantity of raw material harvested by the supplier per delivery
QnPW Quantity of raw material harvested by the supplier in last delivery
ApTotal fi nished goods inventory for producer in T.
IB(t) Retailer’s fi nished goods inventory level at time t.
IPI(t) Producer’s fi nished goods inventory level at time t.
IPW(t) Producer’s warehouse raw materials inventory level at time t.
IS(t) Supplier’s Raw materials inventory level at time t.
TCBRetailer total cost.
TCPProducer’s total cost.
TCPW Producer’s warehouse total cost.
TCSSupplier’s Total cost.
TC Global total cost(TCS + TCPW + TCP + TCB)
D Retailer’s demand rate for fi nished goods.
A Finished goods’ ordering cost for retailer per order.
Table 1: Notation used in the Mathematical Model
Cristhian Guillermo Acosta Imbachi et al. - Design of an inventory management system in an agricultural supply chain consider-
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FBFinished goods’ receiving cost for retailer perreception.
HBFinished goods’ unitary holding cost per unit of time for retailer.
PBDeterioration cost per unit of fi nished goods for retailer.
QBDeterioration rate for retailer’s fi nished goods
P Producer’s production rate for fi nished goods.
SPProducer’s setup cost for each setup.
FPFinished goods’ delivery cost for producer per deliver.
HPFinished goods’ unitary holding cost per unit of time for producer
PPDeterioration cost per unit of fi nished goods for the producer.
QPDeterioration rateof fi nished goods for the producer.
FPW Raw materials’ receiving cost per reception for the producer at warehouse.
HPW Raw materials’ unitary holding cost per unit of time for producer’s warehouse
PpW Deterioration cost per unit of fi nished goods for producer’s warehouse.
QPW Deterioration rate for producer’s raw materials
S Raw materials’ ordering cost per order for the supplier.
FSRaw materials ‘ delivery cost for the supplier per delivery.
HSRaw materials’ unitary holding cost per unit of time for the supplier.
PSDeterioration cost per unit of raw materials for the retailer.
QSDeterioration rate for supplier’s raw materials
Note. Source: Adapted from [8].
d. Retailer: Finished product inventory model
According to [19], the inventory level of fi nished goods at
time t’ can be expressed as follows:
(1)
Solving (1) in its extreme points by the integrating factor
method:
And by multiplying on both sides of the equation (1) by
, then:
,
(2)
The right part of equation (2) can be expressed as the
derivative of a product as follows:
The result obtained by integrating both sides of the equa-
tion and solving the respective integrals can be written
as:
(3)
Multiplying on both sides of (3) by and simplifying:
Applying the boundary condition IB(t) in (4) to obtain the
(4)
integration constant’s value, results in:
Using the constant’s value in the expression (4) and sim-
plifying:
Therefore, by setting the boundary condition IB(0) in (5) it
(5)
Cristhian Guillermo Acosta Imbachi et al. - Design of an inventory management system in an agricultural supply chain considering
the deterioration of the product: the case of small citrus producers in a developing country
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ISSN 1451-4117
is possible to obtain the initial order quantity. In this way,
IB (0)=qB and the resulting expression is:
To obtain the expression forinventory amount of standby
(6)
fi nished products, the equation (6) must be integrated
between 0 and t, as follows:
The total cost of offered goods can be expressed as the
(7)
sum of the cost of the order, the cost of reception, the
cost of maintenance and the cost of deterioration. There-
fore, the total cost of the goods offered to the retailer
during a planning period T, can be expressed as:
Using the following approach:
(8)
Proposed by [8] and substituting in the retailer total cost
equation, the following is obtained:
e. Producer’s warehouse: Raw material inventory
(9)
level
The raw material inventory level of the producer’s ware-
house at time t’can be expressed as follows:
At the extreme points of equation (9), the inventory will
(10)
be expressed by the following equations:
Integrating the expressions (11) and (12) from 0 to t and
(11)
(12)
from 0 to t3 respectively, in the same way as shown in the
retailer’s model, the inventory quantities of standby raw
material at time t and t’are obtained as:
Cristhian Guillermo Acosta Imbachi et al. - Design of an inventory management system in an agricultural supply chain consider-
ing the deterioration of the product: the case of small citrus producers in a developing country
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ISSN 1451-4117
(13)
(14)
Therefore, according to [8], the producer’s total cost for
raw material warehousing per cycle T could be repre-
sented as the sum of the maintenance cost, the receiving
cost and deterioration cost, as follows:
(15)
f. Inventory level of fi nished products by the
producer
When the retailer orders a quantity of fi nished product
from the producer in period T, the producer begins the
production and delivery at time t.
In the fi rst period, the producer achieves a production
of fi nished product equal to in period t. The producer’s
inventory level of fi nished product in the fi rst period can
be represented as follows:
(16)
Solving equation (16), analogous to the differential equa-
tion that represents retailer’s model bearing the integrat-
ing factor method, the inventory level for the extreme
points will be:
(17)
Thus, the inventory level of fi nished products for the nth
delivery after the fi rst one is obtained, according to [8]
with the following differential equation:
(18)
The inventory of fi nished product before the i-delivery is .
Solving the equation (18) by as initial condition,it is pos-
sible to determine the inventory level for the i-th delivery,
like this:
(19)
According to [8], from the previous expression (19) the
lot size from the non-production period can be deter-
mined as:
(20)
In accordance with the model of [8], as soon as the
producer reaches the amount of fi nished product that
the retailer needs per order cycle time T, production is
stopped. The production time is defi ned in (npt+t3). How-
ever, the producer continues to deliver a constant quan-
tity of merchandise, until the entire amount of production
of fi nished products has been delivered to the retailer.
This occurs at time T; when the level the producer’sin-
ventory of fi nished product is equal to zero.
In [19] argue that the fi nal inventory after time t consider-
ing a constant rate of deterioration, can be expressed as:
At time (npt+t3), producer stops production. The inventory
(21)
amount of fi nished goods is Qnon/product ;after time (t-t3) ,
the inventory becomes Qnp1 and in compliance with the
expression of[19], the outcome will be as follows:
The fi nal quantity of inventory of fi nished products for
(22)
time (np+1) can be derived as:
The inventory amount of fi nished product from the pro-
Cristhian Guillermo Acosta Imbachi et al. - Design of an inventory management system in an agricultural supply chain considering
the deterioration of the product: the case of small citrus producers in a developing country
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Journal of Applied Engineering Science Vol. 16, No. 4, 2018
ISSN 1451-4117
ducer for the nth time is equal to the lot size per delivery.
From (23), the lot size of fi nished products can be ob-
tained during the non-production period at t=t3 as:
With Qnon/product(1) and Qnon/product(2) , the values of np y t3
(24)
can be determined. To fi nd the corresponding values
for np, the algorithm proposed by[8] needs be followed,
which consists on assuming Qnon/product(1), Qnon/product(2).
Thus, the equation is equal to zero and t’ is replaced
by t. Subsequently, for each value of n, every np val-
ue is obtainedalong with the parameters needed for the
equation’s solution such as the production rate of the
producer, the rate of deterioration and the lot size of fi n-
ished products per delivery from the producer to the re-
tailer.
To estimate t3, a similar procedure is performed, where
t’ is replaced by t’. Then, Qnon/product(1) and Qnon/product(2 are
equated. In this way, it is possible to fi nd every for its
corresponding value.In [8] an algorithm it is presentedto
fi nd the value of time and , however, in this document
we propose an alternative procedure to determine the
value of by matching the expressions and which cor-
respond to the quantity of inventory at the end of the pro-
duction period and the quantity of inventory at beginning
the period of depletion once production has stopped,
respectively. The resulting equation is expressed as a
function F [t3] throughwhich we obtain the value of that
makes the function equal to zero, this point is defi ned
as the point of intersection with the X axis, which corre-
sponds to value for a number of n defi ned deliveries.
ThroughWolfram Mathematica, this analysis is validat-
ed by making the graph of the mathematical expression,
the value obtained with this method is observed to cor-
respond to the value obtained algebraically. In fi gure 2an
arbitrary interval of (-0.003; 0.003) is obtained for the pa-
rameters associated with a number of deliveries n = 100,
a value of t3 = 0.0145134 corresponding to the point of
intersection with the X axis.
Figure 2: Graphic method for t3 calculation
Note. Source: Author’ own elaboration
The deterioration of the fi nished products’ quality dur-
ing cycle T is the sum of deteriorated fi nished products
quantity from period 1 to n and is written as follows:
(25)
The deterioration cost and the maintenance cost of the
fi nished products per order cycle time T can be obtained
in the following way:
(
(
(
(
(
(
(2
(
(
(
(
4
)
(26)
Producer’s total fi nished goods cost for planning period
T could be represented as the sum of the setup cost, the
delivering cost, the cost of maintenance and the deterio-
ration cost, as follows:
(27)
Cristhian Guillermo Acosta Imbachi et al. - Design of an inventory management system in an agricultural supply chain consider-
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g. Supplier Inventory Model
Considering that the supplier’s opening inventory is des-
ignated as, [19] denote the amount of raw materials per
delivery from the supplier to the producers’ warehouse,
as well as the last quantity provided by the supplier, as
follows:
Should (28) y (29)de integrated from 0 tot, the fi nal in-
ventory of raw materials can be obtained, as:
(28)
(29)
(30)
The same applies for:
In this manner, the quantity of the supplier’s order for
raw material thatsatisfi es the demand of the producers’
warehouse from time 0 to t is also defi ned as:
(31)
Eventually, supplier’s total cost according to [19], could
be represented as the sum of the maintenance cost, set-
up cost, delivery cost and deterioration cost:
(32)
(33)
Finally, the global cost of the integrated inventory model
could be represented as the sum of the supplier, produc-
er and retailer’s individual costs, as follows:
(34)
As presented in equation (34), the Total Cost is the ob-
jective function that must be minimized and it is obtained
through the sum of costs assumed per each echelon in
the supply chain. In order to fi nd the minimum Total Cost,
a number of iterations must be executed, varying the
number of deliveries n. In each iteration the order quan-
tity and total quantities between echelons are derived.
Then, the values of the Total Cost from the different iter-
ations are analyzed and the number of deliveries n that
minimizes the objective function TC is defi ned.
Cristhian Guillermo Acosta Imbachi et al. - Design of an inventory management system in an agricultural supply chain considering
the deterioration of the product: the case of small citrus producers in a developing country
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Table 2: Parameters used in the execution of the model
TABLE OF PARAMETERS USED IN THE EXECUTION OF THE MODEL
BUYER - RETAILER
Parameter Computing Method Value Units
D Time forecast series for constant demand 3.718 [Unit/month]
A Cellphone plan, paperwork order 0,4 [ US$/Order]
FB Cost of loading and unloading per worker per truck 10,8 [US$/Reception]
HB Warehouse leasing cost, area occupied by citrus fruits, inventory
turnover
0,4 [US$/Unit-Month]
PB It is calculated as a 35% from original sales price. 0,7 [US$/Unit-Month]
THB Percentage of lemons damaged by deterioration 0,08
PRODUCER – INTERMEDIARY
P Ability to select good quality lemons and pack them in 1kg nets, with
an available time of 480 minutes per working day, during 28 days a
month
6.240 [Nets of 1kg/
month]
SP Using production capacity, the number of wages required to satisfy
the demand during the planning horizon (1 month) is reckoned and
then multiplied by the value of each one(US$ 9,03/day)
167,7 [US$/order prepa-
ration]
FP Value of retailer transportation cost plus the cost of loading 61,4 [US$/delivery ]
HP The leasing cost between the area of fi nished goods and raw mate-
rial warehouse is prorated. In each part of the warehouse, 1/10 of
production capacity can be stored.
0,1 [US$/Kg*month]
Pp In this case, up to 70% of the original price can be sold. It means
that 30% of the original price fails to be received.
0,3 [US$/Kg]
ThP Percentage of lemons damaged by deterioration 0,01 -
Fpw Cost of loading and unloading a truck per worker 10,9 [US$/reception]
Hpw The leasing cost between the area of fi nished goods and raw mate-
rial warehouse is prorated. In each part of the warehouse, 1/10 of
production capacity can be stored.
0,1 [US$/Kg* month]
Ppw What it is not being perceived if it is sold without packing but con-
sidering CABAZA price market. Bulk sale price: US$54,2; Cost:
US$43,4; Bulk profi t: US$10,8; Deteriorating cost / kg: US$10,8 /
60Kg
0,2 [US$/kg]
Thpw Percentage of lemons damaged by deterioration 0,10 -
SUPPLIER – FARMER
Hs Calculation of monthly maintenance costs of one hectare; estimated
production per tree a month
0,2 [US$/Kg*month]
Ps Probability that a tree does not develop correctly multiplied by the
cost of the tree
0,05 [US$/Unit]
S The survey provides the estimated annual cost of reception, given
that S is for the planning horizon, it is divided into 12
90,3 [US$/order]
Fs Cost of pickup and freight is US$ 72,23 for transportation from the
supplier to the producer or broker’s warehouse
14,8 [US$/delivery
(harvest)]
ThS Percentage of lemons damaged by deterioration 0,15 -
Note.Source: Author’ own elaboration.
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Table 3: Quantities delivered by the echelons and percentage of deteriorated product along the supply
chain for different delivery frequencies
nn
pqBQBqPqPW QPW qnPW QnPW QSPercentage of
Deterioration
1 - 3.871 3.871 5.938 6.563 7.721 4.286 5.042 5.042 36%
2 1 1.897 3.793 3.043 3.199 3.470 851 923 4.393 18%
3 1 1.256 3.768 2.046 2.115 2.233 1.854 1.958 4.190 13%
4 2 939 3.755 1.541 1.580 1.645 764 795 4.086 10%
5 3 750 3.748 1.236 1.261 1.302 118 122 4.028 8%
6 3 624 3.743 1.031 1.049 1.078 735 755 3.987 7%
7 4 534 3.739 885 898 919 277 284 3.959 6%
8 4 467 3.737 775 785 801 720 735 3.939 6%
9 5 415 3.735 690 697 710 366 373 3.922 5%
10 6 373 3.733 621 627 637 84 85 3.910 5%
15 9 249 3.728 415 417 422 73 73 3.871 4%
20 12 186 3.725 311 313 315 67 68 3.852 4%
25 15 149 3.724 249 250 252 64 64 3.840 3%
30 18 124 3.723 208 208 209 61 62 3.832 3%
35 21 106 3.722 178 179 179 60 60 3.827 3%
40 24 93 3.722 156 156 157 59 59 3.823 3%
45 27 83 3.721 139 139 139 58 58 3.820 3%
50 30 74 3.721 125 125 125 57 57 3.817 3%
55 33 68 3.721 113 114 114 56 56 3.815 3%
60 36 62 3.720 104 104 104 56 56 3.813 3%
65 39 57 3.720 96 96 96 55 56 3.812 3%
70 42 53 3.720 89 89 89 55 55 3.811 2%
75 45 50 3.720 83 83 83 55 55 3.809 2%
80 48 47 3.720 78 78 78 54 55 3.808 2%
85 51 44 3.720 73 73 74 54 54 3.808 2%
90 54 41 3.720 69 69 70 54 54 3.807 2%
100 60 37 3.719 62 62 63 54 54 3.806 2%
RESULTS AND DISCUSSION
a) Delivery amounts among echelons
The mathematical model proposed in this work was
solved through Matlab using the parameters defi ned in
table 2. The results obtained in Matlab were exported to
Microsoft Excel in order to display them in a clearer and
more practical way.
As a summary, table 3 shows the delivery quantities that
each echelon is supposed to
carry along the chain. It can be clearly seen that increas-
ing delivery quantities, lowers the amount of product that
deteriorates along the chain.
By increasing the frequency of delivery in the planning
time T, there will be a smaller time interval between de-
liveries. Therefore, the deterioration rate has low conse-
quences for the short time that the product lingers before
reaching the consumer.
b) Optimal independent costs and integrated supply
chain optimal cost
In Table 4 it is possible to determine the lowest overall
cost or optimum total cost of the citrus supply chain un-
der study.It is also possible to establish what the optimal
cost for each independent echelon is and the delivery
conditions for each specifi c situation. The lowest total
cost for the chain is US$ 1.210 a month. This is achieved
when the number of deliveries in the planning period
(one month) is equal to 5.
Analyzing the optimal independent costs, the supplier
must make 8 deliveries during time T, in this case the
total cost of the chain becomes 8% more expensive than
Note.Source: Author’ own elaboration.
Cristhian Guillermo Acosta Imbachi et al. - Design of an inventory management system in an agricultural supply chain considering
the deterioration of the product: the case of small citrus producers in a developing country
532
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n n_p TC_B TC_PT TC_S TC OptimalEchelon
1 - 833 709 1007 2549
2 1 428 603 529 1560
3 1 302 602 383 1288 Producer
4 2 245 637 329 1211
5 3 215 691 303 1210 Integrated SC
6 3 199 738 276 1213
7 4 191 800 272 1264
8 4 187 855 258 1301 Supplier
9 5 187 921 262 1370 Retailer
10 6 189 989 269 1447
15 9 216 1315 288 1819
25 15 303 1983 356 2642
30 18 352 2319 395 3067
35 21 403 2657 436 3496
40 24 454 2995 477 3927
45 27 506 3333 520 4359
50 30 558 3672 563 4793
55 33 611 4011 605 5227
60 36 664 4350 648 5662
65 39 717 4689 692 6098
70 42 770 5029 735 6534
75 45 824 5367 779 6970
80 48 877 5707 822 7406
85 51 931 6046 867 7844
90 54 985 6385 910 8280
100 60 1092 7065 997 9154
the lowest total cost for the global solution in the supply
chain.
From the producer’s perspective, only three deliveries
should be made, generating a greater total cost along the
chain compared with the global optimum. In this scenario
Note. Source: Author’s own elaboration
the total cost of the chain is 6% more expensive than the
integrated supply chain. The reason why the number of
optimal deliveries for the producer is so low is due to cost
of delivering, since the product must be transported to
the customer's warehouse (retailer), located in a city 90
km away. The cost of making each delivery is US$ 61.4.
That is why it is more benefi cial for the producer to store
raw materials and fi nished products and assume mainte-
nance and deterioration costs. The aforementioned im-
pacts on the increase of the other echelons’ costs. Final-
ly, from the retailer's approach, deliveries must be made
every 3 days.In other words, to achieve the optimum cost
of the retail echelon, 9 deliveries must be made in the
planning period of one month; in this case, the total cost
of the chain would be 13% greater than the solution ob-
tained through the mathematical model.
According with results shown in table 4 it is possible ob-
tain the value for n that minimize the total cost on the
studied supply chain. Results are presented in Figure 3
as a graphic that shows different values for n, as well as
the n where the minimum TC is obtained.
Figure 3: Graphical representation TC function and the
optimal value obtained.
Cristhian Guillermo Acosta Imbachi et al. - Design of an inventory management system in an agricultural supply chain considering
the deterioration of the product: the case of small citrus producers in a developing country
533
Table 4: Local and global costs for several delivery frequencies
Journal of Applied Engineering Science Vol. 16, No. 4, 2018
ISSN 1451-4117
c) Inventory control policy for echelons in the lemon
supply chain
Taking into account the results presented above and
considering the defi ned planning horizon (one month),
it is possible to formulate the inventory control policy for
each echelon belonging to the supply chain, thus re-
sponding to the three fundamental questions: Frequen-
cy of revision, moment of ordering and quantity to order.
According to [20]in the case of perishable goods, since
they have a limited lifetime, in order to be able to comply-
ing with the shelf life time, the length time in the supply
chain should not exceed the lifetime value, as each unit
of time that is exceeded in the supply chain represent
deterioration in the products condition. In this sense the
inventory level revisionshould be defi ned as continuous
in each echelon.
Retailer Inventory Management Policy: Review the in-
ventory level continuously; order an amount equal to 750
units of 1 kg of selected lemon when the inventory level
in the warehouse reaches zero.
Producer Inventory Management Policy: Check the in-
ventory level continuously; order an amount equal to
1261 kilograms of virgin lemon, when the inventory of
raw material in the warehouse reaches zero.
Supplier inventory management policy:Review the in-
ventory level continuously; when the level of inventory
of virgin lemon in the warehouse reaches zero, the sup-
plier must harvest an amount equal to 1302 kilograms of
virgin lemon during the fi rst 3 deliveries. Nonetheless, in
the last delivery only 122 kilograms of virgin lemon need
be sent to the producer.
Costing of the current supply chain
In order to determine the costs of the current citrus sup-
ply chain, the deliveries made in a planning period are
defi ned with the information provided by the echelons
through the surveys carried out. Delivery schedule can
be seen in table 5excluding Sundays; 14 deliveries are
made per month. This will be the input used to determine
the cost of the current chain.
When the current number of deliveries is reckoned, the
cost per each component of the relevant total cost can be
computed with the purpose of costing the supply chain
in its current conditions, as presented in table 6. Sub-
sequently, the comparison with the results of the costs
obtained through the proposed model is shown.
Table 5: Current Delivery Schedule: One-month planning period
CURRENT DELIVERY SCHEDULE
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
Monday Tuesday Wednesday
Note. Source: Author’s own elaboration
Once the optimal cost of the inventory control system has
been attained through the model formulated, and after
defi ning each of the operational costs related to the man-
agement of inventory in the supply chain in its current
conditions. It is possible to make a comparison between
both scenarios; in the fi rst scenario (model implemented)
total cost is the objective function minimizedand it is the
sum of costs assumed per each echelon in the supply
chain. Take in account that to fi nd the minimum Total
Cost, a number of iterations must be executed, varying
the number of deliveries n. Then, the values of the To-
tal Cost from the different iterations are analyzed and
the number of deliveries n that minimizes the objective
function TC is defi ned. A summary for the current situa-
tion and the proposed situation results are presented in
table 7. The total monthly cost related to inventory man-
agement in the current supply chain is US$1.862, while
in the proposed model the optimal cost is US$1.210 a
month. A 35% reduction is achieved with the specifi ca-
tions of policies, asproposed by the mathematical model
developed herein.
It is important to highlight the realization that comes to
light with this model regarding the dominance held by the
retailer over the other actors. Currently, the frequency
of deliveries is defi ned by him and the other echelons
must adapt to his orders without issuing any judgment.
From the retailer's point of view, the model suggests to
increase the frequency of receptions up to reaching nine
deliveries a month, the highest frequency suggested in
the optimal local analysis. The high frequency suggested
for the retailer by the model, validates the chain's current
operation, where a large number of deliveries is required
by the retailer.
Effect of variations in deteriorating rate on optimal
result
In order to understand deterioration rate impact in the
Supply chain, a sensitivity analysis is shown in Table 8.
Just one of the rates is modifi ed at the same time remain
the rest constant. Original rate value for each MAX sce-
nario is increased arbitrarily by 75% and each rate for
each MIN scenario is reduced by the same percentage.
Cristhian Guillermo Acosta Imbachi et al. - Design of an inventory management system in an agricultural supply chain considering
the deterioration of the product: the case of small citrus producers in a developing country
534
Journal of Applied Engineering Science Vol. 16, No. 4, 2018
ISSN 1451-4117
RETAILER
Cost of Reception 152 US$/month
Ordering cost 0,4 US $/month
Maintenance cost 34 US $/month
Buyer Monthly Cost 186,4
PRODUCER
Deliveries 860 US$/month
Preparation 168 US$/preparation of order per month
Maintenance Cost 36 US$/month
Producer Monthly Cost 1064
PRODUCER WAREHOUSE
Reception of Raw Material 152 US$/month
Raw Material Maintenance Cost 36 US$/month
Product Warehousing Monthly Cost 188
SUPPLIER
Delivery 15 US$/month
Maintenance 319 US$/month
Reception of Supplies 90 US$/month
Supplier Monthly Cost 424
Table 6: Costs of the current agricultural supply chain
Note.Source: Author’s own elaboration
Table 7: Comparison of the current cost and the optimal cost obtained through the model
Total monthly cost of the current chain US$ 1862
Total monthly cost of the proposed chain US$ 1210
Improvement 35%
Note.Source: Author’s own elaboration
In general, despite huge deterioration rate variation, the
total cost and local costs of each echelon do not vary
more than 3%. In addition,deterioration rate has a great-
er impact on the producer echelon, while in the oppo-
site extreme, the less impact is in the supplier, reaching
around 0.5% of variation in the total cost.
COST ThS=0,15 ThPW=0,1 ThP=0,1 ThB=0,08 ORIGINAL
SCENARIO
MAX MIN MAX MIN MAX MIN MAX MIN
0,2625 0,0375
TCS187 187 187 187 187 187 196 178 187
TCp602 602 611 591 640 560 604 601 602
TCb262 255 259 258 263 257 259 258 258
TC 1216 1203 1216 1203 1241 1175 1226 1189 1210
Table 8: Comparison of the current cost and the optimal cost obtained through the model
Note.Source: Author’s own elaboration
Cristhian Guillermo Acosta Imbachi et al. - Design of an inventory management system in an agricultural supply chain considering
the deterioration of the product: the case of small citrus producers in a developing country
535
Journal of Applied Engineering Science Vol. 16, No. 4, 2018
ISSN 1451-4117
In general, despite huge deterioration rate variation, the
total cost and local costs of each echelon do not vary
more than 3%. In addition,deterioration rate has a great-
er impact on the producer echelon, while in the oppo-
site extreme, the less impact is in the supplier, reaching
around 0.5% of variation in the total cost.
Model limitations
In order to adjust the proposed model to the more real
situation it would be interested to consider agricultural
producer cultivate different product. In that sense this
model has some limitations because does not consider
several fruits but just lemon as a single product in supply
chain. In addition, the capacity of the lemon truck trans-
porting is not included in the analysis. Finally model only
takes in account one single member per echelon when in
this kind of supply chain frequently has a several players
in each of them.
CONCLUSIONS AND OPPORTUNITIES FOR FUTURE
RESEARCH
Effi ciently managing a supply chain involves its overall
optimization. Since supply chains operate under different
conditions due to their nature, it is necessary to imple-
ment an adequate inventory control system bearingthe
integration of each of its echelons as its fundamental
principle in order to maximize the total value generated
by it. An integrated supply chain should seek real-time
information sharing by its members with the aim of gen-
erating such synergy, so that the highest possible perfor-
mance is achieved.
The pertinence of the three-level supply chain proposed
in this work, namely stated as supplier, producer and
retailer, was validated. Data on the costs related to the
management of inventories in each echelon were ob-
tained, which became an important input for the pro-
posed study.
Finally, it is evident that there are large price fl uctuations
of citrus and high-rising supply costs in the chain under
study. In times of oversupply, when the prices fall sig-
nifi cantly, the need to minimize logistics costs along the
chain is met through an integrating model approach.
This research has shown that an optimal supply chain
works perfectly from an integration approach and not
from a particular point of view. The mathematical model
used allowed to defi ne the optimal quantity for orders,
the moment of ordering and the frequency with which the
inventory of the citrus chain under study in the rural area
of Tulua- Andalucia, Valle del Cauca, Colombia, must be
revised.
The integration of the supply chain through the exchange
of information, as posed by the synchronized supply
chain archetype where information on demand and the
inventory level is shared, enables the adequate func-
tioning of the chain's overall performance, allowing the
producer to fi thisyield to the information provided by the
next echelon in the supply chain, thus reducing logistics
costs.
With the goal of validating and proving the mathemati-
cal model with the data collected from the supply chain
under study, and determining ordering optimal quantity
and time, and inventory review frequency, the total cur-
rent chain cost per month was determined (taking into
account that one hectare is suffi cient to satisfy the de-
mand along the supply chain under study), as the sum of
the cost incurred by each echelon from an individualis-
tic approach. To that end, the current delivery schedule,
the reception, delivery, maintenance, loading, unloading
and the ordering cost were taken into consideration. The
current total cost was compared with the optimal cost
obtained through the mathematical model and under an
integration approach, wherein the total cost of inventory
management in the citrus chain under study was found
to have reduced around 35%.
This paper can be the basis for future research consider-
ing some additional conditions in which the citrus supply
chain currently operates. It is relevant to study this model
bearing in mind a bigger supplier basis and bigger num-
ber of retailers. Furthermore, this model does not con-
sider the transport lemon truck capacity and therefore
it is highly recommended to raise this restriction for the
model to resemble reality even more. It is also proposed
to study the rate of deterioration by analyzing the prob-
lem from the chemical and biological standpoints of the
product in different scenarios in order to determine this
percentage more accurately and obtain more reliable re-
sults through this mathematical model.
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the deterioration of the product: the case of small citrus producers in a developing country
537
Paper submitted: 03.06.2018.
Paper accepted: 27.10.2018.
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