1. INTRODUCTION
Most disasters especially natural
disasters cannot be predicted with accuracy beforehand, so it is hard to
forecast the demand of post disaster supply, which is very essential for the
recovery of the affected disaster areas. Uncertainties of the disasters themselves
such as location, timing, degree of severity, and lack of financial and
personal resources make it very difficult to match the demands caused by the
disaster to the supply needed in a timely manner for disaster relief
activities. That is, for the disaster relief supply chain, purchase planning
cannot be made before the disaster happens, but must be fulfilled immediately
after it happens. This is due to transportation difficulties and the absence of
resources to supply disaster victims with needed medical and survival needs.
Storage of enough resources in
strategic locations before a disaster with the use of transshipment can help to
get supplies delivered to the right place after disaster. Humanitarian supplies
such as food, clothing, personnel and medicine delivered to the affected areas
after a disaster require a massive coordination effort. Disaster supply chain
efforts are hampered by coordination difficulties, which may lead to resource
scarcity or oversupply. Organizing relief inventories around the world with the
right amount of supplies to the right place at the right time is important for
the survival of victims of disaster. Many successful inventory models for
commercial supply chains exist, but commercial supply chains are designed to reduce
costs and raise customer-service levels, the supply chain for disaster relief
requires a different model.
In this paper, we will focus on the
inventory policies for both pre-disaster and post-disaster relief supply
management. We will assume that the lead time of purchase is longer than
transshipment from local warehouses, native warehouses and even global
warehouses. Transshipment will be employed to determine how and where to store
before a disaster and how and where to transship after a disaster. In the next
section, we will review current literature based on the actions taken before
and after disasters. In section 3, we will give a theoretic framework of the
current relief supply decision system. We will discuss the sub system of the
relief supply chain called the emergency transshipment system in section 4. We
will simulate the emergency supply chain with analysis in section 5. Conclusions and recommendations for future
research will follow in section 6.
2. LITERATURE REVIEW
2.1.
Humanitarian relief chain
An emergency relief chain may
include many flows, many actors. We will use Yang, et al. (2011) method to
describe the current different emergency relief chains. They described eleven
scenarios of commercial supply chains, such as electronic point of sales,
vendor managed inventory, e-shopping, emergency transshipments, and so on in
flow charts. Simulation was used based on Taguchi’s methodology and multiple
criteria decision-making methods to show that due to information sharing
strategies, e-shopping has the most robust performance in uncertain business
environments. In this paper, we will extend their work and discuss current
literature on emergency supply chains. Pre-production emergency supply,
post-production emergency supply, and post-transshipment emergency supply will
be examined. The main information flows and material flows of each pattern are
given in Figure.1.
There are many actors in an
emergency supply chain, such as international relief organizations, local
relief organizations, local governments, donors, private sector companies and
militaries. They were regarded as distributers or warehouses in Figure 1.
Considering the uncertainties of changing demand, delivery lead time and
transportation time, emergency relief chains are different from commercial
supply chains. Government response can play an important role in the emergency
relief chain, especially in the pre-disaster planning phase. Oloruntobsa (2010)
proved this after analysis of the emergency relief chain for a 2005 cyclone
(Cyclone Larry) in Australia. This is an example of the pre-production
emergency supply, shown as P
However, governments may not have
the resources to provide disaster victims the needed supplies and services. So
they can contract with the private sector to supply these goods and services.
Since the private sector usually responds only in situations where profit is
the motivating factor, it is up to the public sector to respond when the profit
cannot be measured in monetary terms, but in lives saved. Egan (2010)
illustrates how a hybrid system including the private, public, nonprofit, and
local military can respond in a manner dependent on the capacity of each
supporting entity. In Egan’s model, coordination of the pre-disaster plan and
the sharing information among support entities and individual aid workers is
necessary to coordinate all four entities into a more focused system to avoid
redundancies and contribute to a unified response effort. These relations can
be described as post-production emergency supply, shown as P
For the other actors besides
government, Balcik, et al. (2010) gave some representative coordination
procedures used by different entities in the humanitarian supply chain
preceding and throughout the emergency. They divided supply flows into
pre-disaster flow and post-disaster flow. For a pre-disaster flow emergency
supplies and materials are purchased from local or global suppliers and stored
in distribution centers before an anticipated disaster, while for a
post-disaster flow emergency supplies and materials are distributed from
distribution centers to various local distribution points after a disaster.
These relations can be described as post-transshipment emergency supply, shown
as P
2.2.
Disaster relief inventory and transshipment
Lodree and Taskin (2009) formulated
an inventory control problem as an optimal stopping problem with Bayesian
updates. The updates are based on hurricane predictions using a dynamic
programming algorithm to solve the problem. They gave examples involving real
hurricane wind speed data to illustrate the methodology. But like other
inventory models for emergency, they focus on the decision of one warehouse and
pay no attention to transshipment between other warehouses. In fact,
transshipments between warehouses or distribution centers are very efficient
for supply chains, especially for disaster relief supplies.
Traditionally, an inventory system
has a hierarchical design, with transportation flows from manufacturers to
distributors and from distributors to retailers. A flexible system also allows
lateral transshipments between distributors. Members at the same level can
amalgamate their inventories, allowing them to reduce inventory levels and
therefore costs while still attaining adequate service levels (PATERSON et al.,
2010). Transshipments are successfully used in e-business, and also considered
in the return recycling systems for its ability to make supply chains as lean
as possible.
Many works have been done to
construct a network with transshipments. Reyes (2005) used the Shapley value
concept from cooperative game theory as an approach to solve the transshipment
problem. In order to avoid backordering or losing sales, Tang and Yan (2010)
analyzed two typical cross-docking operations: Pre-C, the manufacturer is aware
of demand quantities of each store and tags the products accordingly. Post-C,
handovers the distribution groundwork to the cross-dock, closer to customers.
Pre-C has less operations cost at the cross-dock but a larger quantity of
transshipment while Post-C has a greater operations cost but a smaller quantity
of transshipment. They gave a mathematical model to solve this dilemma and
analyzed the balance between inventory holding, shortage and transshipment
costs. In mathematical models, there are often assumptions. For example, in the
transshipment model, we often assume that the total lead time is less than the
system order cycle and transshipped units reach their destinations at the start
of the last period of the order cycle. Or we will assume that the unfulfilled demand
with in-house stock at a distribution center will be provided by lateral
transshipments from other distribution centers when needed.
As shown earlier, there are many
differences in the environment and characteristics of disaster relief
inventories. For example, when planning for inventory location, besides the
time and cost of transportation to the potential demand points, we must pay
attention to political considerations. Furthermore, the inventory location and
inventory accessibility must be known for monitoring or shipping when the need
arises. Considerations of security, possible government corruption and other
factors usually not considered in the management of inventories for enterprises
need to be accounted for (WHYBARK, 2007). In this paper, we will expand
transshipment to the disaster relief inventory policy.
3. THEORETICAL FRAMEWORK
The theoretical framework of the
relief supply decision system is shown in Figure 2. There are four sub systems
in the framework, called purchase, inventory, distribution, and information
technology and knowledge discovery. In this paper, we assume that the lead time
of transshipment between warehouses is always shorter than the total time of
purchase lead time and order fulfill time from suppliers. Therefore, besides
these four sub systems, we define a new system called emergency transshipment.
And we will describe emergency transshipment based on system dynamics and then
simulate the system.
3.1.
Information technology and knowledge discovery (IT & KD) system
Information sharing is very useful
in solving the uncertainties along the commercial supply chains, companies use
Internet standards internally and externally as well as other information
technologies to improve their competitiveness and quality of customer service.
For a relief supply decision system, information sharing and information
management are rather important. With information technologies, such as GIS, we
can identify the location and geographical information of affected areas. With
information sharing technology, the information of the disaster can be easily
transferred to other areas and departments via information technologies such as
EDI and location tracking. As a result, the distribution centers, suppliers and
even commercial supply chains can be ready to react as soon as possible.
Moreover, after the disaster, even the affected area itself will be uncertain
about the relief demands, such as rescue timeline, materials and personnel
needs. Fortunately, based on local information and history knowledge data bases
of similar disasters, the knowledge discovery method can help. We can identify
the accuracy of relief demand, such as quality and quantity of materials and
available transportation abilities.
Using the information technology and
knowledge discovery (IT & KD) system, we can input affected area
information and output reliable relief plans, such as how to get the relief
supplies, by transshipment or purchasing, purchase natively or globally. If our
relief plan is to purchase, then we go to purchase system, or else we go to the
inventory system to judge if the storages in local warehouse are enough or if
transshipments are necessary, and how to choose the suppliers? In order to meet
the transshipment requirements and facilitate rapid shipping between
warehouses, advanced information systems must be in place to allow actors to
know what other actors have in stock.
3.2.
Purchase system
The purchase system includes two sub
systems called pre-purchase and emergency purchase. The operation characters of
pre-purchase are the same as that of commercial purchase. But the pre-purchase
relief demand is more difficult to predict than commercial demand. Moreover,
the unfulfilled demand cannot be backfilled and the lost sale will lead to
another disaster. In pre-purchase, we can use most of the purchase models of
commercial supply chains, where some parameters and functions will need to be
modified. We will focus on this topic in our lateral works. In this paper, we
assume that the cost of pre-purchasing is higher due to the uncertainties of
demand, hurriedness of lead time and poor transportation conditions. Of course,
purchasing is necessary if all of the regional/local warehouses were seriously
damaged after disaster.
Another important function of our
purchase system in Figure 2 is emergency purchasing, which is always necessary
when disaster happens and some of or even all of local inventories are
seriously destroyed. Emergency purchase is totally different from pre-purchase,
not only in its purchase time and purchase quantity, but also in the probable
inaccessibility of demand points. The suppliers must be prepared to produce
adequate materials for relief and ship them immediately anywhere at any time,
which is impossible.
Before a disaster, warehouses must
place their orders based on the prediction of relief demands and share their
inventories with suppliers via information technologies. If a disaster happens,
the purchase system can work out an emergency purchase plan if the output of IT
& KD system is to purchase and produce instead of using transshipment.
3.3.
Inventory system
In our model, the inventory system
includes warehouse network redesign and storage planning. It manages the raw
material and production of the purchase system and the finished production that
can be transshipped to other areas. Mathematics models are necessary in this
kind of system. Classic inventory models include mathematical models that take
into account surplus, shortage and ordering costs and are used to determine
inventory parameters such as the re-order level (ROL) and re-order quantity
(ROQ). However, the humanitarian relief model does not match the classic
inventory model because of the low and unknown probability of the specific
event, the uncertainty timing, and the difficulties in ascertaining risk levels
and the potential severe consequences. Bonney and Jaber (2010) suggested that
performance measures should encourage the positive aspects of holding
inventory, such as providing flexibility, providing resources that allow things
to be made, acting as a buffer, and satisfying demand immediately. In this
work, we will not use traditional optimal inventory models.
In our model, we suppose that the
frequency of disasters is not known but the maximum demand can be deduced based
on the local disaster records and other similar cases via knowledge discovery
technology. As a result, the inventory policy is to trace a constant which can
minimize the total cost. Higher inventory will make relief easier, however too
much inventory will lead to high purchase and inventory holding costs. But
lower inventory can cause higher risk, if emergency purchasing is inefficient.
Besides the time cost, inventory policies of relief materials are affected by
many factors such as cost to produce, transport and store relief material.
Various effects of these factors can be transferred mathematically into a
parameter, regarded as cost in this work.
3.4.
Distribution system
A distribution system includes
transportation and delivery optimization before and after disaster.
Transportation includes distributing materials from suppliers to store them in
local warehouses before a disaster. Delivery means delivering relief supplies
from local or global warehouses to the affected area after a disaster, just as
order fulfillment in a commercial supply chain. Due to the differences between
relief demand and commercial demand, distribution planning after a disaster is
more important than that of before a disaster. Also, it is different from the
efficient strategies in commercial distribution, such as cross-docking and
direct shipment.
Because the warehouses must
cooperate to fulfill the demand when an emergency occurs, we prefer a
centralized distribution strategy. Centralized distribution can even lead to
global optimization in commercial supply chains when a network is owned by a
single entity or a centralized system that includes many organizations. In
relief supply systems, besides cooperation among warehouses owned by one
distribution center, distribution systems must cooperate with other systems.
For example, a distribution system must cooperate with an inventory system to
judge the optimal transport and storage quantities. Also, the time cost of
distribution and delivery is very important to the decision of transshipment
and purchase systems. Transportation optimization of a disaster relief plan is
more complex than that of commercial logistics because of the possible absence
of an information route condition and other resources. That is, a distribution
system depends most on the IT & KD system.
3.5.
Transshipment system
In commercial inventory models based
on transshipments, when a customer cannot be satisfied by stock on hand or via
lateral transshipment, we can assume that the demand is backordered or a lost
sale (Olsson, 2010). But in our emergency relief chain, if the demand of
post-disaster cannot be satisfied by local storage or via lateral transshipment
from native or global warehouses, we cannot assume backorder or lost sale, we
must switch to purchase or produce. The failure of a transshipment system will be
a disaster for a relief supply chain. Therefore, this sub system must cooperate
well with other sub systems such as inventory, distribution, IT & KD
system, and even purchase systems. That is, the transshipment planning system
is rather complex for the decision variables are outputs of other sub systems
and at the same time the outputs of it will affect the decisions of other sub
systems. Considering this kind of interaction, using a traditional mathematic
model such as stochastic mixed integer program to describe this transshipment
system and try to get the optimized policy is impossible. In the next section,
we will use a system dynamics method to describe an emergency transshipment
system and give a simulation in section 5.
4. EMERGENCY TRANSSHIPMENT SYSTEM
We will consider the emergency
supply pattern with transshipment shown in Figure 1 as P3, where there is one
distribution center and many local and global warehouses belonging to it.
Before a disaster, goods are distributed from distributer centers to local and
global warehouses, the costs include transportation, storage, etc. After a
disaster, the demand can be satisfied first with the nearest undestroyed local
warehouse. If the supplies are not enough, we can switch to other local
warehouses or global warehouses. We will first design a single warehouse model
and then describe the interaction between warehouses, which includes a
transshipment system.
4.1.
Inventory structure for single warehouse with transshipment
Assume there is one distribution
center with many warehouses. Warehouses are denoted as inventory i, j, k...
First, we will model one warehouse, inventory i. An inventory structure of
single warehouse is given in Figure 3.
In Figure 3, local inventory i has
two resources, pre-purchase from distribution center and post-transshipment
from local inventory k. In case of the uncertainty of relief demand, we must
purchase goods and store them as inventories beforehand, we call this
pre-purchase. The basic purchase policy is if the disaster happened and the
local warehouse, inventory i is not destroyed, the relief demands can be
fulfilled by inventory i. The pre-purchase of inventory i is based on the
potential demand and prediction of damages. If the disaster happened and the local
warehouse i is destroyed, the relief demands must be fulfilled by
transshipments. We assume that at least one warehouse will fulfill the relief
demand, in our model marked as inventory k.
Of course, if the disaster does not
happen locally, then inventory i can be used to fulfill the relief demand of
other areas, such as inventory j shown in Figure 3, whose local inventory is
totally destroyed. If no disasters happen before the expiration date of
materials, we must redistribute them or dispose of them, which will lead to
re-transport and other costs.
4.2.
Inventory policy for single warehouse with transshipment
We
use the following parameters:
=probability of region i being destroyed
=probability of inventory i being destroyed and inaccessible
=probability of condition t of region i, where t=1, 2, 3, 4
=inventory of region i
=real demand of region i
=unit pre-purchase and storage cost of inventory i
=unit disposal cost of inventory i
=unit transshipment cost from k to i
=real demand of region i
Condition 1: Region i being
destroyed and inventory i is accessible. Probability of this condition is
Under this condition, there will be
relief demand in region i and this demand can be fulfilled by inventory i. The
total cost of this condition is as follows:
If the real demand Di is less than inventory xi, the storage not used must
be redistributed to commercial supply chain or disposed of. In this paper, we
call this disposal cost, which indeed varies for various goods and warehouses.
But we will define disposal costs to include the cost of purchase, storage,
retransmittal, and disposal.
Condition 2: Region i being
destroyed and inventory i is inaccessible. Probability of this condition is
Under this condition, there will be
relief demand in region i and this demand must be fulfilled by transshipment
from other regions, inventory k. The total cost of this condition is
Condition 3: Region i being safe but
Region j being destroyed and inventory j is inaccessible. Probability of this condition
is
Under this condition, there will be
relief demand in region j and this demand can be fulfilled by inventory i. The
total cost of i is only the pre-purchase and storage cost ci, just the same as
condition 1. Of course there is transshipment cost from i to j, but it belongs
to inventory j.
Condition 4: Region i being safe and
other inventory j is accessible. Probability of this condition is
Under this condition, there will not
be relief demand in any region. The storage must be redistributed to commercial
supply chain or disposed. The total cost is:
Now comes the total cost of
inventory i
[1]
Notice that in equation [1], total
cost depends on many variables: the possibility of disaster and possibility of
warehouse corruption; unit cost of purchase, storage, disposal, transshipment,
redistribution; inventory holdings and real disaster relief demand. It is
impossible to get the optimal solution and minimize the cost. Furthermore, in
relief supply management, we pay more attention to the fulfillment of demand.
Therefore, we will simulate our model using system dynamics and discuss the
sensitivity of the system.
4.3.
Inventory system design with transshipment
In this section, we assume there are
two warehouses located in different areas with different pi,
probability of being destroyed. Each of them is accessible to the other one.
For example, if disaster happens in region i and inventory i is out of order,
then the relief demand can be fulfilled by transshipment from inventory j.
Also, the transshipment of region j can be fulfilled by inventory i if
necessary.
Causal loop diagram of transshipment
is given in Figure 4.
Figure
4: Causal loop diagram of transshipment
In Figure 4, besides the negative
and positive loops of Inventory i and Inventory j, the following loop is very
important:
Inventory i→+transship fulfill
ability i→-emergency purchase j→+ order j→+ Inventory j→+transship fulfill
ability j→-emergency purchase i→+order i→+Inventory i
This loop indicates that the
Inventory i and Inventory j are connected with transshipment. Their inventory
policy can be different due to transshipment. In the next section, we will
prove this via simulation.
5. SIMULATION AND ANALYSIS
5.1.
Data and assumptions
We will discuss three probabilities
of disaster and three inventory policies in our simulation, called high, medium
and low. Different probabilities of disaster are shown in Figure 5. In this
example, inventory equals 100, 200, and 400.
Figure 5. Different probability of relief demand
Now
comes the stock and flow structure of Inventory i, shown in Figure 6.
Figure
6: Stock and flow diagram of one relief warehouse
5.2.
Simulation without transshipment
In order to simulate a single
warehouse relief without transshipment, let:
Transshipment demand j=0
This means inventory i is only used
as local relief and cannot offer transshipment supply to j. In other words,
there would be no C
Emergency purchase i = transshipment
demand i
This equation means there would be no
C
When demand is low, a different
inventory policy can lead to a different total cost, shown in the left of
Figure 7. For medium and high demand, the results are shown in the middle and
right of Figure 7.
Figure
7: Cost of different inventory policy without transshipment
From Figure 7, we can see that if
the relief demand is high, medium or low, the desired inventory should be high
to avoid the high emergency purchase cost. At the same time, high desired
inventory can lead to high disposal and redistribution costs. In fact, because
of the uncertainty of disaster frequency and in order maintain efficiency of
relief, we prefer to keep a high inventory which will lead to high costs and
waste of recourses, especially when relief demand is low.
Notice the negative loop in the
inventory system without transshipment:
Inventory i→+local relief fulfill
ability i→-transshipment demand i→+emergency purchase i→+order i→+order
fulfillment i→+Inventory i.
An ordinary, negative feedback
mechanism can restrict the endless accumulation of inventory. But in this loop,
like in the commercial supply chain, the unfulfilled local relief demand is
directly pushed to emergency purchase, which has a lead time to fulfill. In
disaster relief supply, the lead time may lead to a serious post-disaster.
Therefore, transshipment is introduced to avoid both the cost and inefficiency
of emergency purchase.
5.3.
Simulation with transshipment
Based on different disaster
frequencies, simulations are divided into nine groups, shown in Table 1.
Table 1 Different disaster
frequency
|
Character of Disaster |
Disaster frequency of i |
Disaster frequency of j |
|
FLL |
LOW |
LOW |
|
FLM |
LOW |
MEDIUM |
|
FLH |
LOW |
HIGH |
|
FML |
MEDIUM |
LOW |
|
FMM |
MEDIUM |
MEDIUM |
|
FMH |
MEDIUM |
HIGH |
|
FHL |
HIGH |
LOW |
|
FHM |
HIGH |
MEDIUM |
|
FHH |
HIGH |
HIGH |
In every group, we simulate six
inventory policies, shown in Table 2.
Table 2 Different inventory
policy
|
Inventory policy |
Inventory i |
Inventory j |
|
ILL |
LOW |
LOW |
|
IML |
MEDIUM |
LOW |
|
IMM |
MEDIUM |
MEDIUM |
|
IHL |
HIGH |
LOW |
|
IHM |
HIGH |
MEDIUM |
|
IHH |
HIGH |
HIGH |
5.4.
Total cost of different inventory policies with transshipment
Total cost of six inventory policies
with nine disaster frequency conditions are given in Figure 8-Figure 16.
Figure 8: Total
cost of different inventory policies with transshipment when disaster frequency
is low & low
In Figure 8, under condition FLL,
where the disaster frequencies of i and j are all low, the total cost of
inventory policy IHH is the highest, see line
Figure
9: Total cost of different inventory policies with transshipment when disaster
frequency is low & medium
In Figure 9, under condition FLM,
where the disaster frequency of i is low and the disaster frequency of j is
medium, the total cost of inventory policy IHH is also the highest, see line
Figure 10: Total
cost of different inventory policies with transshipment when disaster frequency
is low & high
In Figure 10, we can see that under
condition FLH, with disaster frequency of i being low while the disaster
frequency of j is high, the total cost of inventory policy ILL is the highest
and the total cost of inventory policy IMM is the lowest, see line 1 and line
Figure 11: Total
cost of different inventory policies with transshipment when disaster frequency
is medium & low
Figure
12: Total cost of different inventory policies with transshipment when disaster
frequency is medium & medium
In Figure 11 and Figure 12, we can
see that under condition FML and FMM, where the disaster frequency of i is
medium and the disaster frequency of j is low or medium, the total cost of
inventory policy IHH is the highest and the total cost of inventory policy IMM
is the lowest, see line 6 and line
Just like the conclusion of Figure
10, when at least one of the disaster frequencies is high, the total cost of
inventory policy ILL is the highest; see line
Figure 13: Total
cost of different inventory policies with transshipment when disaster frequency
is medium & high
In Figure 13, under condition FMH,
where the disaster frequency of i is medium and the disaster frequency of j is
rather high, the best inventory policies are IMM, IHL, IHM and IHH.
Figure
14: Total cost of different inventory policies with transshipment when disaster
frequency is high & low
In Figure 14, under condition FHL,
where the disaster frequency of i is high and the disaster frequency of j is
rather low, the best inventory policies are IML, IMM, IHL, and IHM.
Figure
15: Total cost of different inventory policies with transshipment when disaster
frequency is high & medium
In Figure 15, under condition FHM,
where the disaster frequency of i is high and the disaster frequency of j is
medium, the best inventory policies are IMM, IHL, and IHM.
Figure 16: Total
cost of different inventory policies with transshipment when disaster frequency
is high & high
In Figure 16, under condition FHH,
where the disaster frequencies of i and j are all high, the best inventory
policies are IMM, IHL, IHM and IHH. If only the total are considered, from the
conclusions based on Figure 8 to Figure 16, the best inventory policies under
different disaster frequencies are given in table 3.
Table
3: Best inventory policy under different disaster frequencies
|
Character of Disaster |
Best inventory policy or policies |
|
FLL |
ILL, IML, IMM |
|
FLM |
IMM |
|
FLH |
IMM |
|
FML |
IMM |
|
FMM |
IMM |
|
FMH |
IMM, IHL, IHM and IHH |
|
FHL |
IML, IMM, IHL, and IHM |
|
FHM |
IMM, IHL, and IHM |
|
FHH |
IMM, IHL, IHM and IHH |
From Table 3, for all disaster
frequency conditions, IMM and IHL are better than other inventory policies.
Furthermore, we can conclude that if the probability or frequency of disaster
is uncertain, inventory IMM is the optimized policy. That is, both of the
warehouses only need to keep medium inventory no matter the disaster
frequencies are low, medium or high.
5.5.
Efficiency of transshipment
In order to compare the efficiency
of transshipment, we will discuss the simplest conditions first, both
probabilities of disaster and desired inventories of i and j are the same, that
is:
, Inventory i=Inventory j
Under this condition, the simulation
results of inventory i equals to that of inventory j. therefore, we only need
to analyze the results of inventory i. Suppose probabilities of disaster are
medium, inventory policies is low and medium. Different costs of inventory i
are described as difference lines in Figure 17.
Figure
17: Total cost with and without transshipment
Based on Figure 17, we will do two
groups of comparing:
Comparing different cost without
transshipment, line1 and line 2
Desired inventory of line 1 is 100,
line 2 is 200. Costs of these two policies are all high because emergency
purchase is necessary for both of them. Only when the inventory is high, can
the total cost be reduced (shown line
Comparing different cost with
transshipment: line3 and line 4
When the desired inventory is 100
(line
Figure
18: Cost comparing for different inventory policy with transshipment
We cannot always reduce the total
cost by reducing our desired inventory even when we can get transshipment from
other warehouses. To take advantage of transshipment certain conditions must be
met illustrated in Figure 19.
Figure
19: Cost structure with and without transshipment
In Figure 19 we notice that when
inventory policies are the same (medium), the pre-purchase cost with transshipment
(line 4) is higher than that of without transshipment (line 5). The reason is
that, in order to fulfill the transshipment demand of inventory j, inventory i
must purchase more after relief to j. As a result, transshipment is available
only when the unit emergency purchase cost of i is higher than the unit
pre-purchase cost of i and unit transshipment cost of j.
6. CONCLUSION
This research gives a disaster
relief system based on transshipment which proved to be efficient via our
simulation example. In our simulation, we only discussed a transshipment system
with two warehouses whose unit costs are the same. We assumed that the probable
frequency of a disaster is unknown but the maximum demand is known as a
constant if the disaster happened. Of course the decision makers can describe
the demand and character of different warehouses in detail if they have enough
data. That is, our system given in Figure
The results of our simulation on
transshipment for all disaster frequency conditions showed that if the
probability or frequency of disaster is uncertain, inventory IMM is the
optimized policy. That is, both of the warehouses only need to keep medium
inventory no matter whether the disaster frequencies are low, medium or high.
This is important for warehouse managers to understand in order to minimize
costs and be aware of the ability to provide relief when needed. But, if
inventory levels are too low, then emergency purchasing is high resulting in
increased cost and possible delayed relief to those in need.
Without transshipment, inventory
levels must be kept at a higher level increasing costs and waste. Also,
emergency purchasing in a necessary evil which drives up costs even more.
Management of a disaster system without transshipment would require a more
inventory, planning, and supervisory control.
Transshipment is outperformed when
the pre-purchase costs are factored in due to higher emergency purchase costs.
Otherwise transshipment out performs systems without transshipment.
In all cases, the key to reducing
costs and providing the best care for disaster victims is the information
technology and knowledge discovery subsystem. The accuracy of information
allows for the output of reliable relief plans in order to get relief supplies
to victims by transshipment or purchasing where purchasing is native
(local/regional) or global. If our relief plan is to purchase, then managers
can go to purchase system, or else to the inventory system to judge if the
inventory in the local warehouse is enough or if transshipments are necessary,
and how to choose the suppliers. The transshipment requirements can be met only
with advanced information systems/technology, which allow managers/relief
supervisors to see what other managers/relief supervisors have in stock and
facilitate rapid shipping between warehouses. Knowledge discovery is key to the
process.
Future research will examine more
complex systems for disaster relief, allowing for more variability in the
system. This research is a first step in determining how best to help improve
humanitarian efforts to save lives and help relief organizations and benevolent
organizations provide relief when needed.
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