How to Deploy Port Machines to Improve Handling Efficiency

How to Deploy Port Machines to Improve Handling Efficiency
He xiangyang, Zhang qingnian
School of Transportation,
Wuhan University of Technology, P.R.China, 430063
：
Abstract
How to deploy port machines to improve handling efficiency? in order to achieve higher
productivity and less cost, based upon that allocation of dock crane is a key issue for port efficiency,
using linear programming method, this problem can be divided in two sections: one sets up a model of
dock crane allocation to pursuit higher productivity under simultaneous completing missions constraint;
the subsequently other builds a model of machines network allocation to accomplish such productivity
and keep lower cost. Moreover, by studying a case, main ideas can be illustrated clear.
Key words
Handling efficiency, Dock crane allocation, Linear programming, Machines network
allocation
：
1 Introduction
Why we research the deployment of port machines? It is well known that, with the development of
international logistics, more and more manufacturers and dealers have placed emphasis on the loading
and unloading efficiency of port.
In the process of port loading and unloading, many different type machines may be used, and each
machine handling different cargo may have different productivity by using different handling craft and
different work path, so, how to deploy port machines to improve handling efficiency, is a primary goal
of port. In this section, many scholars have focused on container terminal, because the handling
technology of container terminal is simple, they usually take advantage of simulation technology to
analyze. For example, Pasquale Legato et al (2001) used queuing theory to decide the rational number of
berth and the throughput capacity of port, furthermore, used discrete event simulation method to
optimize allocation of handling machines; Chuqian Zhang et al (2002), by using mixed-integer
programming and Petri net technology, calculated the handling quantity of yard crane and optimized
path of container trailer; Gambardella L.M et al (2001) also used simulation technology to analyze the
deployment of both container crane and yard crane, trying to achieve lower cost and more productivity.
However, few researches have been put on grocery dock. So, this paper stands from grocery dock, based
upon that allocation of dock crane is a key issue for port efficiency, using linear programming method,
divides the deployment of port machines in two sections to achieve higher productivity and less cost:
one sets up a model of dock crane allocation under simultaneous completing missions constraint to
pursuit higher productivity; the subsequently other builds a model of machines network allocation
whose inputs are outputs of dock crane allocation model, to accomplish such productivity and keep
lower cost, moreover, by studying a case, illustrating main ideas clear.
2 Allocation of dock crane is a key issue for port and logistic efficiency
Dock crane is an important fixture among port machines. Its design capacity usually is surplus. It
has many properties, such as more expensive, higher productivity, and less mobility. It can load and
unload many different cargoes, which may have different weight and different package. It bridges
between dock and ship, the higher efficiency it is, the less time ship will stay in port.
On one hand, from the view of port machines usage, allocation of dock crane is a key issue for port
efficiency. The goal, which port authority pursuits, is maximum output under certain cost condition, or
minimum cost under certain output condition. According to the least-cost rule in economics, to produce
a given level of output at least cost, a firm should buy inputs until it has equalized the marginal product
per dollar spent on each input[4]. This implies that, because dock crane is more expensive than other
handling machines in the same loading and unloading assembling line, therefore, the marginal product
of dock crane must be proportional higher than other handling machines. So, in the port loading and
unloading assembling line, dock crane is crucial. If dock crane deploys rational, its handling efficiency
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will be higher, then, port handling efficiency will be higher; and the reverse also is true.
On the other hand, from the view of logistic system, dock crane bridges between dock and ship, so,
its rational allocation will benefit both. In the process of international logistics, port authority and ship
company together constitute effective transportation path, both profit are highly relativity and coherence.
As to ship company, seeking for less time staying in port, forces port authority to allocate dock crane
rationally. So, rationally allocating dock crane, is an “all of winner” result from which port authority and
ship company play a cooperative game, is a pareto improvement, and increases social welfare.
As such, dock crane is an important machine in the loading and unloading assembling line. How it
allocates rationally, is not only related to port handling efficiency, but concerned to logistics efficiency.
3 A models of dock crane allocation
The model of dock crane allocation can be solved by using linear programming method. This
method is under certain resources and missions constraints, finds optimal solutions to meet the request
of objective function[5]. In detail, for a given ship, we face many handling conditions, such as type and
quantity of cargo and dock crane, as well as unit hour handling quantity of dock crane for different cargo,
and we have to find a solution that how to allocate dock crane can get maximum efficiency or minimum
time that ship stays in port.
3.1 Description of dock crane problem
Suppose, a ship has m handling missions; port has n kinds of dock crane; aij represents an hour
handling quantity that the ith dock crane does jth handling mission; hij represents a proportion that the
time, which the ith dock crane does jth handling mission, divides the full time that the ith dock crane
works; b j represents the quantity of the jth handling mission; z j represents the proportion that the
jth handling mission has been finished in an hour; rij equals the number that aij divides b j . From
such description, aij , b j and rij are known variables, so,
n
∑a
zj =
ij
i =1
bj
hij
n
= ∑ rij hij
(1)
i =1
3.2 Model under simultaneous completing missions’ constraint
In practice, we often have to complete missions at the same time, in order to keep the ship safe and
mission balance, so, we must decide hij to maximize z j , the model can be drawn as follow:
Objective function: max z
Subjective to:
(2)
z = z1 = z 2 = L = z m (3)
m
∑h
ij
=1
(4)
j =1
hi j ≥ 0 ,
i = 1, 2 , L , n ;
j = 1, 2 , L , m ; (5)
In such model, if hij equals zero, this means that the ith dock crane does not do jth handling
mission; else if hij equals 1, this means that the ith dock crane does jth handling mission all the time.
4 A model of machines network allocation
A machines network is consisted of different type net machines including forklift, tyre crane, and
tractor under different process flow and work path condition. A process flow and a work path constitute
a net path. For a special net mission, there is a corresponding machines network which handles single
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type cargo in single operational process. The content of the machines network allocation, is how to
select net path, and decides how many machines to be used, in order to get the goal which minimizes the
machines network cost under machines and net missions constraints.
4.1 Model description and assumptions
Suppose, there are m net missions that will be completed by n kinds of net machines,
accordingly, there are m machines networks. For each machines network, the net mission quantity is
z l ; the ith net machine has bi units; there are k net paths, aij represents a machine an hour
handling quantity that the ith net machine does the net mission using jth path; cij represents a
machine an hour handling cost that the ith net machine does the net mission using jth path; xij
represents the number of the ith net machine using jth path, then how to decide xij to achieve the
model goal?
There are several following assumptions of the model:
1) The deployment of port machines is based upon that allocation of dock crane is a key issue for port
efficiency. The allocation of dock crane decides the maximum port productivity in an hour, and net
missions of machines network.
2) aij and cij can be calculated by related formula.
3) m net missions, as well as k net paths, are independent each other. This implies that a machine
can not work in two missions or in two paths at the same time.
4.2 A method to solve such machines network model
From assumptions, we develop a discrete method to solve such machines network model:
1) Firstly, we have to decide the order of different net missions, because different order will change the
value of bi , so, we must calculate permutation and combination of net missions.
2) Secondly, under the situation of certain net missions order, for each net mission, we set up a
corresponding machines network, and search for an optimum solution.
For a certain net mission, we apply following steps to solve such problem:
Step (1): regardless of bi , completely assign the net mission to a net path each time, decide the
number of each kind machine in a net path, calculate both the productivity capacity and corresponding
cost of each net path, then, find the shortest path of cost. If the number of machines in such shortest path
satisfies the constraint, then, such shortest path is an optimized solution. Otherwise, turn to step (2).
Step (2): calculate actual productivity of such shortest path under the constraint of net machines,
then turn to step (1) to assign actual productivity, repeat such step, until find the shortest net path and
corresponding productivity which satisfy the constraint of net machines, then turn to step (3).
Step (3): calculate the surplus of the net mission, then update net paths and bi , and assign the
surplus in the updated net, until the net mission will be completed. So, we get the optimized solution of
the net mission, such as, which net path will be used, what and how many net machines will be deployed
in such path, furthermore, we can get the productivity capacity and cost of such paths.
Step (4): repeat step (1) to (3), assign different net missions, then, we get a summed solution for a
certain net missions order, and record corresponding total cost.
3) Finally, compare different total cost of different net missions order, and find the lowest total cost
whose solution is the optimized result.
5 A case study
5.1 Dock crane data collection and pretreatment
For example, the ship has three unloading missions including three different cargoes, mission 1
unloading collection package from ship to yard, mission 2 unloading small package from ship to truck,
mission 3 unloading steel from ship to yard; port has two type dock cranes, and one type has two cranes,
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the other type has one crane to be used. Detailed data see following table 1.
Table 1
Missions
Different missions and cargoes,
Cargoes
aij (Ton/ hour)
Type
From ship to yard
From ship to truck
From ship to yard
aij and b j
Collection package
Small package
Steel
Ⅰ（2 cranes）
Type
1000*2=2000
800*2=1600
600*2=1200
bj
Ⅱ（1 crane）
1200
900
800
（Ton）
5000
3000
2000
5.2 Dock crane allocation results
According to such data, we used simplex method to solve dock crane allocation model. Under
simultaneous completing missions constrain, we got an optimized solution of dock crane allocation,
which is illustrated in the table2.
1
2
3
Table 2 Optimized allocation of dock crane unit: Ton
Completed
Type
2 cranes
Type
1 crane
mission
Completed
Completed
quantity in
hij
hij
Quantity
Quantity
an hour
In an hour
In an hour
0.48718
974.36
0.32051
384.612
1358.972
0.51282
820.512
0
0
820.512
0
0
0.67949
543.592
543.592
sum
1
Mission
number
Ⅰ（
）
1794.872
Ⅱ（
1
）
928.204
2723.076
Ⅰ
From table 2, we can see that, in an hour, two dock cranes of type spent 0.48718 hours to do
mission 1, and spent 0.51282 hours to do mission 2, and did not do mission 3; one dock crane of type
spent 0.32051 hours to do mission 1, and did not do mission 2, and spent 0.67949 hours to do mission
3. Under such arrangement, the maximized dock crane efficiency could reach to 2723.076 Ton in an
hour, and three missions could be finished simultaneously in 3.66 hours.
At the same time, we got inputs of the model of machines network allocation, which net mission 1
is 1358.972 Ton, net mission 2 is 820.512 Ton, net mission 3 is 543.592 Ton.
5.3 Machines network allocation
We have three different net missions, so, there are six different net missions orders; for a certain
order, we assign three different net missions, and get a corresponding optimized solution as well as total
cost; then, we compare the cost of six different order, and find the lowest total cost whose solution is the
optimized result.
Ⅱ
6 Conclusions
Now, we come to conclusions:
1) Allocation of dock crane is a key issue for port and logistic efficiency. If dock cranes are allocated
rationally, then port and logistic efficiency can be improved; and if we want to improve port and logistic
efficiency, then we have to allocate dock crane rationally.
2) The allocation of dock crane and machines network can be solved by using linear programming
method, but the characters of machines network solution need further investigation.
3) In the process of machines network deployment, the lost of opportunity efficiency resulted from that
the number of machines have to be integer is inevitable.
4) In the process of machines network deployment, the bottleneck problem may be presented, if such
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phenomenon happens, we can find where is bottleneck, then reduce used dock cranes, and redeploy the
machines network; if the bottleneck problem often occurs, then we have to increase machines in the
bottleneck, in order to keep port efficiency.
References
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