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Systems Engineering Procedia 3 (2012) 367 - 371

Procedia

Systems Engineering

Arranging transportation schedule scheme of bulk goods based on

tabular method

Manzhen Duana,b*, Lin Zhanga,b, Hongmei Jiaa,b, Huiyun Caoa,b

aCollege of Civil and Architectural Engineering, Heibei United University, NO.46 Xinhua West Street; Tangshan 063009, Hebei Province,China bEarthquake Engineering Rresearch Center of Hebei Province, NO.46 Xinhua West Street; Tangshan 063009, Hebei Province,China

Abstract

Tabular method is commonly used to solve ring travel route of bulk goods. Generally, it is used to describe the solution process of tabular method, but how to use the optimum value to arrange vehicle schedule scheme is not discussed in depth. In this paper, basic suppositions of the model were put forward; mathematical model is established according to the characteristic of bulk goods transportation. One reasonable way to arrange schedule scheme is proposed based on the optimum of the tabular method, which can provide a good way to solve the problem of transport schedule in the practice for Transportation Engineering.

© 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility ofDesheng Dash Wu.

Keywords: bulk goods transportation; tabular method; Transportation Engineering; schedule scheme

1. Question

Tabular method is commonly used to solve transportation questions. An optimum schedule scheme which usually is the expense lowest or the transportation shortest can be obtained by tabular method. Bulk goods are vehicle transport usually, so ring travel route is used to solve multiple loading point of bulk goods transportation.

The principle of bulk goods transportation is mileage utilization highest. Ll is heavy travel, Lv is spatial travel,

p =—^— x 100%

Pis mileage utilization, so Lr+Lv . yiew from increasing vehicle productivity, mileage utilization is the

bigger the better or spatial travel is the smaller the better.

The optimum value of spatial travel shortest can be obtained according to the conditions given by tabular method, but the suitable conditions of the bulk goods transportation's mathematical model, and how to arrange the vehicle schedule scheme using the optimum of the tabular method without further discussed. Articles about how to arranging ring travel route are rare, witch leading to a mismatch between theory and practice. This article discuss the suitable conditions of the mathematical model for the bulk goods transportation and the way to arrange the vehicle schedule scheme basic on the optimum of the tabular method in view of this blank.

* Corresponding author. Tel.: 13613150186. E-mail address: mz06ss@sohu.com.

2211-3819 © 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of Desheng Dash Wu. doi:10.1016/j.sepro.2011.10.058

2. To solve the travel route of bulk goods based on the tabular method

Here describe how to use the calculation of tabular method to arrange transport scheduling scheme. Example: Daily freight tasks of one goods freight business at a city as shown in table 1, seven vehicles are given to practice the following tasks, K is park, mileages between K park and the goods points in table 2, please arrange the transportation schedule scheme[1].

Table 1 Daily freight tasks of one goods freight business

Tasks Delivery point Discharge point Mileages (km) Transport times (vehicles) Types of goods

1 A E 6 8 gravel

2 B A 3 11 soil

3 C F 5 18 coal

4 D G 10 15 slag

Table 2 Mileages of goods points

Discharge point Delivery point F G E A K

A 5 9 6 0 5

B 2 6 9 3 8

C 5 7 9 3 2

D 6 10 2 8 13

K 7 5 11 5 100

Solving process is as follows:

2.1 Establish mathematical model of the ring travel route for bulk goods transportation

• Basic suppositions of the model[2]:

(1) It is supposes that the transportation question need to deliver P kinds of goods from n delivery points to m discharge points;

(2) The goods deposited different delivery points can be transported by the homogeneous vehicles;

(3) Using same type vehicles in the transportation;

(4) The transportation is short haul, none of them is exceed one day;

(5) Any transportation demand is more than a vehicles' load capacity, namely each transportation need more than one vehicle to complete the task;

(6) The model needs to determine optimum (the transport distance is shortest) transportation plan.

• Parameters and variables of the model are as follows: i: Delivery points of spatial vehicles (discharge point) j: Receiving points of spatial vehicles (delivery point)

Spatial vehicles from point i to point j Spatial vehicles point j needs Spatial vehicles delivered from point i

The mileages from i to j The mathematical model of spatial travel route is as follows: Objective function:

im Lr =YLQvLv

Qj = Qi

.m, Total number of spatial vehicles from one point i to all points j = Total number of spatial vehicles from point i.

S Qj = qj

j=1......n, Total number of spatial vehicles from all points i to one point j = Total number

of spatial vehicles witch point j needs.

la = Z

i=1 7=1

2.2 Solute mathematical model

Keep supply and demand of spatial vehicles balance.

Under the title given in the conditions, qj means spatial vehicles of all points need and Qi means spatial vehicles of all points delivered, are all filled in the table. An optimum value achieved by tabular method as following table 3(Solving process is omitted)[3-5].

Table 3 Solution results of tabular method (km)

Discharge point Delivery point F G E A K Spatial vehicles of q . all points need j

A 5 9 6 0 (8) 5 8

B © 2 6 9 3 8 11

C 5 7 (8) 9 3 (3 2 7 18

D 7 6 10 2 (8) 8 13 15

K 7 5 7 11 5 100 7

Spatial vehicles of all points delivered Qi 18 15 8 11 7 100

Objective function value of the program:

Lv =2 X 11+5 X 0+6 X 7+7 X 8+5 X 7+2 X 8+0 X 8+3 X 3+2 X 7=194 km That is to say the spatial travel of the optimum program is 194 km.

3. Arranging schedule scheme based on the tabular method

• Discovering the first delivery point and the last receiving point of vehicles

It can be seen from table 3 that seven vehicles start from the park K, firstly sent out to the loading point C and returned from the unloading point G to park K after all tasks completed. With this clue, the following program might be arranged.

In order to explain conveniently, with a single arrow lines represents spatial vehicle travel, with the double arrow

line represents heavy vehicle travel, the number on arrow line expresses vehicles of this travel. • Arranging initial travel routes

Principle: Avoid arranging the task whose discharge point is the last.

The vehicles are sent out from park K to loading point C, packed coal and then transport it to the discharge point F. The spatial vehicles are sent out to loading point B (needs eleven spatial vehicles from point F) or D (needs seven spatial vehicles from point F) after unloading goods. Because the discharge point of task 4(loading point D) is G, and it can be seen from table 3 that seven vehicles return park K is from point G after completing all tasks, avoid assigning vehicles to point D first when arrange spatial vehicles. So it is should be priority to sent spatial vehicles to point B.

Seven vehicles filled with soil from point B and then sent to the discharge point A, loaded gravel transported to

discharge point E. then seven spatial vehicles go to point D loading after unloading goods again......, Finally, seven

spatial vehicles return to park K from point G. Figure 1 shows the travel route.

K—^.C F 7 B D ^►G-7-^C -4-=B =t>E^>D k

3 3 = '

„ U ^t

D F—4>D =4>- G

Fig.1 Vehicle travel routes

• Adjusting the travel routes

In order to cause the travel route clearer and more artistic, it needs to reorganize the travel route which first makes, merging some common travel routes. The adjusted route is shown in figure 2.

3 _ G-2-> K

A-H, E=0=. 0:

K 7> C _^ F 7 B E 7 > D=7^G_7>C E-i> D_5_>G

Fig. 2 The adjusted travel routes

• According to the travel routes, arranging its daily freight tasks of each vehicle Table 4 Daily freight tasks of each vehicle

Tasks No.U 2 No.3 No.4, 5, 6 No.7

1 C^F

2 B^A

3 A^E

4 D^G

5 C^F

6 D^G D^G B^A B^A

7 C^F C^F A^E

8 D^G D^G D^G

Note: Five tasks of seven vehicles before are merged because they are same.

• Explains

Because the tabular method will present a multi-solution possibly, the transport programs will be different also. It is very easy to arrange the vehicle's schedule scheme using above method. Certainly, the schedule scheme should be adjusted according to the actual situation of the loading and unloading point and the duty is urgent or not

in the actual production.

4. Conclusion

In this paper, basic suppositions of the model were put forward; mathematical model is established according to the characteristic of bulk goods transportation engineering. One reasonable way to arrange schedule scheme is proposed based on the optimum of the tabular method, which can provide a good way to solve the problem of transport schedule in the practice.

5. Copyright

All authors must sign the Transfer of Copyright agreement before the article can be published. This transfer agreement enables Elsevier to protect the copyrighted material for the authors, but does not relinquish the authors' proprietary rights. The copyright transfer covers the exclusive rights to reproduce and distribute the article, including reprints, photographic reproductions, microfilm or any other reproductions of similar nature and translations. Authors are responsible for obtaining from the copyright holder permission to reproduce any figures for which copyright exists.

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