CHAPTER V

CLOSING

In this research or the steps that we have done everything in this below.

A. SUMMARY

From the problem of research result and explanation in this research, the summary was below:

1. Calculate the schedule of project management by finding the critize path using Lindo program that have several levels such as design the activities tables, design network, design the math model, applied the math model into lindo, shown the output from Lindo. Then visualize into Microsoft Visual Basic 6.0.

B. SUGGESTION

Some of suggestion we offered below:

1. In network and activities list design, we have to understanding the reality then we applied them in order to less mistakes when we design math model and lindo program we have to correctly precise too. From the suggestion above, all the capacity to execute output from lindo.

2. The research result we suggested to Dinas Lalu Lintas Angkutan Jalan Raya Semarang in order to design the schedule of shelter management using Lindo then visualized in Microsoft Visual Basic 6.0

CHAPTER II

BASE THEORY

A. Project Management

With more complicate and harder from our world development, we easier to found example of project cases, start from huge scale until the small scale, commercial project, general services or government project. As an example such as free way development project, shelter project in Jakarta, mass transportation special path, planning of management information system..

All the activities we can called as project meanwhile different kinds of activities such as harvest, earn the employee, college in university we can not said as project? Budi Santoso (2003) explain that project characteristic we could look from aim, complexity, uniquely, life cyclic, and resources conflict that happen non permanently and unordinary. Optimum or schedule project efficiency in case of Semarang mass transportation route start from January 2007 until December 2007.

1. AIM

A project usually is an activity during in several times and several final results. A project can divided into sub works that have finished reaching the whole project aim. Project usually quiet complex in order to coordination and controlling with every sub works in several times, activities queue and the cost.

2. complexity

Usually project related usually project to involve some function from organization such as marketing, human resources development, engineering , production, financial because needed special skill and talent from different kinds of science discipline to finished project works included is existences mass transportation also transportation infrastructure which is easier access and support of mass transportation.

3. uniquely

Every project has special sign that looks different with other finished project. Easier and effectively schedule function also the cost oriented standard measure in ordinary society. Project is an activity that realization, non redundant.

4. life cyclic

The project is a process to reach the aim, during the project process will pass into several levels that we called with project life cyclic. Project, tasks, organization, personal, other resources will changed if the projects reach into a new phase. Start decision point and last decision point from first scheduling mass transportation and non contradiction with other existence mass transportation path and also relate with continuous of mass transportation path until there is period changed from mass transportation path.

5. non permanent

mass transportation path decision measured that indicate with revision from the government and interpretation to other related department then derivate into traffic affair and mass transportation that have authority to change and revision of mass transportation path in his territory. Prjocet is temporary activity. Therefore, we accept of significant critics or partial critics.

6. Unfamiliar

Usually some project using methods or new technology and have not sure and risk element. Fail project affected into the team work.

Meanwhile Semarang city shelter management include planning activity, organize, staffing, controlling, and directing. Therefore, project management is planning activity, to organize, to direct and to control of organization resources to reach special order in special moment also special resources. Transportation department, traffic and mass transportation affair function as quiet enough give an opportunity to mass transportation management.

B. Lindo program

Huge scale project need management and accurate calculating. One of solution to calculate is use the lindo software. Lindo suitable with Windows system and Unix system. Procedural presentation in this final task use Windows system. Main menu from this software such as: File Edit, Solve, Report, Window, and Help. Visualize picture 1 in this below:

Gb1.main menu visual

1. File included

a. New, to make a new file.

b. Open, to open definite file.

c. View, to open model from hard drive.

d. Save, to save the file into the hard drive.

e. Save As, to save with new name.

f. Close, to close the file.

a. Print, to print the file.

b. Print Set Up, to set up the file.

c. Log Output, to open or close the file, recording the task result.

d. Take Commands, to command the program.

e. Basis Read, include finished from the model.

f. Basis Save, to save the file with finished task on PC.

g. Title, to show the file name.

h. Date, to show the date.

i. Elapsed Time, to show the times that had been done start from the beginning until the last.

j. Exit, to exit from this program.

2. Edit menu

In this menu, have several choices include such as:

a. Undo, to cancel the last command.

b. Cut, to cutting or delete the letter that had been drag text it board, similar with Clear.

c. Paste and Copy is function menu in simulate. The point is, both function were to copy in one block in text it board.

d. Find Replace, to find a letter or words in text it board and if we need to change it.

e. Option, to fill several optimum methods, iteration system and others kind of optimize solution process.

f. Go to Line, to drag the cursor in the row from text it board.

g. Paste Symbol, to paste the symbol (variable) in optimum cases.

h. Select all, to drag the whole text it board.

i. Clear all, to clear the whole text it active board.

j. Choose New Font, to choose form of a letter in text it board.

3. Solve menu

Solve to shown the complete result with several choices below:

a. Solve, to shown optimum result in editor board completely. Result visual include decision variable value also the dual price. The decision variable value in zero.

b. Compile Model, to check the data list structure in editor board. If the command was not right, then it will show which the mistake row. In other words, if the command was right the system will continuous to the optimum solution.

c. Pivot, to shown the slack value.

d. Debug, to debug the problem the find the solution which part to optimum solution.

4. Report menu

Report menu at lindo programming were the result activity of optimum solution then will find solution approach by partial then will print in editor board. Report menu included,

a. Solution, to solve the optimum solution from problem in linear program that representation in editor text.

b. Range, to shown the analysis finishing result include allowable increase and allowable decrease.

c. Parametric, to change and shown the result in some row.

d. Statistic, to visual the short report in editor report.

e. Peruse, to shown several of an answer.

f. Picture, to shown the model in matrix form.

g. Basis Picture, to form text of base value and presentation in row queue from the column.

h. Table, to shown the simplex table.

i. Formulation, to shown the model in editor report board.

j. Show Column, to shown some coefficient and variable in the whole row also the dual price.

5. Window menu

Function of the Window menu was to choose the activate windows. Window menu shown to us several options such as:

a. Open Command Window, to execute syntax to operate lindo software.

b. Status Window, to editor board and open activate data file.

c. Send to Back, to activate windows from the last steps.

d. Tile, to show all the windows activate in screen.

e. Arrange Icon, to choose window that has been activate.

f. Close All, to close all the activate files.

6. Help menu

Help menu include,

a. Content, to show the main from lindo program.

b. Search for Help on, to find some topic in the system.

c. How to Use Help, to give some help how to use the help system.

d. About Lindo, to show the important information about lindo.

The command were used in this model design from the lindo program below,

1. MAX to start the entry data that relate with optimum problem.

2. MIN to start the entry data that relate with minimum problem.

3. END to end all the data.

4. GO to solve all problems and print all the solution.

5. LOOK to print which part that had been chosen from the data.

6. EDIT to change the layer form.

7. GIN to find the decision variable with non negative value.

8. INTE to find the decision variable zero value if the command is false and decision variable if the command is true.

9. SUB to measure the optimum value.

10. SLB to measure the minimum value.

11. FREE to find the decision variable which the real number.

If there is no statement, lindo software will execute all the variable decision with higher value or same as zero. To print the optimum result, we solve in two ways which is the first step is save all the optimum result into editor board by using other program. Second way is we can print all the optimum result into editor board from print files.

C. Program Microsoft Visual Basic 6.0

Program Microsoft visual basic 6.0 are one of programming language that exist in society. Applied of this visual basic 6.0 we can see in our daily activities start from database activate program in company until franchise base.

The main function of visual basic is to make easier the project management that need visualize in supporting element form to execute the Semarang city Shelter base on projects management, start from the authority as input data for the element support on shelter which is mass transportation route legally, and the cost according to the authority policy. Visual basic 6.0 program suitable with windows system. The main menu in this program such as: File Edit, Project, Format, debug, Run, Query, Tools, Add-ins, Windows, and Help. The visual form in this below:

Picture 1 Visual form of visual basic 6.0

1. Menu file include:

a. New project, to make a new file.

b. Open project, to open the files in the hard drive.

c. Add project, to add some project in visual basic program.

d. Remove project, to remove project show into recycle bin.

e. Save project, to save the files on hard drive.

f. Save as project, to save the file with a new name.

g. Save form, to save form show on hard drive.

h. Save form as, to save the form show with a new name.

i. Print, to print the file

j. Print setup, to setting the print file

k. Make project.exe, to change file into programming.

l. Exit, to quit from program.

2. Menu Edit

a. undo, to recommend

b. redo, to jump into the next command

c. cut, to cutting or erase some command in the editor board text it, similar with clear

d. Paste and Copy to work together in simulating and copy then paste in another editor board text it.

e. Paste link, to copy from another file

f. Remove, to remove the file from the program

g. Delete, to erase the file from the hard drive

h. Delete table from database, to erase the recorded table from database

i. Select all, to choose all recorded files

j. Select all columns, to choose all recorded columns

k. Table, to show the recorded table

l. Find, to find the recorded file in the hard drive

m. Find next, to find the next file

n. Indent and out dent, to setting the files.

o. Go to row, to show the visual form in the program.

3. Menu View

a. code, to show the code visual

b. object, to show the object from the program

c. definition, to appears the unknown command

d. last position, to show the last visual position

e. object browser, to direct object in those program

f. immediately window, to show the windows

g. locals window, to show the windows faster

h. watch window, to show the visual windows

i. project explorer, to appears the project

j. properties window, to show the tools program

k. form layout window, to setting visual position

l. property pages, to look the properties page

m. zoom, to increase the visual

n. show panel, to show the panel

o. toolbox, to show the toolbox in visual program

p. data view window, to look data in the windows

q. color palette, to setting all colors

r. toolbars, to show toolbars program

s. Visual component manager, to setting all components visual.

4. Menu Project

a. Add form, mdi module, class module, user control, properties pages, to add visual in the program.

b. Add DTHML, data report, web class, Microsoft connection, more active X designer, to add from the extern path from the hard drive.

c. Add file, to add the data from the hard drive.

d. Remove data report, to erase data from report

e. References, component, project properties, to continue setting the visual.

5. Menu Debug

To identification the wrong command in programming language. Include step into, step out, step over, add watch, and edit watch, quick watch which is all the function in the module project.

6. Menu Run

To execute the language program running in visual basic in module project.

7. Menu Query

To show the files from another program start from add data, erase the data interface program.

8. Menu Diagram

To show the diagram from the programs.

9. Menu Tools

To add another function of the available property.

10. Menu Add-Ins, to add some infrastructure in visual basic program.

11. Menu Window, to choose which windows in activates. Windows menu include this below:

a. Split, to partition the module project into two parts.

b. Tile horizontally and vertically, to change the position of module project become horizontal and vertical.

c. Cascade, for module project standard.

d. Arrange icon, to change icon on module project

e. To show the entire visual program.

12. Menu Help

Menu Help include:

a. Content, to show the main of visual basic system.

b. Index, to find some words according to alphabetic.

c. Search, to find several topics in the system.

d. Technical support and Microsoft on web, to find another support in web.

e. About Microsoft visual basic, to show the important information about Microsoft Visual Basic system.

D. Operation research

One case in transportation, trading, human mobilization, more complex and complicate. From the all problem need development in methodology to solve them. The best way to solve them needs technical in operational research.

Definition of Operational research were management tools to unite the science, math, logic in order to solve the problems in our daily activities, therefore we can reach the optimum (Subagyo, 1993:4).

Operation Research identification as applied from science methods in complex problems that appears in the bigger system management that involve human, machines, material and money relate with industry, trading, government, and the security. Operational research we an applied base on needs to allocate the limited resources in order to more effective and efficiency. The main aim from this operational research is to help management decide the policy and science action.

Operational research is one of the methods to solve the optimum problem. Operational research includes dynamic programming, network analysis, markov chain, games theory, non linier programming, and integer linier programming.

In this final task, we interested in analysis network. Analysis network include some of problems such as transportation, job description, shortest path, maximum path and scheduling. For more specific we just explore about scheduling project. This scheduling project we will find the methods how to know the costs and route in order to definite the route not complicate. Therefore, shelter project will success when we applied in Semarang.

A model we can definite quite well if that model were benefit to answers the problems. Before build the models in operational research we have to look the measure principal such as:

1. Do not build the complicate model if we can build the simple models.

2. Do not change the problem in order to suitable with the methods that we will use.

3. Deduction process as good as well.

4. Validate process we have to try it first before we use it.

5. Do not selfish to answers some question or problem from our model that we build to answers that question.

6. All kinds model have several characteristic; in order to the summary for this model have to simple and interesting.

7. A model that developed need the accurate from entry data

E. Optimum model

Optimum problem always we meet in all aspects. Some special form of optimum problem we can call as linear programming. Linear programming were optimum problem, the function from optimum were validate solving. The optimum function was a valuable result. Value that we expected was the biggest value which is the aim function in maximum form such as: financial problem and the smallest which is the aim function such as: the costs problem in linear result and the problems we express in different equation or non equation linear also the variable and constant. One of the several technicals which is linear program.

F. Network Model

Network Model is a kind of diagram to help finished the problems in mathematics problem that complicate in order to become simple and easier. Problems could be finished by network such as: network planning, transportation problem, tools reusable problem, the shortest path problem, and job description. Principal, Network planning was relation dependent between several works or variable that description then visualize with diagram. Therefore, we have to explain the definition then another part of project in order to easier and simple jobs.

2

1

3

4

6

5

7

8

Initial event

Terminal event

picture 2. Activities Network

In this final task we will explore about network to give description in society by explain with diagram below.

The symbols will describe several activities such as:

1. Arrow, represent kind of activity or activity in one project. We will definition with as a wok that need duration in all kinds of resources start by terminal shelter, branch shelter, interface shelter. Head of the arrow shown to us direct of activity, when the activity start from beginning point shelter into another shelter from the left to the right. Short or long of the arrow it does not any meaning at all. So we do not need scale.

2. Node, represent kind of activity or event. Event we definition with point as connector with several activities. An activity represent an event therefore we decribe with a lot of point such as start point and the last point. The first and the last point as an activity bcause we used to be know as head and tail activity.an activity must be done first before continue into another point or node.

3. Pseudo arrow, represent as an activity or dummy activity. Every single arrow has multifunction to represent an activity and to help showing the relation between first nodes to another node.

4. Bold arrow, represent an activity in critize path.

Beside the symbols above, we have understand about the rules such as:

1. between two nodes only have one activity, dan

2. all activities we can accelerate if there is no others ways to decribe relation of activities that shown in network.

In order listing the network, we have to follow the rules such as:

1. Setiap kegiatan diwakili oleh satu dan hanya satu anak panah dalam jaringan kerja, atau di antara dua kejadian (event) yang sama hanya boleh digambarkan satu anak panah. Gambar anak panah hanya sekedar menunjukkan urutan di dalam mengerjakan pekerjaan saja, sehingga panjang dan arahnya tidak menunjukkan letak dari pekerjaan.

2. Nama suatu kejadian dinyatakan dengan huruf atau dengan nomor event. Setiap lingkaran kejadian diberi nomor sedemikian rupa, sehingga tidak terdapat lingkaran yang berulang kembali agar tidak terjadi circularity.

3. Kejadian harus mengalir dari event bernomor rendah ke event bernomor tinggi.

Tidak ada dua kegiatan yang dapat diidentifikasi dengan kejadian ekor dan kejadian kepala yang sama. Sebuah situasi seperti ini dapat timbul ketika dua kegiatan atau lebih dapat dilakukan secara bersamaan. Dalam situasi ini prosedur yang diberlakukan adalah memasukkan sebuah kegiatan dummy baik pada awal suatu network maupun pada kegiatan akhir suatu network.

Adapun logika kebergantungan kegiatan-kegiatan itu dinyatakan sebagai berikut:

1. Jika kegiatan A harus diselesaikan dahulu sebelum kegiatan B dapat dimulai, maka hubungan antara kedua kegiatan tersebut dapat dilihat dalam Gambar 3.

1

2

3

A

B

Gambar 3. Kegiatan A merupakan pendahulu kegiatan B

2. Jika kegiatan C, D, dan E harus selesai sebelum kegiatan F dapat dimulai, dapat dilihat dalam Gambar 4.

C

D

E

F

1

2

4

3

5

Gambar 4. Kegiatan C,D dan E merupakan pendahulu kegiatan F

3. Jika kegiatan G dan H harus selesai sebelum kegiatan I dan J, dapat dilihat dalam Gambar 5.

G

H

I

J

2

33

4

5

6

Gambar 5. Kegiatan G dan H merupakan pendahulu kegiatan I dan J

4. Jika kegiatan K dan L harus selesai sebelum kegiatan M dapat dimulai, tetapi kegiatan N sudah boleh dimulai bila kegiatan L sudah selesai, dapat dilihat dalam Gambar 6.

K

L

M

N

2

3

5

4

7

6

	Gambar 6. Kegiatan L merupakan pendahulu kegiatan M dan N

Fungsi dummy di atas adalah memindahkan seketika itu juga (sesuatu dengan anak panah) keterangan tentang selesainya kegiatan L dari lingkaran kejadian no. 4 ke lingkaran kejadian no. 5.

5. Jika kegiatan P, Q, dan R mulai dan selesai pada lingkaran kejadian yang sama, maka kita tidak boleh menggambarkannya seperti dalam Gambar 7.

31

32

P

Q

R

Gambar 7. Gambar yang salah bila kegiatan P,Q dan R mulai dan selesai pada kejadian yang sama

P

R

31

32

33

Q

34

P

Q

R

31

32

33

34

	Gambar 8. Kegiatan P, Q dan R mulai dan selesai pada kejadian yang sama

Kegiatan P = (31,32) P = (32,34)

Q = (31,34) atau Q = (31,34)

R = (31,33) R = (33,34)

Dalam hal ini tidak menjadi soal di mana saja diletakkannya dummy-dummy tersebut, pada permulaan ataupun pada akhir kegiatan-kegiatan tersebut.

G. Penjadwalan Proyek

Setelah proyek dipecah-pecah menjadi paket-paket pekerjaan selanjutnya dapat dibuat penjadwalanya. Yang perlu diperhatikan disini adalah waktu pengerjaan tiap paket pekerjaan dan kejadian apa yang dihasilkan dari serangkaian paket kerja tertentu.

Yang perlu dijadwalkan adalah aktivitas atau paket pekerjaan. Sedangkan kejadian (events) dan lintasan kritis (milestone) hanyalah akibat dari selesainya aktifitas. Jika jalur trayek melintasi beberapa shelter maka itu disebut aktifitas, mulai atau selesainya rute trayek melewati shelter adalah kejadian. Sedangkan aktivitas pembebasan tanah akan menghasilkan milestone tersedianya lahan untuk bangunan. Milestone digunakan untuk menandai telah selesainya beberapa aktifitas yang kritis dan sulit.

Bagi manajemen puncak jadwal proyek mungkin tidak perlu sedetail apa yang diperlukan oleh personel operasional di lapangan. Jadwal dari aktifitas besar ini sering disebut jadwal induk proyek. Jadwal ini dikembangkan selama tahap inisiasi dan dapat diperbarui setelah itu.

Penjadwalan pertama kali dikembangkan oleh Henry G yang sering disebut Gantt charts. Diagram Grantt charts adalah hubungan antar aktifitas mana yang harus mulai dulu dan aktifitas mana yang menyusulnya. Diagram tersebut dapat dilihat dalam tabel 1.

	Aktifitas	Minggu
		1	2	3	4	5	6	7	8
1	Penentuan kualitas yang perlu dikendalikan
2	Mengumpulkan data
3	Merancang peta control
4	Sosialisasi rancangan SPC
5	Training operator
6	Uji coba pelaksanaan SPC
7	Implementasi
8	Analisis penyebab cacat
9	Menghitung kemampuan proses
10	Dokumentasi

Tabel 1. Macam-macam aktivitas yang ada;

2. Ketergantungan antar aktivitas, mana yang lebih dahulu diselesaikan mana yang menyusul;

3. Urutan logis dari masing-masing aktivitas;

4. Waktu penyelesaian tiap aktivitas.

Ada dua pendekatan dalam hal menggambarkan diagram jaringan kerja, yang pertama, kegiatan digambarkan dengan simpul (node), Activity On Node (AON). Sedangkan perstiwa atau event, diwakili oleh anak panah.

Yang kedua aktivitas digambarkan dengan anak panah, Activity On Arch (AOA). Sedangkan kejadian digambarkan dengan simpul. Di sini kita akan menggunakan AOA.Seperti Gambar 9.

x

ES n LS

Anak panah

A

Simpul

n : nomer kejadian ES : waktu mulai paling awal (Earliest Start)

A : nama aktivitas LS : waktu mulai paling akhir (Latest Start)

anak panah : aktivitas

simpul : kejadian

A B

Aktivitas A selesai sebelum aktivitas B dimulai

Gambar 9. Activity On Arch (AOA) (Santoso,2003:57)

Khusus untuk lambang-lambang dalam simpul yang mengakhiri aktivitas, maka istilah ES menjadi EF atau saat selesai paling awal dan LS menjadi LF atau saat selesai paling akhir.

H. Lintasan Kritis

Lintasan kritis (Critical Path) melalui aktivitas-aktivitas yang jumlah waktu pelaksanaannya paling lama. Jadi, lintasan kritis adalah lintasan yang paling menentukan waktu penyelesaian proyek secara keseluruhan, digambar dengan anak panah tebal (Badri,1997:23).

Manfaat yang didapat jika mengetahui lintasan kritis adalah sebagai berikut.

1. Penundaan sebuah jalur trayek pada lintasan kritis menyebabkan seluruh jalur trayek proyek tertunda penyelesaiannya.

2. Proyek sebuah trayek dapat dipercepat penyelesaiannya, bila jalur trayek yang ada pada lintasan kritis dapat terselesaikan disetiap rute jalur trayek.

3. Pengawasan atau kontrol dapat dikontrol melalui penyelesaian jalur kritis yang tepat dalam penyelesaiannya dan kemungkinan di trade off (pertukaran waktu dengan biaya yang effisien) dan crash program (diselesaikan dengan waktu yang optimum dipercepat dengan biaya yang bertambah pula)

4. Time slack atau kelonggaran waktu terdapat pada jalur trayek yang tidak melalui lintasan kritis. Ini memungkinkan bagi keinginan user (penumpang) lebih leluasa.

I. Program Linier

Program Linier (PL) merupakan suatu model umum yang dapat digunakan dalam pemecahan masalah pengalokasian sumber-sumber yang terbatas secara optimal. Masalah tersebut timbul apabila seseorang diharuskan untuk memilih atau menentukan tingkat setiap kegiatan yang dilakukannya,dimana masing-masing kegiatan membutuhkan sumber yang sama sedangkan jumlahnya terbatas. PL adalah matematika terapan dari aljabar linier. Menurut Suyitno (1997:2) pemecahan persoalan dunia nyata dapat digambarkan alurnya secara jelas dalam gambar 10.

DUNIA NYATA DUNIA MATEMATIKA

Masalah kongkret Model Matematika

Abtraksi

Operasi/manipulasi

Jawaban masalah

Secara kongkrit Jawaban Model

Penafsiran

Gambar 10. Bagan alur pemecahan permasalahan nyata

Persoalan yang dikembangkan dalam program linier adalah bagaimana mencari nilai minimum atau maksimum dari variabel yang saling terkait dan terbatas. Program linier (PL) atau Linear programing merupakan suatu metode untuk memecahkan permasalahan optimasi (minimasi atau maksimasi)

Menurut Suyitno (1997:2) Prinsip utama Program Linier adalah dengan adanya:

1. Tujuan yang akan dicari optimalnya (fungsi tujuan) maksimal atau minimal;

2. Kendala (constraints) pembatas yang merupakan keterbatasan sumber daya atau sering disebut fungsi kendala;

3. Model matematika yang merupakan penuangan permasalahan kedalam bahasa matematika. Model matematika berisi fungsi tujuan yang harus berupa fungsi linier dan fungsi kendala yang berupa pertidaksamaan atau perasamaan linier;

4. Adanya keterkaitan atar variabel.

Menurut Suyitno (1997:3) model matematika dalam program linier dirumuskan sebagai berikut.

Fungsi tujuan

Z= c₁x₁+ c₂x₂+ …..+ c_nx_n

Harus memenuhi fungsi kendala

a_i1x₁+ a_i2x₂+…..+ a_inx_n ³,=,£ b_i, i = 1,2,…..,m

Dengan penjelasan istilah dalam Program Linier

x_n melambangkan variabel keputusan (decision variable) adalah kumpulan lambang / simbol matematika yang akan dicari untuk menentukan nilainya.

b_i melambangkan nilai ruas kanan (righ hand side value) yaitu nilai-nilai yang biasanya menunjukkan jumlah (kuantitas, kapasitas, dan waktu) ketersediaan sumber daya untuk dimanfaatkan sepenuhnya.

x_n melambangkan koefisien teknis menyatakan setiap pengunaan a_in dari setiap variabel b_i, dilambangkan dengan x_n.

Z adalah fungsi tujuan yang belum diketahui dan yang akan dicari nilai optimumnya (dibuat sebesar mungkin untuk masalah maksimumdan dibuat sekecil mungkin untuk minimum).

c_n melambangkan koefisien fungsi tujuan yaitu nilai yang menyatakan kontribusi per unit kepada Z untuk setiap x_n.

Petunjuk penyusunan model matematika.

1. Menentukan tipe dari masalah.

a. Masalah maksimasi menyangkut keuntungan, dan

b. Masalah minimasi menyangkut biaya dan waktu.

2. Mendefinisikan variabel keputusan. Koefisien kontribusi digunakan untuk menentukan tipe masalah dan untuk membantu mendefinisikan variabel keputusan.

3. Merumuskan fungsi tujuan. Sesudah mementukan tipe masalah dan variabel keputusan dilanjutkan mengkombinasikan informasi ke rumusan fungsi tujuan.

4. Merumuskan kendala. Tahap ini lebih merupakan seni dari pada ilmu pengetahuan. Ada dua macam pendekatan dasar yaitu:

a. Pendekatan ruas kanan merupakan besar maksimum dari sumber daya yang tersedia dalam masalah maksimum maupun minimum dari sumber daya yang tersedia dalam masalah minimum, dan

b. Pendekatan ruas kiri merupakan koefisien teknis dari daftar dalam tabel atau baris-baris. Meletakkan semua nilai sebagai koefisien teknis dan daftarnya dalam baris dan kolom.

5. Persyaratan non negatif

Untuk menyelesaikan permasalahan Program Linier dapat digunakan berbagai macam metode yaitu: metode grafik, metode vektor, metode simplek dan metode titik dalam. Perhitungan manual dapat digunakan jika permasalahan yang dihadapi sederhana, tetapi untuk permasalahan yang memerlukan perhitungan yang rumit, panjang dan ketelitian yang tinggi cara tersebut kurang efektif. Untuk perhitungan yang rumit dan panjang dapat mengunakan bantuan komputer untuk mengolahnya. Pada skipsi ini peneliti mengunakan piranti lunak (software) yang khusus untuk perhitungan program linier yaitu lindo dan divisualisasikan dalam program visual basic 6.0.

J. Aplikasi Program Lindo

Penyelesaian masalah program linear dengan banyak variabel akan lebih mudah dengan mengunakan komputer. Perhitungan yang digunakan pada lindo pada prinsipnya mengunakan motode simpleks yang kita kenal. Untuk menentukan nilai optimal suatu program linier dengan lindo dilakukan beberapa tahapan yaitu.

1. Menentukan model matematika berdasarkan data;

2. Menentukan formulasi program untuk lindo;

3. Membaca hasil report yang dihasilkan lindo.

Cara untuk menyelesaikan program linier mengunakan lindo untuk pertama kalinya yang dioperasikan melalui windows. Pilih klik kemudian pilih Program dan arahkan pada Winston, dilanjutkan kearah Lindo dan diklik seperti Gambar 11 berikut.

Gambar.11 Tampilan Windows

Pada layar akan muncul text it / untitled baru yang siap untuk tempat mengetikkan formulasi seperti Gambar 12 berikut.

Gambar 12 Tampilan Lindo

K. Penjadwalan Proyek Shelter Angkutan Jalan Kota Semarang

Semakin besarnya volume kendaraan baik itu kendaraan pribadi maupun kendaraan umum yang tidak diimbangi dengan semakin baiknya fasilitas jalan berupa perluasan bahu jalan raya yang ada di semarang menuntut pemerintahan daerah semakin berpacu menguras otak untuk menggubah tatanan transportasi yang terlanjur semrawut di setiap wilayah di kota Semarang. Titik fokus kendaraan dicurahkan kepada kendaraan berbasis massal semisal kendaraan angkutan umum yang marak dan bertambah kian tahun.

Proyek pengadaan shelter untuk trayek angkutan jalan raya merupakan solusi memecah permasalahan kemacetan karena transportasi. Cikal bakal program Visual Basic dapat ditempatkan disetiap shelter yang terbentuk sebagai informasi bagi user ( penumpang ) kendaraan angkutan jalan raya kota Semarang. Pada perencana perhitungan dalam mencari lintasan kritis mengunakan Kurva S Schedule.

Macam-macam aktivitas proyek yang penting meliputi penentuan titik-titik shelter yang digunakan di setiap titik kemacetan kendaraan. Kemudian dilakukan perencanaan proyek pada jalur trayek yang akan dilalui titik shelter tersebut. Jika terjadi dummy tetap dimasukkan dalam bagian perencanaan dan dikembangkan selanjutnya dalam proses entry shelter yang telah terpola dengan baik. di eksekusi data shelter tersebut dengan program winston dan divisualisasikan melalui program visual basic 6.0.

Dalam penelitian ini, penjadwalan proyek yang akan dibahas adalah mencari lintasan kritis dari setiap titik-titik shelter di kota Semarang serta keuntungan-keuntungan yang akan diperoleh jika waktu yang didapatkan lebih cepat dari perhitungan perencana dari pihak dinas lalu lintas dan angkutan jalan raya.

.