Slide 1

MODEL TRANSPORTASITabel AwalAturan NWC (Nort West Corner)Metode INSPEKSI (Ongkos terkecil)Metode VAM (Vogel Approkximation Method)

Tabel OptimumMetode Steppingstone (batu loncatan)Metode MODI (Modified Distribution)Metode Pemecahan MasalahLearning ObjectivesWhen you complete this module, you should be able to:Identify or Define:Transportation modelingFacility location analysis3Learning ObjectivesNorthwest-corner ruleStepping-stone methodWhen you complete this module, you should be able to:Explain or Be Able to Use:4Transportation ModelingAn interactive procedure that finds the least costly means of moving products from a series of sources to a series of destinationsCan be used to help resolve distribution and location decisions5This slide provides some reasons that capacity is an issue. The following slides guide a discussion of capacity.Transportation ModelingA special class of linear programmingNeed to knowThe origin points and the capacity or supply per period at eachThe destination points and the demand per period at eachThe cost of shipping one unit from each origin to each destination6This slide provides some reasons that capacity is an issue. The following slides guide a discussion of capacity.Transportation ProblemToFromAlbuquerqueBostonClevelandDes Moines$5$4$3Evansville$8$4$3Fort Lauderdale$9$7$5Table C.17This slide can be used to frame a discussion of capacity.

Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have maximum capacity, many factors prevent us from achieving that capacity on a continuous basis.

Students should be asked to suggest factors which might prevent one from achieving maximum capacity.Transportation Problem

Albuquerque(300 unitsrequired)Des Moines(100 unitscapacity)Evansville(300 unitscapacity)Fort Lauderdale(300 unitscapacity)Cleveland(200 unitsrequired)Boston(200 unitsrequired)Figure C.18This slide can be used to frame a discussion of capacity.

Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have maximum capacity, many factors prevent us from achieving that capacity on a continuous basis.

Students should be asked to suggest factors which might prevent one from achieving maximum capacity.Transportation MatrixFromToAlbuquerqueBostonClevelandDes MoinesEvansvilleFort LauderdaleFactory capacityWarehouse requirement300300300200200100700$5$5$4$4$3$3$9$8$7Cost of shipping 1 unit from FortLauderdale factory to Boston warehouseDes MoinescapacityconstraintCell representing a possible source-to-destination shipping assignment (Evansville to Cleveland)Total demandand total supplyClevelandwarehouse demandFigure C.29This slide can be used to frame a discussion of capacity.

Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have maximum capacity, many factors prevent us from achieving that capacity on a continuous basis.

Students should be asked to suggest factors which might prevent one from achieving maximum capacity.Northwest-Corner RuleStart in the upper left-hand cell (or northwest corner) of the table and allocate units to shipping routes as follows:Exhaust the supply (factory capacity) of each row before moving down to the next rowExhaust the (warehouse) requirements of each column before moving to the next columnCheck to ensure that all supplies and demands are met10This slide can be used to frame a discussion of capacity.

Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have maximum capacity, many factors prevent us from achieving that capacity on a continuous basis.

Students should be asked to suggest factors which might prevent one from achieving maximum capacity.Northwest-Corner RuleAssign 100 tubs from Des Moines to Albuquerque (exhausting Des Moiness supply)Assign 200 tubs from Evansville to Albuquerque (exhausting Albuquerques demand) Assign 100 tubs from Evansville to Boston (exhausting Evansvilles supply) Assign 100 tubs from Fort Lauderdale to Boston (exhausting Bostons demand) Assign 200 tubs from Fort Lauderdale to Cleveland (exhausting Clevelands demand and Fort Lauderdales supply)11This slide can be used to frame a discussion of capacity.

Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have maximum capacity, many factors prevent us from achieving that capacity on a continuous basis.

Students should be asked to suggest factors which might prevent one from achieving maximum capacity.To(A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouse requirement300200200Factory capacity300300100700$5$5$4$4$3$3$9$8$7FromNorthwest-Corner Rule100100100200200Figure C.3Means that the firm is shipping 100 bathtubs from Fort Lauderdale to Boston12This slide can be used to frame a discussion of capacity.

Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have maximum capacity, many factors prevent us from achieving that capacity on a continuous basis.

Students should be asked to suggest factors which might prevent one from achieving maximum capacity.Northwest-Corner RuleComputed Shipping CostRouteFromToTubs ShippedCost per UnitTotal CostDA100$5$ 500EA20081,600EB1004400FB1007700FC2005$1,000Total: $4,200Table C.2This is a feasible solution but not necessarily the lowest cost alternative13This slide can be used to frame a discussion of capacity.

Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have maximum capacity, many factors prevent us from achieving that capacity on a continuous basis.

Students should be asked to suggest factors which might prevent one from achieving maximum capacity.Intuitive Lowest-Cost MethodIdentify the cell with the lowest costAllocate as many units as possible to that cell without exceeding supply or demand; then cross out the row or column (or both) that is exhausted by this assignmentFind the cell with the lowest cost from the remaining cellsRepeat steps 2 and 3 until all units have been allocated14This slide can be used to frame a discussion of capacity.

Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have maximum capacity, many factors prevent us from achieving that capacity on a continuous basis.

Students should be asked to suggest factors which might prevent one from achieving maximum capacity.Intuitive Lowest-Cost MethodTo(A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouse requirement300200200Factory capacity300300100700$5$5$4$4$3$3$9$8$7From100First, $3 is the lowest cost cell so ship 100 units from Des Moines to Cleveland and cross off the first row as Des Moines is satisfiedFigure C.415This slide can be used to frame a discussion of capacity.

Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have maximum capacity, many factors prevent us from achieving that capacity on a continuous basis.

Students should be asked to suggest factors which might prevent one from achieving maximum capacity.Intuitive Lowest-Cost MethodTo(A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouse requirement300200200Factory capacity300300100700$5$5$4$4$3$3$9$8$7From100100Second, $3 is again the lowest cost cell so ship 100 units from Evansville to Cleveland and cross off column C as Cleveland is satisfiedFigure C.416This slide can be used to frame a discussion of capacity.

Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have maximum capacity, many factors prevent us from achieving that capacity on a continuous basis.

Students should be asked to suggest factors which might prevent one from achieving maximum capacity.Intuitive Lowest-Cost MethodTo(A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouse requirement300200200Factory capacity300300100700$5$5$4$4$3$3$9$8$7From100100200Third, $4 is the lowest cost cell so ship 200 units from Evansville to Boston and cross off column B and row E as Evansville and Boston are satisfiedFigure C.417This slide can be used to frame a discussion of capacity.

Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have maximum capacity, many factors prevent us from achieving that capacity on a continuous basis.

Students should be asked to suggest factors which might prevent one from achieving maximum capacity.Intuitive Lowest-Cost MethodTo(A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouse requirement300200200Factory capacity300300100700$5$5$4$4$3$3$9$8$7From100100200300Finally, ship 300 units from Albuquerque to Fort Lauderdale as this is the only remaining cell to complete the allocationsFigure C.418This slide can be used to frame a discussion of capacity.

Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have maximum capacity, many factors prevent us from achieving that capacity on a continuous basis.

Students should be asked to suggest factors which might prevent one from achieving maximum capacity.Intuitive Lowest-Cost MethodTo(A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouse requirement300200200Factory capacity300300100700$5$5$4$4$3$3$9$8$7From100100200300Total Cost= $3(100) + $3(100) + $4(200) + $9(300)= $4,100Figure C.419This slide can be used to frame a discussion of capacity.

Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have maximum capacity, many factors prevent us from achieving that capacity on a continuous basis.

Students should be asked to suggest factors which might prevent one from achieving maximum capacity.Intuitive Lowest-Cost MethodTo(A)Albuquerque(B)Boston(C)Cleveland(D) Des Moines(E) Evansville(F) Fort LauderdaleWarehouse requirement300200200Factory capacity300300100700$5$5$4$4$3$3$9$8$7From100100200300Total Cost= $3(100) + $3(100) + $4(200) + $9(300)= $4,100Figure C.4This is a feasible solution, and an improvement over the previous solution, but not necessarily the lowest cost alternative20This slide can be used to frame a discussion of capacity.

Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have maximum capacity, many factors prevent us from achieving that capacity on a continuous basis.

Students should be asked to suggest factors which might prevent one from achieving maximum capacity.Tabel AwalAturan NWC (Nort West Corner)Metode INSPEKSI (Ongkos terkecil)Metode VAM (Vogel Approkximation Method)

Tabel OptimumMetode Steppingstone (batu loncatan)Metode MODI (Modified Distribution)Metode Pemecahan MasalahMatriks:

Keterangan:Ai= Daerah asal sejumlah iSi= Supply, Ketersediaan barang yang diangkut di i daerah asalTj= Tempat tujuan sejumlah jdj= Permintaan (demand) barang di sejumlah j tujuanxij= Jumlah barang yang akan diangkut dari Ai ke Tjcij= Besarnya biaya transport untuk 1 unit barang dari Ai ke TjBiaya transport = cij . xiJumlah permintaan = Jumlah ketersediaanMETODE NWC (North West Corner)Merupakan metode untuk menyusun tabel awal dengan cara mengalokasikan distribusi barang mulai dari sel yang terletak pada sudut paling kiri atas.Aturannya:(1) Pengisian sel/kotak dimulai dari ujung kiri atas.(2) Alokasi jumlah maksimum (terbesar) sesuai syarat sehingga layak untuk memenuhi permintaan.(3) Bergerak ke kotak sebelah kanan bila masih terdapat suplai yang cukup. Kalau tidak, bergerak ke kotak di bawahnya sesuai demand. Bergerak terus hingga suplai habis dan demand terpenuhi.Contoh Soal:Suatu perusahaan mempunyai 3 pabrik produksi dan 5 gudang penyimpanan hasil produksi. Jumlah barang yang diangkut tentunya tidak melebihi produksi yang ada sedangkan jumlah barang yang disimpan di gudang harus ditentukan jumlah minimumnya agar gudang tidak kosong. Tabel matriks berikut menunjukkan jumlah produksi paling banyak bisa diangkut, jumlah minimum yang harus disimpan di gudang dan biaya angkut per unit barang. Dalam smu (satuan mata uang):

Prosedur Penyelesaian:Isikan kolom mulai kolom di kiri atas (north west) dengan mempertimbangkan batasan persediaan dan permintaannya.Selanjutnya isikan pada kolom di sebelah kanannya hingga semua permintaan terpenuhi.Biaya total:Z = (50) 400 + (80) 400 + (70) 500 + (60) 100 + (60) 300 + (40) 800 = 143.000

Pabrik/ GudangG1G2G3G4G5SP150

80

60 60 30

800P24070 7060

50

600P38040

60 6040

1100d400

400500400800400400500100300800000000000Metode Inpeksi (Matrik Minimum)Merupakan metode untuk menyusun tabel awal dengan cara pengalokasian distribusi barang dari sumber ke tujuan mulai dari sel yang memiliki biaya distribusi terkecilAturannya 1. Pilih sel yang biayanya terkecil 2. Sesuaikan dengan permintaan dan kapasitas 3. Pilih sel yang biayanya satu tingkat lebih besar dari sel pertama yang dipilih 4. Sesuaikan kembali, cari total biayaContoh Pabrik/ GudangG1G2G3G4G5SP150

80

60 60

30

800P240

70

70

60

50

600P380

4060 60

40

1100d400400500400800800400200400500200000000000Biaya Total = (800 x 30) + (400 x 40) + (400 x 40) + (60 x 200) + (60 x 500) + (60 x 200) = 110.00029Metode VAM (Vogel Approkximation Method )Metode VAM lebih sederhana penggunaanaya, karena tidak memerlukan closed path (jalur tertutup). Metode VAM dilakukan dengan cara mencari selisih biaya terkecil dengan biaya terkecil berikutnya untuk setiap kolom maupun baris. Kemudian pilih selisih biaya terbesar dan alokasikan produk sebanyak mungkin ke sel yang memiliki biaya terkecil. Cara ini dilakukan secara berulang hingga semua produk sudah dialokasikan .

Prosedur Pemecahan:(1)Hitung perbedaan antara dua biaya terkecil dari setiap baris dan kolom. (2)Pilih baris atau kolom dengan nilai selisih terbesar, lalu beri tanda kurung. Jika nilai pada baris atau kolom adalah sama, pilih yang dapat memindahkan barang paling banyak.(3)Dari baris/kolom yang dipilih pada (2), tentukan jumlah barang yang bisa terangkut dengan memperhatikan pembatasan yang berlakubagi baris atau kolomnya serta sel dengan biaya terkecil.(4)Hapus baris atau kolom yang sudah memenuhi syarat sebelumnya (artinya suplai telah dapat terpenuhi).(5) Ulangi langkah (1) sampai (4) hingga semua alokasi terpenuhi. Contoh SoalPabrik/ GudangG1G2G3G4G5SIP150

80

60 60

30

800P240

70

70

60

50

600P380

4060 60

40

1100d400400500400800ITerbesar50- 40 = 10

60 60 = 0

60 60 = 0

40 30= 10

70 40 = 30

4000050 30 = 2050 40 = 1040 40 = 0Pabrik/ GudangG1G2G3G4G5SIIP150

80

60 60

30

800P240

70

70

60

50

600P380

4060 60

40

1100(700)d400400500400800II04000050-30= 2050-40= 1060-40= 2050-40= 1060-60= 060-60= 040-30= 1008000000Pabrik/ GudangG1G2G3G4G5SIIIP150

80

60 60

30

8000P240

70

70

60

50

600P380

4060 60

40

1100(700)d400400500400800III00400008000000080-40= 4060-60= 1070-60= 1060-40= 3060-60= 04000200Pabrik/ GudangG1G2G3G4G5SIVP150

80

60 60

30

8000P240

70

70

60

50

600(200)P380

4060 60

40

1100(700)d400400500400800IV0004000040000800000020020070-60= 1060-60= 070-60= 1060-60= 105000Biaya Total = (400.40) + (800.30) + (400.40) + (500.60) + (200.60) + (200.60) = 110.000