Members:

1. MOHD AQHAIRI BIN BAHARI B050810175

2. LAW MEI LIN B050810007

3. AZMI BIN HASSAN B050810064

4. MOHD NAZIH BIN JAAFAR B050810237

1

7.5 Transportation Method7.5.1 Introduction to Transportation Problem7.5.2 The Greedy Heuristic7.5.3 Solving Transportation Problems with Linear Programming7.5.4 Generalizations of the Transportation Problem

7.5.4.1 Infeasible Routes7.5.4.2 Unbalanced Problems

7.5.6 More General Network Formulations

2

Transportation ProblemIs a mathematical model for optimally

scheduling the flow of goods from production facilities to distribution centers.

Ex: Plants Warehouses

3

Assumptions:1.Fixed amount of product is transported from

a group of sources (plants) to a group of sinks (warehouses).

2.The unit cost of transporting from each source to each sink is known.

Goals:1.Find the optimal flow paths2.Amounts to be shipped to minimize the total

cost of all shipments.

4

Example 1:The Pear Disk Drive Corporation produces several capacities of Winchester

drives for personal computers. In 1999, Pear produced drives with capacities from 20 to 160 gigabytes (GB), all in the 3.5 –inch form factor. The most popular product is the 80-GB drive, which is sold to several computer manufacturers. Pear produces the drives in three plants located in Sunnyvale, California; Dublin, Ireland; and Bangkok, Thailand. Periodically, the shipments are made from these three production facilities to four distribution warehouses located in the United States in Amarillo, Texas; Teaneck, New Jersey; Chicago, Illinois; and Sioux Falls, South Dakota. Over the next month, it has been determined that these warehouses should receive the following proportions of the company’s total production of the 80-GB drives:

Warehouse Percentage of Total Production

Amarillo 31Teaneck 30Chicago 18Sioux Falls 21

5

The production quantities at the factories in the next month are expected to be (in thousands of units)

Since the total production at the three plants is 260 units, the amount shipped to the four warehouses will be (roundded to the nearest unit)

Plant Anticipated Production (in 1000s of units)

Sunnyvale 45Dublin 120Bangkok 95

Warehouse Total Shipment Quantity (1000s)

Amarillo 80Teaneck 78Chicago 47Sioux Falls 55 6

  TOFROM

  Amarillo Teaneck Chicago Sioux FallsSunnyvale 250 420 380 280Dublin 1280 990 1440 1520Bangkok 1550 1420 1660 1730

Shipping costs per 1,000 Units in RM

Unforseen problems: 1.Forced shutdown at a plant2.Unanticipated swings in the regional demand3.Poor weather along some routes

7

The Greedy HeuristicConstructing a transportation tableau.

8

9

10

Solving Transportation Problems with Linear Programming

Let m be the number of sourcesLet n be the number of sinks

xij = flow from source i to sink j

for 1 i m and 1 j n

cij = cost of shipping one unit from i to j

Total cost of all shipments: cij xij

m

i

n

j1 1

11

Constraints:1.Total amount shipped out of each source

equals the amount available at that source2.The amount shipped into any sink equals the

amount required at that sink.

12

Let ai be the total amount to be shipped out of source iLet bj be the total amount to be shipped into sink

xij = ai for 1 i m

xij = bj for 1 j n

xij 0 for 1 i m and 1 j n

n

j 1

m

i 1

13

For the case of Pear Disk Drive Company,

m = 3 and n = 4Total cost of shipments:

250x11 + 420x12 + 380x13 + …… + 1730x34Constraints:

x11 + x12 + x13 + x14 = 45x21 + x22 + x23 + x24 = 120x31 + x32 + x33 + x34 = 95x11 + x21 + x31 = 80x12 + x22 + x32 = 78x13+ x23 + x33 = 47x14 + x24 + x34 = 55

Nonnegativity constraints : xij 0 for 1 i 3 and 1 j 4

14

Problem entered in Excel Solver.Solution:

Note: 1. For Cell O9: =SUMPRODUCT (B9:M9,B5:M5).

Copied to O10 to O15

2. For Cell O7 = SUMPRODUCT (B5:M5,B7:M7).

Total cost is RM297,80015

Solver Parameter

16

Infeasible RoutesRoutes Dublin Chicago & Bangkok

Sioux Falls were eliminated.

Total cost is RM298,400.

17

Unbalanced ProblemsTotal amount shipped from the sources is not

equal to the total amount required at the sinks.Reason: Demand exceeds the supply and vice

versa.Solution:

Method 1 : Add either a dummy row or a dummy column to absorb the excess supply or demand Method 2: Alter the appropriate set of constraints to either

or form.

18

Example

Total demand is 278 while total supply is 260.To balance problem, add an additional fictitious

factory for the 18-unit shortfall.Greedy Heuristic: Add dummy row (4 rows and 4

colums) (All shortfall to Sioux Falls warehouse )p/s: One can assign zero to all costs in the dummy

column.

Warehouse Total Shipment Quantity (1000s)

Amarillo 90Teaneck 78Chicago 55Sioux Falls 55

19

Linear Programming:

The optimal solution calls for assigning the shortfall:8 units to Chicago and 10 units to Sioux Falls.

20

More General Network Formulations

Solving more complex network distribution problems.

Ex: Transshipment problem.A transshipment node is either a supply or a

demand node.Balance of flow rules:If Apply the Following rule at each

Node:

1. Total suppy > total demand

Inflow – outflow supply or demand

2. Total supply < total demand

Inflow – outflow supply or demand

Total supply = total demand

Inflow – outflow = supply or demand

21

Supply = negative number attached to the node

Demand = Positive number attached to the node

Ex: Pear Disk Drive Problem with taransshipment nodes

22

There are a total of 10 decision variables.The objective function is to minimize 250 x16 + 76 x14 + 380 x15 + 1440 x25 + 1660 x35 +

110 x46 + 95 x48 + 180 x56 + 120 x57 + 195 x58

Total supply available = 260 unitsDemand = 285 unitsThus, apply rule 2..

23

By applying rule 2, eight constraints for this problem:

Node 1 : - x14 - x15 - x16 -45

Node 2 : - x25 -120

Node 3 : - x35 -95

Node 4 : x14 – x46 – x48 25

Node 5 : x16 + x46 + x56 –x56 –x57 –x58 47

Node 6 : x16 + x46 + x56 80

Node 7 : x56 78

Node 8 : x48 + x58 55

24

25

26

Design in terms of Manufacturing.-Also known as DFM (Design for Manufacturing/Manufacturability)-general engineering art of designing products in such a way that they are easy to manufacture.-This design practice not only focuses on the design aspect of a part but also on the producibility. -In simple language it means relative ease to manufacture a product, part or assembly.-the important part that need to be reconsider before make a product. (design, product processing) 27

Design for Logistic1. Economic packaging and transportation

Designing products that can be efficiently packed and stored

2. Concurrent and parallel processing Modify the manufacturing process (product

design)

3. Postponement/delay differentiation Aggregate demand information is more

accurate than disaggregate data.

28

Advantages More compact Better freight rate (transportation) Allows better management of warehouse

spaceReduce lead time (processing)

29

Case Study 1(Transportation)IKEA – Home furnishing products

Problem Description : To create and maintain flexible transport solutions in order to meet all the service needs of customers in the most efficient and environmentally aware way.Solution : Uses railway and combined road-rail transport

30

.

31

Case Study 2 (Parallel Processing)-Parallel processing is the ability to carry out multiple operations or tasks simultaneously.-The concept of parallel manufacturing has been applied in many industries including the high tech and the automobile industries.

32

Parallel ProcessingExample :

33

Case Study 3 (Postponement)- Deliberate action to delay final manufacturing or distribution of a product until receipt of a customer order.- The concept of postponement was first suggested by Alderson in 1950. He recommended that producers should add options or make differentiating changes to the product close to the time of purchase by the end use customer.-Benetton, instead of dyeing the yarn first like other sweater makers, knit plain wool into sweaters and postpone colouring the entire inventory.

34

Postponement

35

PostponementThe advantage of postponement is based on two fundamental understandings:

-Aggregate demand of similar products (or same product group) is more predictable compared to demand for individual types

- and that it is the finished product which has the short life cycle and high risk of obsolescence.

36

7.7 Global Supply Chain

An integrated process where several business entities such as suppliers, manufacturers, distributors, and retailers work together to plan, coordinate and control materials, parts and finished goods from suppliers to customers. One or more of these business entities operate in different countries.

37

Objective function of GSCMGSGM minimizes a weigted of total cost and

activity days

38

Advantage of Global Supply ChainReduced total costs.

Inventory reductionImproved fulfillment cycle

timeReduce cycle time

Increased forecast accuracyProductivity increase

Improved capacityExpend international

connectionsIncrease intellectual assets

Delivery improvement39

OBSTACLES:

40

41

42

43

44

45

46

47

48

SELECTING A GLOBAL SELECTING A GLOBAL SUPPLY CHAIN SUPPLY CHAIN

MODEL :MODEL :

49

50

51

52

53

54

55

56