Members: 1. MOHD AQHAIRI BIN BAHARI 2. LAW MEI LIN 3. AZMI BIN HASSAN 4. MOHD NAZIH BIN JAAFAR B050810175 B050810007 B050810064 B050810237

1

7.5 Transportation Method

7.5.1 Introduction to Transportation Problem 7.5.2 The Greedy Heuristic 7.5.3 Solving Transportation Problems with Linear Programming 7.5.4 Generalizations of the Transportation Problem 7.5.4.1 Infeasible Routes 7.5.4.2 Unbalanced Problems 7.5.6 More General Network Formulations 2

Transportation Problem

 Is a mathematical model for optimally scheduling the flow of goods from production facilities to distribution centers.

 Ex:

Plants Warehouses

3

 Assumptions: 1.

2.

Fixed amount of product is transported from a group of sources (plants) to a group of sinks (warehouses).

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

 Goals: 1.

Find the optimal flow paths 2.

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 Amarillo Teaneck Chicago Sioux Falls Percentage of Total Production

31 30 18 21 5

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

Plant Sunnyvale Dublin Bangkok Anticipated Production (in 1000s of units)

45 120 95  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)

Warehouse Amarillo Teaneck Chicago Sioux Falls Total Shipment Quantity (1000s)

80 78 47 55 6

Shipping costs per 1,000 Units in RM

F R O M

Sunnyvale Dublin Bangkok Amarillo 250 1280 1550

TO

Teaneck 420 990 1420 Chicago Sioux Falls 380 1440 1660 280 1520 1730 Unforseen problems: 1. Forced shutdown at a plant 2. Unanticipated swings in the regional demand 3. Poor weather along some routes 7

The Greedy Heuristic

 Constructing a transportation tableau.

8

9

 Solution: Let x ij be the amount of flow from source i to sink j, x 11 = 45, x 21 = 35, x 22 = 78, x 23 = 7, x 33 = 40, x 34 = 55, other x ij = 0  The total cost for this solution is (45 )(250) + (35)(1280) + …. = RM 304,900 10

Solving Transportation Problems with Linear Programming

 Let m be the number of sources  Let n be the number of sinks x ij = flow from source

i

to sink

j

for 1

i m and

1

j n

c ij = cost of shipping one unit from

i

to

j

 Total cost of all shipments:

i

1

j n m

   1 c ij x ij 11

 Constraints: 1.

2.

Total amount shipped out of each source equals the amount available at that source The amount shipped into any sink equals the amount required at that sink.

12

Let a i be the total amount to be shipped out of source i Let b j be the total amount to be shipped into sink

j n

  1 x ij = a i

i m

  1 x ij = b j for 1

i m

for 1

j n

x ij 0 for 1

i m

and 1

j n

13

 For the case of Pear Disk Drive Company,     m = 3 and n = 4 Total cost of shipments: 250x 11 + 420x 12 Constraints: + 380x 13 + …… + 1730x 34

x

11 + x 12 + x 13 + x 14

x

21 + x 22 + x 23 + x 24

x

31 + x 32 + x 33 + x 34

x

11 + x 21 + x 31

x

12 + x 22 + x 32 = 45 = 120 = 95 = 80 = 78

x

13 + x 23 + x 33

x

14 + x 24 + x 34 = 47 = 55 Nonnegativity constraints : x ij  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 RM297,800 15

 Solver Parameter 16

Infeasible Routes

 Routes Dublin were eliminated.

Chicago & Bangkok Sioux Falls  Total cost is RM298,400.

17

Unbalanced Problems

 Total 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  18

Warehouse Amarillo Teaneck Chicago Sioux Falls

Example

Total Shipment Quantity (1000s)

90 78 55 55  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. 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 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 x 16 + 76 x 14 + 380 x 15 110 x 46 + 95 x 48 + 180 x 56 + 1440 x 25 + 120 x 57 + 1660 x 35 + 195 x 58 +    Total supply available = 260 units Demand = 285 units Thus, apply rule 2..

23

 By applying rule 2, eight constraints for this problem: Node 1 : Node 2 : Node 3 : Node 4 : Node 5 : Node 6 : Node 7 : Node 8 : - x 14 - x 15 - x 16 - x 25  -120 - x 35  -95

x

14 – x 46 – x 48   -45 25

x

16 + x 46 + x 56 –x 56 –x 57 –x 58

x

16 + x 46 + x 56  80

x

56 78

x

48 + x 58 55  47 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 Logistic

1.

2.

3.

 Economic packaging and transportation Designing products that can be efficiently packed and stored  Concurrent and parallel processing Modify the manufacturing process (product design) 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 space  Reduce 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 Processing

Example : 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

Postponement

The 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 GSCM

 GSGM minimizes a weigted of total cost and activity days 38

Advantage of Global Supply Chain

Reduced total costs.

Inventory reduction Improved fulfillment cycle time Reduce cycle time Increased forecast accuracy Productivity increase Improved capacity Expend international connections Increase intellectual assets Delivery improvement 39

OBSTACLES: Potential Global Supply Chain obstacles

• Inefficient transportation and distribution systems • Market instability • Language barriers • Customs • Political turmoil • Trade imbalances • Export surges and recessions 40

Combating obstacles

• Join nation groups • Be innovative • Be flexible • Research • New technology • Vertically integrate • Form consortiums 41

Classical Logistic Issues

Facility Locations Sourcing Distribution 42

Cost

• Local labor rates • Local space cost • International freight tariffs • Currency exchange rates 43

Customs Duty • Duty rates differ by commodity and level of assembly • Duty drawback • Impact of GATT: Changes over time • Transfer pricing • Duty Suspension

44

Taxes on Corporate Income

• Different markups by country • Tax havens and not havens • Make vs. buy effect 45

Offset Trade and Local Content

• Local content requirement for government purchases • Content for preferential duty rates • Offset trade requirements 46

Export Regulations

• Export licenses • Denied parties list 47

Time • Lead time • Cycle time • Transit time • Export license approval cycle • Customs clearance 48

SELECTING A GLOBAL SUPPLY CHAIN MODEL : Different Type of Global Supply Chain Supply Models

Own and manage your own infrastructure Use strategic alliances Partner with an asset based third party Partnership with a global integrator of logistics services 49

Own and manage your own infrastructure Pro Con Maximum Control Heavy costs 50

Use strategic alliances Pro

Convenience Large areas covered

Con

Unreliable alliances prone 51

Partner with an asset- based third-party Pro Con

Operational standards Uniform identity and marketing strength Dedicated management structure Ignorance of complex customs regulation Lack of connections Local economic downturns 52

Partnership with a global integrator of logistics services Pro Con

Customer friendly In-country knowledge True information systems integration Uniform standards Limited use Less control 53

By implemented a global supply chain model:

• Reduced plants from 33 to 12 • Manufacturing costs decreased by $500 million • Logistics cost decreased by more than $300 million • Reduce service facilities from 34 to 17 • Annual cost reductions of more than $80 million • Physical assets reduced by $34 million • Inventory reduced by $74 million • Increased unit reduction by 500 percent • Increase revenue • Five time more computers were manufactured 54

Summary of Global Supply Chains

55

56