Modeling in Transportation Logistics Assignment.docx

7/29/2019 Modeling in Transportation Logistics Assignment.docx

1/6

Part A: (I)I Transportation technique method

Movement No. of Units Rate Cost

D (C) + R (Cups) 2400 1.0 2400

D (A) + R (Bowls) 1000 1.1 1100

D (C) + R (Mugs) 600 1.1 660

D (A) + R (Mugs) 1000 1.2 1200

D (B) + R (Mugs) 2400 1.4 3360

D (B) + R (Dummy) 600 0 0

Total 8000 8720

Machines ProductsMugs

4000

Cups

2400

Bowls

1000A 2000 1.2 1.3 1.1

B 3000 1.4 1.3 1.5

C 3000 1.1 1.0 1.3


4000

Cups

2400

Bowls

1000

Dummy

600A 2000 1.2 1.3 1.1 0

B 30001.4 1.3 1.5 0C 3000 600 1.1 1.0 2400 1.3 0


4000

Cups

2400

Bowls

1000

Dummy

600A 2000 1000 1.2 1.3 1.1 1000 0

B 3000 1.4 1.3 1.5 0

C 3000 600 1.1 1.0 2400 1.3 0


4000

Cups

2400

Bowls

1000

Dummy

600A 1000 0 1.2 1000 1.3 1.1 1000 0

B 3000 600 1.4 2400 1.3 1.5 0 600

C 600 0 1.1 600 1.0 2400 1.3 0


2/6

Actual Costs (in US$) If D (A) = 0, then

D (C) + R (Cups) = 1.0 R (Mugs) = 1.2-0 = 1.2

D (A) + R (Bowls) = 1.1 R (Bowls) = 1.1

D (C) + R (Mugs) = 1.1 D(C) = -0.1

D (A) + R (Mugs) = 1.2 D (B) = 0.2

D (B) + R (Mugs) = 1.4 R (Cups) = 1.1

D (B) + R (Dummy) = 0 R (Dummy) = -0.2

Shadow Costs (in US$)

D (A) + R (Cups) = 0+1.1 = 1.1

D (B) + R (Cups) = 0.2+1.1 = 1.3

D (B) + R (Bowls) = 0.2+1.1 = 1.3

D (C) + R (Bowls) = -0.1 + 1.1 = 1.0

D (A) + R (Dummy) = 0 + (-0.2) = (-0.2)

D (C) + R (Dummy) = (-0.1) + (-0.2) = (-0.3)

Actual Costs Shadow Costs Variance

D (A) + R (Cups) 1.3 1.1 0.2

D (B) + R (Cups) 1.3 1.3 0.0

D (B) + R (Bowls) 1.5 1.3 1.2

D (C) + R (Bowls) 1.3 1.0 0.3

D (A) + R (Dummy) 0.0 (-0.2) 0.2

D (C) + R (Dummy) 0.0 (-0.3) 0.3


3/6

Step 1: Identifying the least cost of each row.

Step 2: Row reduction.

Step 3: Column reduction.

Product

Machine Mugs Cups Bowls

A 1.20 1.30 1.10

B 1.40 1.30 1.50

C 1.10 1.00 1.30

Product


A 0.10 0.20 0

B 0.10 0 0.20

C 0.10 0 0.30

Product


A 0 0.20 0

B 0 0 0.20

C 0 0 0.30


4/6

Step 4: Identifying the optimal allocation.

Machine Allocation

A Mugs* /Bowls

B Mugs/Cups

C Mugs/Cups

According to the above allocation there will be only 1 changeover which is likely tooccur in machineA.

In machine - A bowls production can be fulfilled according to the demand of 1000units.

Cups production also can be fulfilled completely in the machine B which is therequirement of 2400 units.

Finally mugs can be fulfilled in machine C the total capacity of 3000 units thatmachine can produce and rest can be catered through machine A. It is only 1000

units.

Optimal Solu tion

Products

Mugs Cups Bowls Dummy SupplyMachines

A

1.20

1000

1.30 1.10

1000

0.00

2000

B

1.40

3000

1.30 1.50 0.00

600 3000

C

1.10 1.00

2400

1.30 0.00

3000

Demand 4000 2400 1000 600 8000


5/6

Objective Function

Z = 600X1 + 400X2o X1 = Matarao X2 = Chilaw

Constraints

1500X1 + 1500X2 20000 3000X1 + 1000X2 40000 2000X1 + 5000X2 44000

Optimal Total Cost Solution = 600$*(12) + 400$*(4) = 7200$ + 1600$ = 8800$

Note: 1500X1 + 1500X2 20000 constraint is known as the Redundant Constraint.

Non- unique practical solution to a transportation problem that contains less than (m+n-1)

non negative distributions in independent locations. In support of (mxn) transportation

problem practical resolution is called degenerative if;

I. Total number of allocations is unequal.II. When allocations arent at independent positions.

At this point, by independent position it means that it is always impractical to outline a closed

loop by combining these allocations by a sequence of level and upright lines from one

allocated cell to another.

Explain above abc answer below.

In the direction of resolving imbalanced transportation algorithm, it can be balancedby adding an untrue supply joint or an untrue demand joint to balance the problem

before beginning the algorithm.

Beginning are normally listed beside the left side of the table with supply amountslisted beside the right side of the table, and Demands are usually listed next to the topof the table with demand amounts listed by the side of the bottom side of the table.


6/6

Each unit transportation costs are given in small boxes at the top of each cell in therectangular matrix, where a zero unit cost is used for an unshipped units column and

either a zero unit cost or a penalty unit cost is used for a shortage row.

To determine degeneracy a zero allocation is distributed to one of the unused squares.

Although there is a great deal of flexibility in choosing the unused square for the zero,the general procedure, when using the North-West Corner Rule, is to allot it to a

square in such a way that it upholds an continuous sequence of squares.

Nevertheless, where the Vogel's method is used, the zero distribution is carried in asmallest cost amount independent cell. An independent cell in this situation strive that

a cell which will not show the way to a closed-path on such distribution.

Documents

Modeling in Transportation Logistics Assignment.docx