logistics system analysis current situation

8/4/2019 Logistics System Analysis Current Situation

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Discussion on current situation on Herman Millers

transportation and Transshipment models

In this part, we would like to have an overall of Herman Millers transportation systembetween warehouses and dealers. The companys products and services are offered to most

of customers under standard trade credit terms and are sold through distribution channels. In

our case, we are focus on the distribution channels in Michigan. Herman Miller distributes its

stocks through three warehouses which located at Holland, Springlake and Zeeland within

Michigan. All of these warehouses are responsible to fulfil any product orders. For the next

few months, seven dealers which are located around the three warehouses with large demand

of Herman Millers star product Aeron chair. The three major warehouses need to fill the

market demand with their safety stocks, but the quantity available at each warehouse is

limited which is just enough to cover total demand. And the backup safety stock for each

warehouses are 2000units (Holland), 1500 units (Springlake), 1500 units (Zeeland). The

following table shows demand requirement of each dealer.

Dealers

Total order quantity (unit)

Pontiac

650

Ann Arbor

575

Frankenmuth

550

Grand rapids

417

Pottage

310

Lansing

205

Traverse

190


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According to Herman Millers Annual report (2010), freight expenses as a percentage of

sales, were modestly higher in fiscal 2010 compared to fiscal 2009 levels. Contributing to the

additional freight expenses is a significant increase in diesel prices in the United States. Inorder to maximum profit, Herman Miller dedicated to consolidate shipment, increase trailer

utilization, and engage lower cost carriers. Reflect to our case, the distance between dealers

and each warehouse vary, which causes the difference in transportation costs. The

transportation costs of per Aeron chair delivery from each warehouse to each dealer are

shown as follow.

Dealers

Warehouses

Pontiac

Ann Arbor

Frankenmuth

Grand rapids

Pottage

Lansing

Traverse

Holland

$7

$7

$6

$2

$4

$5

$9

Springlake


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$2

$7

$7

$3

$5

$5

$6

Zeeland

$7

$6

$6

$2

$4

$5

$7

Now distribution managements objective is to determine the routes to be used and the

quantity to be shipped via each route that will provide the minimum total transportation costs.

Warehouse dealers

Pontiac

Holland Ann Arbor

Frankenmuth

Springlake Grand Rapids

Pottage

Lansing

Zeeland Traverse


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.Data Analysis:

Let X11=the amount of Aeron chair Holland supply to Pontiac

X12=the amount of Aeron chair Holland supply to Ann Arbor

X13= the amount of Aeron chair Holland supply to Frankenmuth

X14= the amount of Aeron chair Holland supply to Grand Rapids

X15= the amount of Aeron chair Holland supply to Pottage

X16= the amount of Aeron chair Holland supply to Lansing

X17= the amount of Aeron chair Holland supply to Traverse

X21= the amount of Aeron chair Springlake supply to Pontiac

X22= the amount of Aeron chair Springlake supply to Ann Arbor

X23= the amount of Aeron chair Springlake supply to Frankenmuth

X24= the amount of Aeron chair Springlake supply to Grand Rapids

X25= the amount of Aeron chair Springlake supply to Pottage

X26= the amount of Aeron chair Springlake supply to Lansing

X27= the amount of Aeron chair Springlake supply to Traverse


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X31= the amount of Aeron chair Zeeland supply to Pontiac

X32= the amount of Aeron chair Zeeland supply to Ann Arbor

X33= the amount of Aeron chair Zeeland supply to Frankenmuth

X34= the amount of Aeron chair Zeeland supply to Grand Rapids

X35= the amount of Aeron chair Zeeland supply to Pottage

X36= the amount of Aeron chair Zeeland supply to Lansing

X37= the amount of Aeron chair Zeeland supply to Traverse

Objective Function: ZMin:

7X11+7X12+6X13+2X14+4X15+5X16+9X17+2X21 +7X22+7X23+3X24+5X25+5X26+6X

27+7X31+6X32+6X33+2X34+4X35+5X36+7X37

Constraints:

X11+X12+X13+X14+X15+X16+X17


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Warehouses

Pontiac

Ann Arbor

Frankenmuth

Grand Rapids

Pottage

Lansing

Traverse

Holland

0

0

550

7

0

0

0

Springlake

650

0

0

0

0

0

190

Zeeland

0

575


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0

410

310

205

0

Therefore, the minimum total transportation cost is $ 12289.

Sensitivity Analysis on Constraints

Constraints

Final


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Shadow

Constraint

Allowable

Allowable

Cell

Name

Value

Price

R.H. Side

Increase

Decrease

$W$6

Constrait1 lhs

557

0

2000

1E+30

1443

$W$7

Constrait2 lhs

840

0

1500

1E+30


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660

$W$8

Constrait3 lhs

1500

0

1500

7

410

$W$9

Constrait4 lhs

650

2

650

660

650

$W$10

Constrait5 lhs

575

6

575

410

7

$W$11


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Constrait6 lhs

550

6

550

1443

550

$W$12

Constrait7 lhs

417

2

417

1443

7

$W$13

Constrait8 lhs

310

4

310

410

7

$W$14

Constrait9 lhs

205

5


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205

410

7

$W$15

Constrait10 lhs

190

6

190

660

190

Constraint1:

The safety stock in Holland warehouse can have an infinite increase and a decline of 1443

without altering the objective function. This is because the other two warehouses have

enough stocks to satisfy market demand. As long as Holland warehouse has enough stock or

more to satisfy the demand, the transport cost would not be changed. However, if the safety

stock of Holland decreased by more than 1443 units, the objective function will be changed,

and the change would be unkown.

Constraint2

The safety stock in Springlake can have an infinite increase and a decrease of 660 without

changing objective function. Same with Holland, as long as Springlake warehouse has

enough stock or more to satisfy the damned, the transport cost would not be changed.

Constraint3

The safety stock in Zeeland can be changed within the range of 1190 units to 1507 units with

changing the objective function according to the shadow price. Again, the transportation costwill not be changed.

Constraint4

The Aeron chair market demand for Pontiac can fluctuate within the range of 0 units to 1310

units with changing the objective function according to the shadow price. For every one unit

of demand which changes within the range, will result in the transportation cost changing by

2. This occurs due to Pontiac receiving all its Aeron chair from the Springlake which has


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spare stock. The transportation cost of each unit of Aeron chair between Pontiac and

Springlake is $2.

Constraint5

Market demand for Aeron chair in Ann Arbor can be changed within the range of 568 units to

985 units. This can be obtained through altering the objective function according to theshadow price. For each unit of demand which changes within the range, will result in the

transportation cost changing by 6. Thus, because Ann Arbor is getting all its Aeron chair

from Zeeland, the transportation cost of each unit of Aeron chair between Ann Arbor and

Zeeland is $6.

Constraint6

Market demand for Aeron chair in Frankenmuth can be changed within the range of 0 unit to

1993 units with changing the objective function according to the shadow price. For each unit

of demand which changes within the range, will result in the transportation cost changing by

6. Thus, because Frankenmuth is getting all its Aeron chair from Holland (spare stockavailable), the transportation cost of each unit of Aeron chair between Frankenmuth and

Holland is $6.

Constraint7

Market demand in Grand Rapids for Aeron chair can be changed within the range of 410

units to 1860 units with changing the objective function according to the shadow price. For

each unit of change in demand, the transportation cost will be changed by $2.

Constraint8

Pottage's market demand for Aeron chair can be changed within the range of 303 units to

720 units with changing the objective function according to the shadow price. And Pottage is

getting all its Aeron chair from the Zeeland warehouse, for each unit of change in demand,

the transportation cost will be changed by $4.

Constraint 9

Lansing's market demand for Aeron chair can be changed within the range of 198 units to

615 units by changing the objective function according to the shadow price. For each unit of

demand which changes within the range, will result in the transportation cost changing by $5,

and Lansing gets all of Aeron chair from Zeeland. The transportation cost between Lansing

and Zeeland is $5.

Constraint 10

Market demand in Traverse for Aeron chair can be changed within the range of 0 unit and

850 units through changing the objective function according to the shadow price. For each

unit of demand which changes with the range, the transportation cost will be changed by $6,


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it gets stock from Springlake which has spare stock. The transportation cost between

Traverse and Springlake is $6.

logistics system analysis current situation

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