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ahker ahker
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4 years ago
A manufacturer of cat towers wishes to locate a super assembly facility to meet their cat tower assembly needs for the next millennium. Currently, carpet, cylinders, yarn and fasteners are purchased in bulk from suppliers in North Haverbrook, Ogden, and Springfield in the quantities shown in the table. The super assembly facility would ship to distribution centers located in Seattle, Lubbock, Nashville, and Philadelphia. The locations of all of these cities on an x-y grid, transportation costs on a ton per mile basis, and total tonnage are all contained in the table. Formulate and solve a model that will minimize the shipping costs to the super assembly center.

Sources/Markets   Transportation Cost $/ton mile (Fn)   Quantity in Tons (Dn)   Xn   Yn
Supply            
North Haverbrook   1.1   650   700   1200
Ogden   1.2   450   250   600
Springfield   1.4   400   225   825
Market            
Seattle   2.25   300   50   1200
Lubbock   2.25   200   450   300
Nashville   2.25   500   800   250
Philadelphia   2.25   500   950   1100

Where should the new plant be located and what is the total system shipping cost?
Textbook 

Supply Chain Management: Strategy, Planning, and Operation


Edition: 6th
Authors:
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OFRD_GRLOFRD_GRL
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4 years ago
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More questions for this book are available here
The model requires that the weighted rectilinear distance between the Super Assembly Center and all sources and sinks of materials and product be minimized.
rectilinear distance is given by dn = 
and transportation cost is given by TC =   from n = 1 to 7
Formulating this nonlinear model (and running it in the nifty table provided by the authors) results in a location for the Super Assembly Center of (550.6,808.3) and total cost of $2,586,342.

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