Question

A sub assembly manufacturer builds four different types of assemblies at three of its locations. The location-assembly build combination may be assumed to be a transportation problem.

The time required to build one assembly, regardless of the type of the assembly at each of the locations are: Location 1 - 23 minutes, Location 2 - 17 minutes, and Location 3 - 17 minutes. The costs per assembly at each location is shown in the table below. Location 3 - Assembly 4 is not a possible combination.

	Assembly 1	Assembly 2	Assembly 3	Assembly 4
Location 1	$50	$30	$25	$20
Location 2	$40	$40	$30	$30
Location 3	$45	$30	$25

Each week, 100 of each assembly must be produced. Each location as a 71 hour work week.

What is the minimal cost solution and how much of each assembly does each location create?

Please use Lingo and show code as sets and data.

Answer 1

Formulation:

Min 50 x11 + 30 x22 + 25 x23 + 20 x24 + 40 x21 + 40 x22 + 30 x23 + 30 x24 + 45 x31 + 30 x32 + 25 x33 + 99 x34

Subject to,

x11 + x12 + x13 + x14 <= 71*60/23 i.e 185.2174 which will be rounded down to 185
x21 + x22 + x23 + x24 <= 71*60/17 i.e 250.5882 which will be rounded down to 250
x31 + x32 + x33 + x34 <= 71*60/17 i.e 250.5882 which will be rounded down to 250

x11 + x21 + x31 = 100
x12 + x22 + x32 = 100
x13 + x23 + x33 = 100
x14 + x24 + x34 = 100

xjk >= 0

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LINGO Code:

MODEL:
SETS:
LOCATION : CAPACITY;
ASSEMBLY : DEMAND;   
LINK( LOCATION, ASSEMBLY): COST, VOLUME;
ENDSETS
! The objective;
MIN = @SUM( LINK( I, J):
COST( I, J) * VOLUME( I, J));

! The capacity constraints;
@FOR( LOCATION( I):
@SUM( LINK( I, J): VOLUME( I, J)) <=
CAPACITY( I));

! The demand constraints;
@FOR( ASSEMBLY( J):
@SUM( LINK( I, J): VOLUME( I, J)) = DEMAND( J));

! data;
DATA:
LOCATION = L1 L2 L3;
CAPACITY = 185 250 250;
ASSEMBLY = A1 A2 A3 A4;
DEMAND = 100 100 100 100;
COST = 50 30 25 20
40 40 30 30
45 30 25 99;

ENDDATA
END

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Solution: