Consider a supplier order allocation problem under multiple sourcing, where it i
ID: 346987 • Letter: C
Question
Consider a supplier order allocation problem under multiple sourcing, where it is required to buy 2000 units of a certain product from three different suppliers. The fixed set-up cost (independent of the order quantity), variable cost (unit price), and the maximum capacity of each supplier are given in Table 5.15 (two suppliers offer quantity discounts). The objective is to minimize the total cost of purchasing (fixed plus variable cost). Formulate this as a linear integer programming problem. You must define all your variables clearly, write out the constraints to be satisfied with a brief explanation of each and develop the objective function.
table : 5.15
supplier data for exercise 5.5
supplier fixed cost capacity unit price
1 $100 600 unit $10 /unit for first 300 units
$7/ unit for remaining 300 units
2 $500 800 units $2 /unit for all 800 units
3 $300 1200 units $6/unit for first 500 units
$4/unit for remaining 700 units
Supplier Fixed Cost Capacity Unit price $100 600 units $10/u for up to 300 units $7/u entire order for more tharn 00 units $2/unit for all 800 units $500 $300 200 units $6/unit for up to 500 units 800 units $4/unit entire order for more than 700 unitsExplanation / Answer
LET X1 - Units ordered from supplier 1
X2- units ordered from supplier 2
X 3- units ordered from supplier 3
Then X1+X2+X3 =2000.............. eq 1
also X1=< 600 ......... eq 2
X2 =< 800........eq3
X3 =< 1200..............eq 4
These 4 are your constraints Now we will work on objective function
Let C1- Cost of purchasing from supplier 1
C2- Cost of purchasing from supplier 2
C3- Cost of purchasing from supplier 3
THEN OBECTIVE FUNCTION =
MINIMIZE TOTAL COST (C1+C2+C3) ......... by varying X1, X2 and X3
C1= 100+ 10* X1...... if X1<= 300
= 100+ 10*300 + 7* (X1-300) .............. if X1>300
C2= 500+ 2*X2
C3= 300+ 6*X3 ....... For X3<= 500
= 300+ 6*500+ 4* (X3-500) ...... For X3> 500