Consider a supplier order allocation problem under multiple sourcing, where it i
ID: 338317 • 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 units $10/unit for the first 300 units
$7/unit for the remaining 300 units
2 $500 800 units $2/unit for all 800 units
3 $300 1200 units $6/unit for the first 500 units
$4/unit for the remaining 700 units
Explanation / Answer
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 units $10/unit for the first 300 units
$7/unit for the remaining 300 units
2 $500 800 units $2/unit for all 800 units
3 $300 1200 units $6/unit for the first 500 units
$4/unit for the remaining 700 units