2 (20 points A company has two production facilities, #1 and #2 and the capaciti

Question

2 (20 points A company has two production facilities, #1 and #2 and the capacities of facilities at #1 and #2 are Ki and 2 respectively. There are fixed costs 1 and 2 to build facility #1 and #2, respectively. The company needs to meet demand from four markets at different locations. Assume the cost of producing and shipping one unit product from facility i (i 1,2) to market j ( 1,2,3,4)isc The demand from all markets are given as D, G 1,2,3,4). The company's goal is to allocate the demand from different markets to the two facilities so that the cost is minimized Formulate an optimization model; and identify decision variables, objective function and constraints.

Explanation / Answer

VARIABLE S:

We need to find how much of each product to be produced by each production facility that will make its way to a particular market.

So, xij = amount of each product produced, i is the market number and j is the production facility.

CONSTRAINTS:

Limit imposed on the production by individual capacity of each production facility

x11 + x21 + x31 + x41 <= K1

x12 + x22 + x32 + x42 <= K2

Limit imposed by the demand in the various markets gives,

x11 + x12 >= D1

x21 + x22 >= D2

x31 + x32 >= D3

x41 + x42 >= D4

OBJECTIVE FUNCTION:

To minimize cost we have to minimize the function,

c11x11 + c12x12 + c21x21 + c22x22 + c31x31 + c32x32 + c41x41 + c42x42

[Note: that there will be an additional fixed cost of f1 and f2 which are required to build the facilities 1 and 2]

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.