Components of Constrained Optimization Models

Constrained optimization models consist of three major components:

• Decision variables

• Objective functions

• Constraints  

Decision variables

Decision variables are the physical quantities that operations managers can control. The optimal values of these variables will be determined after solving the problem through a constrained optimization model. For example, the decision variable could be the number of units of a product to be produced in a particular month, or the number of units of inventory to be held in a particular week.

Objective function

The objective function of an optimization model states the criteria on which the alternatives are to be evaluated. The objective function is a mathematical function of the decision variables and it states what is to be maximized (e.g. profit, sales revenue, etc.) or minimized (e.g. cost, distance to travel, etc.).

Constraints

The practical limitations that restrict the choice of the decision variables of a problem are stated as constraints. These constraints can be mathematically represented by: less than (<), greater than (>), less than equal to (≤) or equal to (=) or greater than equal to (≥). A ≤ constraint imposes an upper limit on function of decision variables like utilization of the available raw materials or machinery. A ≥ constraint provides the lower limit on some function of decision variables. For example, the constraints may specify that the number of units of a product to be produced should exceed the demand of the product. An equal to constraint states that the number of products to be manufactured must be equal to a certain quantity.

The following example gives a clear idea of the three components of a constrained optimization problem: A firm produces three products A, B and C. It generates a profit of Rs. 9, Rs. 11, and Rs. 15 from the products A, B and C respectively. The operations manager of the firm wants to identify the right mix of the products to be produced that maximizes the profits of the firm. Suppose the firm has raw material to produce only 10 units of C and time to produce only 7 units of B.

Here, the objective is to maximize the profit by considering all the constraints involved in this problem.

Decision variables are the number of products to be produced of each product A, B, and C.

Therefore, the objective function is,

Maximize Z = 9A+11B+15C (where the coefficient of each term is the unit profit of that particular product)

Subject to the constraints:

C ≤ 10 (material limitation) and

B ≤ 7 (time limitation)              

Email based Operations Management assignment help - homework help at Expertsmind

Are you searching Operations Management expert for help with Constrained Optimization Models questions? Constrained Optimization Models topic is not easier to learn without external help?  We at www.expertsmind.com offer finest service of Operations Management assignment help and Operations Management homework help. Live tutors are available for 24x7 hours helping students in their Constrained Optimization Models related problems. We provide step by step Constrained Optimization Models question's answers with 100% plagiarism free content. We prepare quality content and notes for Constrained Optimization Models topic under Operations Management theory and study material. These are avail for subscribed users and they can get advantages anytime.

Why Expertsmind for assignment help

1. Higher degree holder and experienced experts network
2. Punctuality and responsibility of work
3. Quality solution with 100% plagiarism free answers
4. Time on Delivery
5. Privacy of information and details
6. Excellence in solving Operations Management questions in excels and word format.
7. Best tutoring assistance 24x7 hours