Please help me for all of these Operations Research questions. Describe main pri

Question

Please help me for all of these Operations Research questions.

Describe main principles and general structure of unconstrained optimization algorithms. Define the total cost function for deterministic continuous-review inventors management model Describe the trade-off between holding costs and ordering costs Illustrate this trade-off graphically. Derive the expression for calculating EOQ. Use exponential smoothing and moving average to predict value for the 7th time period of the series given in the table. Find critical path for the network of project activities given in the figure below. The table below shows project's scheduling information and resource requirements. Use the data to identify potential scheduling conflicts. Apply resource leveling to eliminate the potential conflicts.

Explanation / Answer

1. Unconstrained optimization problems are problems of minimizing or maximizing an objective function of real variables having no restrictions on their values. Mathematical structure of the problem is as given below:

Let x Rn be a real vector with n1components and let f : RnR be a smooth function. Then, the unconstrained optimization problem is min f(x) or max f(x).

Unconstrained optimization problems can have direct applications as well they can be indirectly reformulated from constrained optimization problems.

Constrained optimization problems can be reformulated replacing the constraints of optimization problem with penalty elements in the objective function.

2. Total cost = Ordering cost + Holding cost. Optimal quantity is related with minimum total cost, which is the point on cost curve, where holding cost and ordering cost intersect.

Holding cost = H*Q/2 , where H is the holding cost per unit. Q is the order qty .

Ordering cost = D/Q*O , where O is the ordering cost per order. D is annual demand.

For EOQ, Holding cost = Ordering cost

H*Q/2 = D/Q*O

Q = EOQ = (2*D*O/H)

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