Reference no: EM132512251
BIM 303 Optimizing and Modeling Assignment - Emirates College of Technology, UAE
Question 1 - Problem Solving
Customers arrive at a cashier counter with a mean rate of 12 customers per hour. Based on the FCFS service discipline, a customer is served every 4 minutes on average and leaves the cashier counter. We assume that the cashier counter queueing system is an M/M/1 process in steady-state condition.
1. Describe the M/M/1 queueing model. What is the importance of the assumption above?
2. Find the cashier counter performance measures L, Lq, W, Wq.
Question 2 - Problem Solving
Company operates a hydraulic pump which declines in productivity from over-heating. End of month inspection classifies pump state as: 0: Good as new; 1: Operable-Low overheating; 2: Operable-High overheating; 3: Inoperable-Failure.
Depending on the pump state, there are three possible decisions D1, D2, and D3 the company manager can make, which are defined as follows:
D1: Do nothing, applicable to states 0, 1, 2.
D2: Pump Overhaul (takes pump back to state 1), applicable to state 2 only.
D3: Replace pump with new (takes system back to state 0), applicable to states 2, 3.
The company manager has to choose between the three following maintenance policies (based on D1, D2, and D3) to minimize cost:
Ra: D1 in states 0, 1, 2; D3 in state 3
Rb: D1 in states 0, 1; D2 in state 2; and D3 in state 3
Rc: D1 in states 0, 1; D3 in states 2, 3
Assume that Ra, Rb, and Rc are stationary policies with respective transition matrices as follows:
1. Describe the Markov property in this case, and comment on the assumption made.
2. Based on the transition matrices above, determine the steady-state probabilities π0 (state 0), π1 (state 1), π2 (state 2), and π3 (state 3) for one of the three policies Ra, Rb, or Rc.
3. Now, if the operation costs according to the pump state are as follows:
|
Costs* (AED)
|
|
State
|
Lost production
|
Lost profit
|
Overhaul (Maintenance)
|
Replacement
|
|
0
|
0 (only D1)
|
0 (only D1)
|
0 (only D1)
|
0 (only D1)
|
|
1
|
1000 (only D1)
|
0 (only D1)
|
0 (only D1)
|
0 (only D1)
|
|
2
|
3000 for D1, 0 for D2 / D3
|
2000 for D2 / D3, 0 for D1
|
2500 for D2, 0 for D1 / D3
|
4000 for D3, 0 for D1 / D2
|
|
3
|
0 (only D3)
|
2000 (only D3)
|
0 (only D3)
|
4000 (only D3)
|
and the steady-state probabilities for the three policies are as follows:
|
steady-state probabilities
|
|
Policy
|
π0 (state 0)
|
π1 (state 1)
|
π2 (state 2)
|
π3 (state 3)
|
|
Ra
|
2/9
|
3/9
|
2/9
|
2/9
|
|
Rb
|
2/13
|
7/13
|
2/13
|
2/13
|
|
Rc
|
2/7
|
3/7
|
1/7
|
1/7
|
Find the optimal (minimum cost) policy based on the expected average operating cost per month.
Question 3 - Problem Solving
Solve the following BIM problem by 0-1 Knapsack (Branch and Bound Algorithm)
Maximize z = 9x1 + 3x2 + 4x3
subject to: 8x1 + 3x2 + 5x3 ≤ 14
xj = 0 or 1, j = 1, 2, 3
Attachment:- Optimizing and Modeling Assignment Files.rar