BIM 303 Optimizing and modeling Assignment

Reference no: EM132691315

BIM 303 Optimizing and modeling - Emirates College of Technology

Question 1: Problem solving

Below is a network of metro stations where the numbers above the arcs are distances between stations. A passenger wants to take the shortest route from station A to station G. Apply the dynamic programming approach to solve this problem (optimal route), by the following steps:

1. Write down the number of stages n, the decision variables xn, the objective function fn(s, xn) and its minimum f∗(s).
2. Construct the tables for n = 3, n = 2, and n = 1.
3. Using the tables you constructed write down the shortest route (optimal route) from station A to station G, and the minimum overall trip distance.
4. Represent the optimal solution graphically on the network in bold.

Question 2: Problem solving

A fish trader serves three markets. He just received 3 baskets of oyster from his supplier. The fish trader's objective is to find the best allocation of oyster baskets to the three markets in order to maximize the total profit. The estimated expected profits from sales of oyster baskets (in Dirhams) for each market are in the table below.

Number of baskets	Profits (AED)
Number of baskets	Market 1	Market 2	Market 3
0	0	0	0
1	600	500	300
2	800	700	900
3	1200	1200	1100

Apply the deterministic dynamic programming approach to solve this problem (optimal allocation), by the following steps:
1. Construct the tables for n = 3, n = 2, and n = 1. Show the calculations.
2. Based on the tables you constructed write down the optimal allocation, and the maximum total profit.

Question 3: Problem solving
Vehicles arrive at a fuel pump with a mean rate of 18 vehicles per hour. Based on the FCFS service discipline, a vehicle is refueled every 3 minutes on average and leaves the fuel pump. We assume that the fuel pump queueing system is an M/M/1 process in steady-state condition.
1. Describe the M/M/1 queueing model. Comment on the assumption above.
2. Find the fuel pump performance measures L, Lq, W, Wq.

Reference no: EM132691315

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