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JOMO KENYATTA UNIVERSITY OF AGRICULTURE AND
TECHNOLOGY
EEE/ECE/ME.
Date: 14/03/2025 SMA 2472/EMG 2515: OPERATIONS RESEARCH ASSIG TWO Time: 1
Month
INSTRUCTIONS: Attempt ALL questions.
(a) The table below gives network relationship and their time estimates.
Activity Optimistic Time (t 0 ) Pessimistic Time (tp) Most Likely Time (tm) 1 – 2 5 10 8 1 – 3 18 22 20 1 – 4 26 40 33 2 – 5 16 20 18 2 – 6 15 25 20 3 – 6 6 12 9 4 – 7 7 12 10 5 – 7 7 9 8 6 – 7 3 5 4
Required. (i) Identify the critical path and time required to complete the project (ii) What is the probability that the project will be completed in 41.5 weeks. (iii) The duration of the project that will have 95 per cent chance of being completed. (b) The data on the running costs per year and resale price of equipment A, whose purchase price is KSh 200,000 are as follows:
Year 1 2 3 4 5 6 7 Running cost (KSh) 30,000 38,000 46,000 58,000 72,000 90,000 110, Resale value (KSh) 100,000 50,000 25,000 12,000 8,000 8,000 8,
(i) What is the optimum period of replacement? (^1) Please turnover · · ·
(ii) When equipment A is two years old, equipment B, which is a new model for the same usage, is available. The optimum period for replacement is 4 years with an average cost of KSh 72,000. Should equipment A be changed with equipment B? If so, when?
(c) A tax consulting firm has 3 counters in its offices to receive the people who have problems concerning their income and the sales tax. On an average 48 persons arrive in 8hrs a day. Each tax advisor spends 15 min an on average for a arrival of the arrival time follows a Poisson distribution and the service time follows an exponential distribution. (i) Find the average number of customer in the system. (ii) Average waiting time of the customer in the system. (iii) Average number of customers waiting the queue for service. (iv) Average waiting time of the customers in the queue. (vi) Probability that a customer has to wait before he gets service.
(d) LubeCar specializes in fast automobile oil change. The garage buys car oil in bulk at $3 per gallon discounted to $2.50 per gallon if the order quantity is more than 1000 gallons. The garage services approximately 150 cars per day, and each oil change takes 1.25 gallons. LubeCar stores bulk oil at the cost of $0.02 per gallon per day. Also, the cost of placing an order is $20. There is a 2-day lead time for delivery. Determine the optimal inventory policy.
(e) Neon lights on the U of A campus are replaced at the rate of 100 units per day. The physical plant orders the neon lights periodically. It costs $100 to initiate a purchase order. A neon light kept in storage is estimated to cost about $0.02 per day. The lead time between placing and receiving an order is 12 days. Determine the optimal inventory policy for ordering the neon lights. (f) A railway Company specializing in coal handling had empty cars at the following towns in quantities indicated: Town Supply of Cars M 35 Y 60 P 25 The following towns need coal cars, and the mileage table is as follows:
To CV CT CJ CS
From
M 50 30 60 70
Y 20 80 10 90
P 100 40 80 30
Demand for Cars 30 45 25 20
You are required to minimize total miles over which cars are moved to new locations. Use North West Corner Rule to determine the initial feasible solution.
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