The document provides instructions for a semester 2 operations research assignment for Zambian Open University students. It includes 5 questions on topics such as transportation problems, machine assignment, project scheduling, and queueing models. Students are to determine optimal distributions and assignments to maximize profit or minimize costs, construct networks, and analyze queues using Poisson and exponential distributions. The assignment is due on October 12, 2020.
The document provides instructions for a semester 2 operations research assignment for Zambian Open University students. It includes 5 questions on topics such as transportation problems, machine assignment, project scheduling, and queueing models. Students are to determine optimal distributions and assignments to maximize profit or minimize costs, construct networks, and analyze queues using Poisson and exponential distributions. The assignment is due on October 12, 2020.
The document provides instructions for a semester 2 operations research assignment for Zambian Open University students. It includes 5 questions on topics such as transportation problems, machine assignment, project scheduling, and queueing models. Students are to determine optimal distributions and assignments to maximize profit or minimize costs, construct networks, and analyze queues using Poisson and exponential distributions. The assignment is due on October 12, 2020.
The document provides instructions for a semester 2 operations research assignment for Zambian Open University students. It includes 5 questions on topics such as transportation problems, machine assignment, project scheduling, and queueing models. Students are to determine optimal distributions and assignments to maximize profit or minimize costs, construct networks, and analyze queues using Poisson and exponential distributions. The assignment is due on October 12, 2020.
A company has three factories at A, B and C, which supply warehouses at D, E, F and G
respectively. Monthly product capacities of these factories are 250, 300 and 400 units respectively. The current warehouse requirements are 200, 275 and 300 units respectively. Unit transportation costs from factories to warehouses are given below.
1 To D E F G A 11 13 17 14 B 16 18 14 10 C 21 24 13 10
Determine the optimum distribution to minimize cost.
QUESTION TWO
A company has four manufacturing plants and five warehouses. Each plant manufactures the same product, which is sold at different prices at each warehouse area. The cost of manufacturing and cost of raw materials are different in each plant due to various factors. The capacities of the plants are also different. These data are given in the following table:
Item/ Plant 1 2 3 4
Manufacturing cost (K) per 12 10 8 7
unit Raw material cost(K) per 8 7 7 5 unit Capacity per unit time 100 200 120 80
The company has five warehouses. The sale prices, transportation costs and demands are given in the following table:
Warehouse Transportation cost (K) per unit Sale Price demand
(plants) (K) per unit 1 2 3 4 A 4 7 4 3 30 80 B 8 9 7 8 32 120 C 2 7 6 10 28 150 D 10 7 5 8 34 70 E 2 5 8 9 30 90
(i) Formulate this into a transportation problem to maximize profit
(ii) Find the solution using VAM method (iii) Test for optimality and find the optimal solution.
2 QUESTION THREE
A manager has the problem of assigning four new machines to three production facilities. The respective profits derived are as shown. If only one machine is assigned to a production facility, determine the optimal assignment.
Profits (K’000) production facility
Machine A B C
A 10 10 14
B 10 11 13
C 12 10 10
D 13 12 11
QUESTION FOUR
A project has the following characteristics:
Activity Optimistic time Pessimistic time Most likely time
1–2 1 5 1.5
2–3 1 3 2
2–4 1 5 3
3–5 3 5 4
4–5 2 4 3
4–6 3 7 5
5–7 4 6 5
6–7 6 8 7
3 7–8 2 6 4
7–9 5 8 6
8 – 10 1 3 2
9 – 10 3 7 5
(a) Construct the network
(b) Find the critical path and variance for each event (c) Find the project duration at 95% probability.
QUESTION FIVE
(a) A self – service store employs one cashier at its counter. Nine customers arrive on an average every 5 minutes while the cashier can serve 10 customers in 5 minutes. Assuming Poisson distribution for arrival rate and exponential distribution for service time, find i. Average number of customers in the system ii. Average number of customers in the queue or average queue length iii. Average time a customer spends in the system iv. Average time a customer waits before being served (b) A tax consulting firm has 3 counters in its office to receive people who have problems concerning their income, wealth and sales taxes. On the average 48 persons arrive in an 8 –hour day. Each tax adviser spends 15 minutes on an average on an arrival. If the arrivals are Poissonly distributed and service times are according to exponential distribution, find i. The probability of there being no customer in the system ii. The average number of customers in the system iii. Average number of customers waiting to be served iv. Average time a customer spends in the system v. Average waiting time for a customer
