Management science - Coursework Example

……………………………………………. PART A Question weekly supply   weekly demand   probability 20 25 40 60     20 0 60 $50 $20 20)     25 0.3 $60 $75 $45 $5   400.5$60 $75 $120 $80   600.1$60 $75 $120 $180          the profit per pound is $3     the cost per pound $2              Attached is an excel fileQuestion 2Regret table    weekly supply           weekly demand  probability20254060  200.1$0 $10 $40 $80   250.3$15 $0 $30 $70   400.

5$60 $45 $0 $40   600.1$120 $105 $60 $0         Attached find an excel fileQuestion 3 expected value criterion20254060$6 $5 $2 ($2)$18 $22.50 $13.50 $1.50 $30 $37.50 $60 $40 $6 $7.50 $12 $18 $60 $73 $88 $58 So the expected highest value is $88 which is obtained from supplying 40 pounds of steak.Question 4Maximum likelihood criterion gives a value of $120 obtained from supplying 40 pounds of steak. This is because it has the highest probability and then we proceed to pick the highest payoff from the weekly demand which happens to coincide with the weekly supply.

Question 5Decisions for part 3 and 4 are not the same. This is because in the expected value criterion, it utilizes the probabilities of the states of nature in calculating the possible pay-offs. This is a more realistic method which is used to determine the best values obtainable based on probabilities. The maximum likelihood criterion makes use of the best pay-offs in the highest probability row for the weekly demand. It only picks one value from the highest state of nature.Question 6a. maxmax decision criterion would give 60 pounds of steak since it has the highest value of $180b.

Using the minmax regret, we use the regret table whereby the highest values of the loss for the pounds supplied is taken. In this case, we have $120 for 20 pounds, $105 for 25 pounds, $60 for 40 pounds and $80 for 60 pounds. So picking the lowest value from the obtained maximum losses, we get $60 for 40 pounds. So by supplying 40 pounds Geoffrey will make minimum losses.c.  measure of realism    20254060MR$60.0 $57.50 $50.0 $40.0 So the appropriate decision is to supply 20 pounds of steak since it has the highest MR.

Question 7The food store will be willing to pay $32 since the highest possibility of the pay offs from the maximum likelihood is $120.Part BQuestion 8When there is a single doctor working in the emergency room, and he takes 5minutes to attend to one patient, therefore it means that the doctor will serve 12 patients in an hour. Since the arrival rate of the patients is 14/hour, then a queue is expected. When another doctor is introduced and are working together, that means it is a single model.

Question 9The appropriate operating characteristic for this single queue model is the average number of patients waiting to see a doctor and in this case it should not be more than 6 patients. The model has an arrival rate which is exponentially distributed and the patients follow the first come first served. Question 10The formula above is used to show the expected number of patients in the queue. The administrator wants at most six patients in the queue and the least number of doctors required to meet the requirement will be given by substituting Lq with 6 (Lq