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2-658-03 Introduction to Operations Research Group Assignment #2, Winter 2010 (team of 2-5 students) Deadline: Thursday, April 1st, 2010, 4 p. Submit...

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2-658-03 Introduction to Operations Research Group Assignment #2, Winter 2010 (team of 2-5 students) Deadline: Thursday, April 1 st , 2010, 4 p.m. Submit to the secretariat of MQG (office 4.632). Clearly indicate your names, ID numbers and group (A01). 2-658-03 Assignment 2 – Winter 2010 Page 1 of 6 PROBLEM 1 (Network Modeling) 25 points MRO Airlines offers 6 daily flights between Montreal and Toronto. From 10 a.m. to 8 p.m., a flight leaves Montreal every two hours. A ticket for any of these flights costs $300. The aircraft that serve the three first flights have a capacity of 50 passengers while the ones for the later three flights can accommodate up to 75 passengers. If too many tickets were sold for a flight (typically referred as an overbooked flight), some passengers will need to be re-assigned to some later flights. The monetary compensation for delaying a passenger is expressed in the following table: Delay Compensation 2 hours $70 4 hours $90 6 hours $130 8 hours $170 10 hours $230 12 hours $290 For example, a passenger that purchased a ticket for the 10 a.m. flight and ends up being re-assigned to the 12 p.m. flight will receive $70 in compensation. Passengers that are not re-assigned to one of the six flights of MRO Airlines will be assigned to a flight at 10 p.m. that is offered by a different airline company. Since this 10 p.m. flight is not very popular, one can assume that it does not have a maximum capacity. The number of tickets that were sold for next Monday’s flights are described in the following table: Departure time Number of tickets sold Maximum capacity 10 a.m. 55 50 12 p.m. 60 50 2 p.m. 48 50 4 p.m. 75 75 6 p.m. 81 75 8 p.m. 71 75 MRO Airlines would like to find out the flow of passengers that will lead to the lowest total amount of compensations. Use the concepts that you learned in sessions 6 and 7 to help MRO Airlines make these decisions. a) Draw a complete network representation (nodes, arcs, bounds, costs, and external flows) that can be used to solve this problem. (12 points) b) With Excel, solve the linear program associated with this network. Make sure that your spreadsheet is consistent with your answer for question a) : i.e., all the variables and constraints should be the same as those that are associated to your proposed network. (10 points) c) Describe the optimal solution (i.e., for each flight, how many passengers are taking the flight, how many will be re-assigned to this flight, and how many ticket holders for this flight will be delayed). (3 points)
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2-658-03 Assignment 2 – Winter 2010 Page 2 of 6 PROBLEM 2 (Binary linear programming) 35 points In Québec, the aging population, the congestion of hospitals, and the increasing demand for health care are all factors that encourage us to reconsider how health care is managed. Authorities have become more interested in putting in place a structure where a larger range of cares can be provided at one’s home. Proper organization and synchronization of human resources is critical to the success of such a project. In the city of Saint-Operational, Modeline is the head nurse in charge of coordinating the work load of a team of nurse that provide care at home. Obviously, not all of their patients require the same amount of care; the respective amount of care needed by each patient is called his (or her) acuity. Each nurse is responsible for a group of patients and the sum of acuity in this group is considered her total work load. According to labour standards the work load of a nurse should not be larger than a maximum amount. This maximum work load will however depend on the nurse’s number of years of experience. This is because a more experienced nurse will be more efficient at taking care of a patient. Years of experience [0; 0,5] [0,5; 3] [3, 8] [8, 20] Maximum total acuity 50 67 72 77 The team dedicated to care at home in Saint-Operational is composed of 5 nurses. Some information about each of them is presented in the following table: Nurse Sex Years of experience 1 F 7 2 F 0,25 3 M 4 4 F 12 5 M 1,5 In order to ensure that the total work load is evenly distributed among the nurses, Modeline wishes that each nurse be responsible for at least 3 patients and not more than 5 patients in her day of visits. Next is the list and characteristics of each patient in Saint-Operational: Patient Sex Acuity Zone 1 F 10 A 2 F 16 A 3 M 15 A 4 M 14 A 5 M 12 A 6 F 18 B 7 M 16 B 8 F 11 B 9 M 12 B 10 M 21 C 11 M 9 C 12 F 6 C 13 F 8 C 14 F 18 C 15 F 22 C 16 M 7 C 17 F 13 D 18 M 16 D 19 M 17 D 20 F 8 D
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