Introduction to Operations Research
DEPARTMENT OF APPLIED MATHEMATICS BSc Honours in Operations Research and Applied Statistics SMO 1101 Introduction to Operations Research TUTORIAL QUESTIONS
1. List and discuss the six major steps in the quantitative modeling process. 2. What is the difference between a i. descriptive and a normative model? ii. discrete and a continuous variable? 3. Show that the set ℜ n is a convex set. 4. Is the linearity assumption, in LP models, realistic in applications? 5. Print-Rite assembles printers for personal computers. These printers are assembled at five different points along the production line. Each production line consists of five work teams with different levels of skill. Each team can be assigned to any of the five assembly points. The following table gives the time, in minutes, to perform the tasks at each assembly point for the individual teams. Assembly 2 26 24 26 24 26 Point 3 40 30 28 36 30 4 30 32 36 30 40 5 26 18 18 20 24
Team A B C D E
1 20 22 24 20 20
Formulate a linear programming model that will minimize the total assembly time for a printer. 6. Why is implementation a difficult aspect of the quantitative modeling process?
Caston Sigauke 2006
1
7. A post office requires different numbers of full-time employees on different days of the week. The number of full-time employees required on each day is given in the table below. Employee Requirements for Post Office Day 1 = Monday Day 2 = Tuesday Day 3 = Wednesday Day 4 = Thursday Day 5 = Friday Day 6 = Saturday Day 7 = Sunday Number of Full-time Employees Required 17 13 15 19 14 16 11
Union rules state that each full-time employee must work five consecutive days and then receive two days off. The post office wants to meet its daily requirements using only fulltime employees. Formulate an LP model to minimize the number of full-time employees that must be hired. 8. The Suny Corporation, a manufacturer of VCRs (video cassette recorders), wants to plan its production and inventory levels for the next
1. List and discuss the six major steps in the quantitative modeling process. 2. What is the difference between a i. descriptive and a normative model? ii. discrete and a continuous variable? 3. Show that the set ℜ n is a convex set. 4. Is the linearity assumption, in LP models, realistic in applications? 5. Print-Rite assembles printers for personal computers. These printers are assembled at five different points along the production line. Each production line consists of five work teams with different levels of skill. Each team can be assigned to any of the five assembly points. The following table gives the time, in minutes, to perform the tasks at each assembly point for the individual teams. Assembly 2 26 24 26 24 26 Point 3 40 30 28 36 30 4 30 32 36 30 40 5 26 18 18 20 24
Team A B C D E
1 20 22 24 20 20
Formulate a linear programming model that will minimize the total assembly time for a printer. 6. Why is implementation a difficult aspect of the quantitative modeling process?
Caston Sigauke 2006
1
7. A post office requires different numbers of full-time employees on different days of the week. The number of full-time employees required on each day is given in the table below. Employee Requirements for Post Office Day 1 = Monday Day 2 = Tuesday Day 3 = Wednesday Day 4 = Thursday Day 5 = Friday Day 6 = Saturday Day 7 = Sunday Number of Full-time Employees Required 17 13 15 19 14 16 11
Union rules state that each full-time employee must work five consecutive days and then receive two days off. The post office wants to meet its daily requirements using only fulltime employees. Formulate an LP model to minimize the number of full-time employees that must be hired. 8. The Suny Corporation, a manufacturer of VCRs (video cassette recorders), wants to plan its production and inventory levels for the next