Exam 4: Linear Programming Models

Exhibit 4-1A hospital emergency room requires different numbers of nurses on different days of the week. The number of full-time employees required to be working (i.e. not on call) each day is given in the table below. Hospital rules require that nurses work four consecutive days, are on call for one day, and then receive two days off. The hospital wants to meet its daily requirements, while minimizing the number of nurses that must be on staff. Mon Tue Wed Thu Fri Sat Sun 18 15 12 13 20 28 22 -Refer to Exhibit 4-1. Use Solver to formulate and solve the hospital's problem.

Multiple optimal solutions are quite common in linear programming models.

If Xij refers to the number of hours employee i works in week j , then to indicate that the number of working hours of 4 employees in week 3 should not exceed 160 hours, we must have a constraint of the form

In aggregate planning models, the number of workers available influences the possible production levels.

Solver does not offer a sensitivity report for models with integer constraints.

When a workforce scheduling problems is formulated as an integer programming model, it has:

In blending problems, if a quality constraint involves a quotient, then the problem will be nonlinear.

Exhibit 4-4 A company blends nitrogen and phosphorous to produce two types of fertilizers. Fertilizer 1 must be at least 50% nitrogen and sells for $55 per pound. Fertilizer 2 must be at least 55% phosphorous and sells for $45 per pound. The company can purchase up to 9000 pounds of nitrogen at $20 per pound and up to 12,000 pounds of phosphorous at $12 per pound. -Refer to Exhibit 4-4. Suppose the company could acquire 1,000 pounds more of either nitrogen or phosphorous. Which should it choose? What would be the resulting impact on profit?

Exhibit 4-1A hospital emergency room requires different numbers of nurses on different days of the week. The number of full-time employees required to be working (i.e. not on call) each day is given in the table below. Hospital rules require that nurses work four consecutive days, are on call for one day, and then receive two days off. The hospital wants to meet its daily requirements, while minimizing the number of nurses that must be on staff. Mon Tue Wed Thu Fri Sat Sun 18 15 12 13 20 28 22 -Refer to Exhibit 4-1. Suppose the hospital has 40 nurses and is not allowed to hire or fire any employees, and cannot temporarily schedule nurses on their on call days. Determine a schedule that maximizes the number of weekend days off received by the nurses.

An advertising model in which we try to determine how many excess exposures we can get at different given budget levels is an example of a:

Exhibit 4-2A construction company is preparing for a nine-month project, and will need to develop a staffing plan. The company can assign up to 30 of its own full-time employees to the project, and will hire short-term contract employees to make up any shortage in meeting the personnel requirements. Company employees earn $6,000 per month, while short-term contract employees make $8,600/month. Contract employees can be assigned to the project beginning in any month, and their contract period is two months. The number of workers required for the project by month is shown below: Month of Project 1 2 3 4 5 6 7 8 9 Required 15 23 59 65 71 77 64 43 21 -Refer to Exhibit 4-2. The project manager is evaluating options to complete the project early so that the company can earn a bonus. He has determined that the project schedule can be compressed into a six-month schedule, with the same total number of worker-months. In that case, the staffing requirements are as shown below.Develop an optimal staffing plan for the project under the accelerated schedule. Month of Project 1 2 3 4 5 6 Required 26 38 84 105 101 84