More Advanced Optimization

  Advanced optimization techniques are often necessary to solve real problems in health care. Techniques like goal programming and data envelopment analysis are often used to solve multiple objective problems, such as minimizing cost while maximizing access measures. Other advanced techniques are often required for problems that sometimes seem straightforward. Although you may not encounter the use of advanced optimization techniques on a day-to-day basis, understanding the methodology and application of these techniques is a valuable skill for the healthcare administration leader. For this Assignment, review the resources for this week. Reflect on, and consider, the advanced optimization techniques highlighted. Think about how you might apply these advanced optimization techniques to healthcare delivery challenges in a health services organization. For Chapter 14, problems 80 and 90, you will need to download the files P14_80.xlsx and P14_90.xlsx (attached). The Assignment: (5 pages) • Complete Problem 80 (pharmaceutical company) and Problem 90 (brain tumor) on pages 751 and 753 of your course text (Problems are below). Note: You will be using Excel and Solver for this Assignment. By Day 7 Submit your answers and embedded Excel analysis as a Microsoft Word management report. The Problems Problem 80 A pharmaceutical company produces the drug NasaMist from four chemicals. Today, the company must produce 1000 pounds of the drug. The three active ingredients in NasaMist are A, B, and C. By weight, at least 8% of NasaMist must consist of A, at least 4% of B, and at least 2% of C. The cost per pound of each chemical and amount of each active ingredient in one pound of each chemical are given in the fileP14_80.xlsx. It is necessary that at least 100 pounds of chemical 2 and at least 450 pounds of chemical 3 be used. a. Determine the cheapest way of producing today’s batch of NasaMist. b. Use Solver Table to see how much the percentage of requirement of A is really costing the company. Let the percentage required vary from 6% to 12%.   Based on Sonderman and Abrahamson (1985). In treating a brain tumor with radiation, physicians want the maximum amount of radiation possible to bombard the tissue containing the tumors. The constraint is, however, that there is a maximum amount of radiation that normal tissue can handle without suffering tissue damage. Physicians must therefore decide how to aim the radiation so as to maximize the radiation that hits the tumor tissue subject to the constraint of not damaging the normal tissue. As a sample example of this situation, suppose there are six types of radiation beams (beams differ in where they are aimed and their intensity) that can be aimed at a tumor. The region containing the tumor has been divided into six regions: three regions contain tumors and three contain normal tissue. The amount of radiation delivered to each region by each type of beam is shown in the file (14_90.xlsx. If each region of normal tissue can handle at most 60 units of radiation, which beams should be used to maximize the total amount of radiation received by the tumors?