Question

A community hospital is planning to expand its services to three new service lines in the medical diagnostic categories (MDC-2, MDC-19, and MDC-21). Five common resources must be allocated among these three new service lines according to which will bring the most revenue. The resources are LOS, nursing hours, radiology procedures, laboratory procedures, and operating rooms. The health care manager in charge of this expansion project obtained the average consumption patterns of these resources for each MDC from other peer institutions, and estimated the resources that can be made available (per year) for the new service lines as listed below. Based on the available information the average revenues from MDC - 2, MDC - 19, and MDC - 21 are $8,885, $ 10,143, and $12,711, respectively.

MDC-2	MDC-19	MDC-21	Available Resources
3.3	6.1	4.4	19,710
3	5	4.5	16,200
0.5	1		3,000
1	1.5	3	6,000
2	4		1,040

1. What are the decision variables?
2. What are constrains on manager's decision?
3. What is the Objective Function?
4. Using Excel Solver to solve the problem and answer the following questions:

1. Which service(s) should be offered to get the most revenue?

1. What are the optimal volumes for the service(s) to be offered?

1. What is the total expected revenue from the new services?

1. Looking at the Sensitivity report for Solver results, answer the following questions:

1.) Which resources should be expanded and,

2.) How much additional revenue can be expected if resources are selected for expansion without violating the current solution?

Answer 1

ANSWER::

(OR)   

5.1)

The table in the report is:

		Final	Shadow	Constraint	Allowable	Allowable
Cell	Name	Value	Price	R.H. Side	Increase	Decrease
$C$16	Length of stay	19444	0	19710	1E+30	266
$C$17	Nursing Hours	16170	0	16200	1E+30	30
$C$18	Radiology Procedures	3000	10143	3000	6	3000
$C$19	Lab. Procedures	5280	0	6000	1E+30	720
$C$20	Operating Room	1040	3177.75	1040	26.66666667	1040

For the resources which have a non-negative shadow price, if we expand those resources, there will be an increase in the optimal value of the desired function by the corresponding shadow price.

Hence, Radiology procedures and operating room resources should be expanded

5.2)

Allowable increase in radiology = 6

Allowable increase in operating room = 26

Hence, increase in optimal revenue = 6*10143 + 3177.75*26

= $143479.5

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