PROBLEM 2

Sequoia Clinic is a private hospital that has a fluctuating demand for nursing care, since some days typically have higher admissions of patient than others. Management of the Clinic is trying to set up a work schedule for full time nurses that will allow them two consecutive days off each week. Clinic can also hire part-time nurses who will work a Friday-Sunday-Monday schedule. Daily pay for a full-time nurse is $120, except for Saturdays and Sundays when they earn $150 and $180 respectively. Part-time nurses earn $240 per 3-day workweek. The minimum required number of nurses on duty each day of the week is given in table below.

Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
17	14	12	15	22	10	15

A cost-minimizing model to determine the number of full-time nurses that should start their workweek each day of the week and the number of part-time nurses that should be hired is formulated and solved below.

The following decision variables are used:

MON, TU, WED, TH, FR, SA,SU = the number of full-time nurses who start 5 consecutive day shifts on Monday, Tuesday, etc., respectively

P = the number of part-time nurses who work a Friday-Sunday-Monday schedule.

MinZ = 600MON + 630TU + 690WED + 690TH + 690FR + 690SA + 660SU + 240P

Subject to

C1 1MON + 1TH + 1FR + 1SA + 1SU + 1P >= 17 Monday requirement

C2 1MON + 1TU + 1FR + 1SA + 1SU >= 14 Tuesday requirement

C3 1MON + 1TU + 1WED + 1SA + 1SU >= 12 Wednesday requirement

C4 1MON + 1TU + 1WED + 1TH + 1SU >= 15 Thursday requirement

C5 1MON + 1TU + 1WED + 1TH + 1FR + 1P >= 22 Friday requirement

C6 1TU + 1WED + 1TH + 1FR + 1SA >= 10 Saturday requirement

C7 1WED + 1TH + 1FR + 1SA + 1SU + 1P >= 15 Sunday requirement

***** POM Program Output *****

Z =12180.000

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Variable Value Reduced Cost

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MON 2.000 0.000

TU 9.000 0.000

WED 0.000 180.000

TH 1.000 0.000

FR 0.000 60.000

SA 0.000 60.000

SU 3.000 0.000

P 11.000 0.000

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Constraint Slack/Surplus Shadow Price

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C1 0.000 -180.000

C2 0.000 -180.000

C3 2.000 0.000

C4 0.000 -240.000

C5 1.000 0.000

C6 0.000 -210.000

C7 0.000 -60.000

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Objective Coefficient Ranges

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Lower Current Upper AllowableAllowable

Variables Limit Values Limit Increase Decrease

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MON 420.000 600.000 660.000 60.000 180.000

TU 450.000 630.000 660.000 30.000 180.000

WED 510.000 690.000 No limit No limit 180.000

TH 630.000 690.000 870.000 180.000 60.000

FR 630.000 690.000 No limit No limit 60.000

SA 630.000 690.000 No limit No limit 60.000

SU 600.000 660.000 840.000 180.000 60.000

P 60.000 240.000 260.000 20.000 180.000

Right Hand Side Ranges

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Lower Current Upper Allowable Allowable

Constraints Limit Values Limit Increase Decrease

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C1 16.500 17.000 20.000 3.000 0.500

C2 13.000 14.000 15.000 1.000 1.000

C3 No limit 12.000 14.000 2.000 No limit

C4 14.000 15.000 15.500 0.500 1.000

C5 No limit 22.000 23.000 1.000 No limit

C6 9.500 10.000 13.000 3.000 0.500

C7 12.000 15.000 16.000 1.000 3.000

***** End of Output *****

QUESTIONS FOR SEQUOIA CLINIC (treat each question independently)

1. What is the minimum cost of staffing the clinic for one week?

1. How many full-time and how many part-time nurses are required?

1. On which day of the week the minimum number of nurses required was exceeded? By how many?

1. By how much can the wages of part-time nurses increase without their affecting the optimal solution?

1. If you could reduce admissions on one of the days of the week so that this day's nurse requirement would be reduced, on which day should you attempt to do it? Why?

1. If you could shift admissions from one day to another and thus reduce stuffing requirement from one day to another, what day's requirement you would attempt to reduce and what day's requirement you would attempt to increase? Explain why. What affect, if any, will the change have on weekly cost?

1. If you could cut the daily pay for those full-time nurses who's 5-day work week does not include either Saturday or Sunday by $10 per day, how would this affect the weekly cost of staffing the clinic? Would the optimal staffing schedule change?

1. If one of the part-time nurses called in and informed the hospital that she is not able to work on Friday, but will be working her Monday and Sunday schedule. Will the hospital be able to meet the daily requirement without changing the staffing schedule? Explain why or why not. How does the weekly cost change?

1. Suppose you would like to reduce the weekly pay for those nurses who start their 5-day work week on Thursday and Sunday by of $20 and $10 respectively. Would this affect your optimal staffing schedule? What about the weekly cost?

1. You can reduce the weekly pay for full-time nurses by $20, but only for one type of shift, i.e. you could give this reduction to either to all nurses who start on Monday, or to all nurses who start on Tuesday, ... etc., or to all nurses who start on Sunday. Where should you reduce the wages then? Explain why.