10 PTS. II) SCHEDULING NURSING STAFF AT A CALL CENTER THE MANAGER OF THE CLEARWA

Question

 10 PTS.  II) SCHEDULING NURSING STAFF AT A CALL CENTER THE MANAGER OF THE CLEARWATER HOSPITAL WISHES TO STAFF A NURSE CALL CENTER FOR PATIENTS WITH ROUTINE CONCERNS OR WHO WISH A REFERRAL TO A PHYSICIAN.  THE CALL LINES ARE TO BE STAFFED FROM 3 A.M. TO MIDNIGHT ON A DAILY BASIS.  BRAD HOGAN, THE MANAGER, HAS DECIDED ON THE MINIMUM STAFF REQUIREMENTS FOR EACH THREE HOUR PERIOD OVER THE COURSE OF THE DAY. THESE ARE AS SHOWN IN THE TABLE BELOW.  EACH NURSE WILL BE ASSIGNED TO A SIX HOUR DAY (TWO CONSECUTIVE THREE HOUR TIME PERIODS).  IT IS DESIRED TO DETERMINE AN ASSIGNMENT OF NURSES TO EACH SIX  HOUR SHIFT IN SUCH A WAY AS TO TRY TO MINIMIZE THE COST OF STAFFING THE NURSE CALL CENTER.  NURSES WORKING BEFORE THE HOURS OF 9 A.M. OR AFTER THE HOURS OF 6 P.M. ARE PAID AT A RATE OF $32 PER HOUR.  NURSES WORKING BETWEEN THE HOURS OF 9 A.M. AND 6 P.M. ARE PAID AT A RATE OF $22 PER HOUR.  THE REQUIRED STAFFING LEVELS FOR EACH THREE HOUR TIME PERIOD ARE AS SHOWN BELOW:                              STAFF    TIME PERIOD            REQUIRED    3 AM  -  6 AM              15   6 AM  -  9 AM              18   9 AM  - 12 PM              22  12 PM  -  3 PM              25   3 PM  -  6 PM              21       6 PM  -  9 PM              17    9 PM  - 12 AM              15   BRAD WISHES TO DEVELOP A TENTATIVE SCHEDULE OF NURSING STAFF. FORMULATE THIS AS AN INTEGER PROGRAMMING PROBLEM, MAKING SURE TO DEFINE VARIABLES,AND WRITE YOUR OBJECTIVE FUNCTION AND CON- STRAINTS.  EXPLAIN WHY YOU WOULD USE INTEGER PROGRAMMING TO SOLVE THIS PROBLEM, AND NOT LINEAR PROGRAMMING.  YOU CAN ANS- WER THIS IN ONE SENTENCE.  DETERMINE A REASONABLE SCHEDULE USING AN APPROPRIATE TABLE.  YOU DO NOT HAVE TO USE THE COMP- UTER TO SOLVE THIS PROBLEM!!!!!  MAKE SURE TO INCLUDE A BRIEF SUMMARY AND INDICATE YOUR RESULTS IN THE FOLLOWING TABULAR FORMAT:                              #OF NURSES   DAILY COST FOR NURSE SHIFT  SHIFT TIME(S)    ON SHIFT   EACH NURSE ON SHIFT      1     2     3     4     5     6                    TOTAL # OF NURSES NEEDED?________________                  TOTAL DAILY COST FOR ALL NURSES?___________    

Explanation / Answer

Integer program:

Decision variables: X1, X2, .... X6 = Number of Baristas starting at hour 6AM, 8AM, 10AM, 12PM, 2PM, 4PM respectively.

Objective: Min 25*6*X1+(25*4+18*2)*X2+(25*2+18*4)*X3+(18*6)*X4+(25*2+18*4)*X5+(25*4+18*2)*X6

s.t.

X1 >= 10

X1+X2 >= 14

X1+X2+X3 >= 16

X2+X3+X4 >= 19

X3+X4+X5 >= 13

X4+X5+X6 >= 12

X6 >= 10

X1, X2, X3, X4, X5, X6 >= 0

X1, X2, X3, X4, X5, X6 integer

We need to use Integer programming, and not linear programming, because number of baristas can be integer only and not fractions.

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