# Mama Kitchen

Submitted By sampating
Words 656
Pages 3
A LINGO model of a staffing problem
Decision variables
Xi = the # of employees who start to work on ith shift. ( i = 1, 2, ... , 6 )

LP Formulation
MIN 36 X1 + 36 X2 + 36 X3 SUBJECT TO X1 X1 + X2 X1 + X2 + X3 X1 + X2 + X3 + X4 X2 + X3 + X4 + X5 X3 + X4 + X5 + X4 + X5 + X5 +
©Dennis Bricker Dept of Mechanical & Industrial Engineering The University of Iowa

+ 30 X4 + 30 X5 + 30 X6 2 3 5 5 3 2 4 6 3 (min # of busers on duty at 5am) (min # of busers on duty at 6am) (min # of busers on duty at 7am) (min # of busers on duty at 8am) (min # of busers on duty at 9am) (min # of busers on duty at 10am) (min # of busers on duty at 11am) (min # of busers on duty at 12pm) (min # of busers on duty at 1pm) (Sign restrictions)

Xi >= 0

>= >= >= >= >= X6 >= X6 >= X6 >= X6 >= (for i = 1,2,3,4,5,6)

Mama’s Kitchen

9/9/2002

page 1 of 8

Mama’s Kitchen

9/9/2002

page 3 of 8

“Mama’s Kitchen” serves from 5:30 a.m. each morning until 1:30 p.m. in the afternoon. Tables are set and cleared by busers working 4-hour shifts beginning on the hour from 5:00 a.m. (shift #1) through 10:00 a.m. (shift #6). Most are college students who hate to get up in the morning, so Mama’s pays \$9 per hour for the 5:00, 6:00, and 7:00 a.m. shifts, and \$7.50 per hour for the others. The manager seeks a minimum cost staffing plan that will have at least a minimum number of busers on duty each hour: 5 am 2 6 am 3 7 am 5 8 am 5 9 am 3 10am 2 11am 4 Noon 6 1 pm 3

OBJECTIVE FUNCTION VALUE 1) 360.0000 VARIABLE X1 X2 X3 X4 X5 X6 ROW 2) 3) 4) 5) 6) 7) 8) 9) 10) VALUE 3.000000 0.000000 2.000000 0.000000 3.000000 3.000000 SLACK OR SURPLUS 1.000000 0.000000 0.000000 0.000000 2.000000 6.000000 2.000000 0.000000 0.000000 REDUCED COST 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 DUAL PRICES 0.000000 0.000000 -6.000000 -30.000000 0.000000 0.000000 0.000000 -30.000000 0.000000

#reqd...

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