hw02solutions

hw02solutions - IEOR 162 Linear Programming Spring 2007...

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IEOR 162 Linear Programming Spring 2007 Homework 2 Solutions 3.5.1 (4 points) Data: h i = number of labor hours required for day i d ij = 1 if a worker who starts on day i is working on day j Variables: x i = number of full-time workers to hire that start their week on day i y i = number of part-time workers to hire that start their week on day i Formulation: min 15 7 i =1 8 x i + 10 7 i =1 4 y i s.t. 8 7 i =1 d ij x i + 4 7 i =1 d ij y i c j j = 1 , . . . , 7 (1) . 25 ± 7 i =1 8 x i + 7 i =1 4 y i ² 7 i =1 4 y i (2) x i , y i 0 i = 1 , . . . , 7 (3) The objective minimizes the total cost of labor per week. Constraint set 1 ensures that each day’s labor requirements are met. Constraint 2 ensures that part-time labor comprises no more than 25% of the total labor used. Finally, constraint set 3 ensures that all variables are non-negative. 3.5.7 (4 points) Data: T = the set of time periods (i.e. 10am, 11am, etc.) c t = number of checks received at time t
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hw02solutions - IEOR 162 Linear Programming Spring 2007...

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