This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: IEOR 162, Fall 2011 Suggested Solution to Homework 02 Problem 1 (Problem 3.5.5) To formulate this problem, we label the four shifts as in the following table. Shift Number 1 2 3 4 Time 0  6 6  12 12  18 18  24 The decision variables are x ij = number of officers working at shifts i and j , i = 1 ,..., 4, j = i + 1 ,..., 4. The problem can then be formulated as min 144( x 12 + x 23 + x 34 + x 14 ) + 216( x 13 + x 24 ) s.t. x 12 + x 13 + x 14 15 (Demand in shift 1) x 12 + x 23 + x 24 5 (Demand in shift 2) x 13 + x 23 + x 34 12 (Demand in shift 3) x 14 + x 24 + x 34 6 (Demand in shift 4) x i i = 1 ,..., 4 . Here 144 = 12 12 is the per worker wage for one who works in two consecutive shifts. Similarly, 216 = 18 12 is that for one who works in two nonconsecutive shifts. 1 The objective function minimize the total payments while the constraints guarantee that there are enough workers for every shifts. 2 Problem 2 (Problem 3.8.2) Let x 11 = number of pounds of grade 9 oranges sold in bags, x 12 = number of pounds of grade 9 oranges used to produce juice, x 21 = number of pounds of grade 6 oranges sold in bags, and x 22 = number of pounds of grade 6 oranges used to produce juice....
View
Full
Document
This note was uploaded on 10/24/2011 for the course IEOR 162 taught by Professor Zhang during the Fall '07 term at University of California, Berkeley.
 Fall '07
 Zhang

Click to edit the document details