PRELIM 3
Closed book exam. Justify all work.
ORIE 321/521
April 15, 2008
1. (a) (20 points) Suppose the members of n committees C1 , . . . , Cn are drawn from a common pool of individuals i = 1, . . . , m ; i.e., Cj cfw_1, . . . , m , for j = 1, . . . , n

PRELIM 1
ORIE 3310/5310
Feb. 17, 2011
Closed book exam. Justify all work.
1. Consider again the following LP decomposition model from the homework assignment. The rst two
constraints are the linking constraints; the remaining constraints dene the two subp

PRELIM 4
Closed book exam. Justify all work.
ORIE 321/521
April 29, 2008
1. Suppose jobs j = 1, 2, . . . , n are available for processing at time 0. Job j requires t j units of processing time and each job may be assigned to any one of m identical machine

PRELIM 2
Closed book exam. Justify all work.
ORIE 321/521
March 13, 2008
1. In the context of the Bellman-Ford shortest path algorithm, suppose G = (V, E) is a digraph with vertices V = cfw_1, , n and arc cost data ci,j , (i, j) E , not necessarily nonneg

PRELIM 1
Closed book exam. Justify all work.
ORIE 321/521
February 26, 2008
1. Consider the following linear programming problem, to which the decomposition procedure is applied using two subproblems (SUB1, SUB2). The first two constraints are the linking

Prelim 1 Problem 2 rough grading guide
(a) Correct condition: 4 - 1 1 - 2 2 > 0 for some 1 , 2 such that 21 + 32 = 4 and 1 , 2 0. Grading: -2 pts points if the conditions on = (1 , 2 ) were missing; -1 pt if the inequality was not strict. (b) LP sufficien

PRELIM 2
ORIE 3310/5310
March 10, 2011
Closed book exam. Justify all work.
1. For an acyclic digraph G = (V, E ) with V = cfw_1, 2, . . . , n and edge lengths cij , (i, j ) E , we
studied the fundamental problem of determining a shortest (1, n) -path.
(a)

PRELIM 3
ORIE 3310/5310
April 7, 2011
Closed book exam. Justify all work.
1. The following classical model is known as the Caterers problem. Napkins can be laundered overnight
at a cost of $0.025 each, but with one days delay at the cheaper rate of $0.015

PRELIM 4
ORIE 3310/5310
May 3, 2011
Closed book exam. Justify all work.
1. For internet sales a company receives credit card payments from four regions of the country: West,
Midwest, East, South. The average daily value of the payments due to sales in the