Dr. Maddah
ENMG 500 Engineering Management I
10/21/07
Computational Procedure of the Simplex Method
The optimal solution of a general LP problem is obtained in the
following steps:
Step 1. Express the problem in tableau form.
Step 2. Select a starting b

FHA network RM
Product
O
D
11, 12
21, 22
31, 32
41, 42
51, 52
61, 62
CDG
CDG
DXB
DXB
BEY
BEY
BEY
DXB
BEY
CDG
DXB
CDG
Revenue
Capacity constraints
actual available
70
70
70
70
50
50
50
50
Demand
Fares
Class 1 Class 2 Class 1 Class 2
13
11
14
12
12
11
$25,2

A Capital Budgeting Problem
Welend Bank is in the process of devising a loan policy that
involves a maximum of $12 million. The following table provides
the pertinent data about available types of loans.
Type of loan
Interest rate Bad debt %
Personal
14%

Dr. Maddah
ENMG 500 Engineering Management I
11/29/06
The transportation problem (TP) involves
a) Finding the best way for moving stuff around.
b) Reducing storage costs.
c) Reducing shipping costs.
d) Time traveling at warp speed.
In the TP, destinatio

Dr. Maddah
ENMG 500 Engineering Management I
11/29/06
The dual simplex method
a) Solves the dual first and then obtains primal solution.
b) Starts with dual feasibility & converges to primal feasibility.
c) Utilizes two (deux) simplex tableaus.
d) Starts

Dr. Maddah
ENMG 500 Engineering Management I
11/29/06
Changing the right hand side of a LP affects
a) Optimality conditions.
b) Weather conditions.
c) Political conditions.
d) Feasibility Conditions.
Changing the right hand side of a LP will
a) Always c

Dr. Maddah
ENMG 500 Engineering Management I
11/29/06
Every LP has a second half called
a) Spouse.
b) Partner.
c) Girl friend.
d) Dual.
The dual of the dual of the dual of the dual of the dual is the
a) Primal.
b) Primer.
c) Dual.
d) Mother in-law.
Com

Dr. Maddah
ENMG 500 Engineering Management I
11/29/06
Changing the objective functions of a LP affects
a) Optimality conditions.
b) Synergy conditions.
c) Feasibility conditions.
d) Amers Mussa conditions.
For a min problem, the reduced cost of a nb var

Dr. Maddah
ENMG 500 Engineering Management I
10/17/06
In a LP with 2 variables and 3 constraints, a basis has
a) Exactly 2 variables .
b) Exactly 3 variables .
c) 2 or more variables.
d) 3 or more variables.
There are four variants of the simplex method

Dr. Maddah
ENMG 500 Review Quiz 2
10/04/06
Consider the modified BM company problem.
A good solution is
a) E(4, 9)
b) F(0, 3)
F
c) C(2,0)
d) A(0,1)
A feasible solution is
a) O(0, 0)
b) F(0, 3)
c) H(1, 1)
d) E(4, 0)
The optimal objective value, Z*, is s

Workforce Scheduling
A post office requires different number of full-time
employees on different days of the week. The number of full-time
employees required on each day is as shown below. Union rules
state that each full-time employee must work five cons

Airline Network Revenue Management
Lebanons first private airlines, Fly High Airlines (FHA), operates between
three cities, Dubai (DXB), Paris (CDG), and Beirut (BEY) (see Figure 1).
FHA utilizes Beirut as a hub and flies one round-trip daily between Beir

Marriage Theorem
Brad Pitt, Ben affleck, and Tobey Mcguire are marooned
(abandoned) on a desert island with Jennifer Aniston, Jennifer
Lopez and Reese Witherspoon. The compatibility measures in
Table 2 indicate how much happiness each couple would
experie

American University of Beirut
Faculty of Engineering and Architecture
Engineering Management Program
ENMG 500 Engineering Management I
Fall 2009, CRN 11332, TTH: 11:00 AM - 12:15 PM, Bechtel 208
Instructor
Bacel Maddah, Ph.D.
Oce: Bechtel 519A. E-mail: ba

Dr. Maddah
ENMG 500 Engineering Management I
11/28/06
The Dual Simplex Method
Underlying Theory
Consider the LP (P) and its dual (D)
(P) min
s.t.
Z = cx
Ax b
y
(D) max
s.t.
x0
w = by
yA c
y0
The primal (P) optimality conditions are
z j c j 0, for all v

Temporary website http:/filebox.vt.edu/users/bmaddah/ENMG_500/
Dr. Maddah
ENMG 500 Engineering Management I
10/12/05
A complete example on simplex method in tabular form
Consider the LP
max Z = 3x1 + 2 x2 + 5 x3
s.t.
x1 + 2 x2 + x3 430
3x1 +
+ 2 x3 460

American University of Beirut
Faculty of Engineering and Architecture
Engineering Management Program
ENMG 500 Engineering Management I
Fall 2012, CRN 10355, TTH: 11:00 AM - 12:15 PM, ALH
Instructor
Bacel Maddah, Ph.D.
Oce: Bechtel 519A. E-mail: bacel.madd

LP for RM problem. Let x1 and x2 be the amounts of exterior and interior
paints produced respectively.
max 5 x1 + 4 x2
subject to
6 x1 + 4 x2 24
x1 + 2 x2 6
x1 + x2 1
x2 2
x1 , x2 0
Suppose RM uses quantity discounts for the sales of exterior paint. If m

B. Maddah
ENMG 500 Class Project
12/03/12
(Hotel Revenue Management) Its Wednesday evening, the manger at down
town Beirut Stay Here Hotel (SHH) is planning the capacity control policy for
Thursday, Friday and Saturday nights. SHH manager is not concerned

A Production Planning Problem
Acme Manufacturing Company has received a contract to deliver
home windows over the next 6 months. The successive demands
for the six periods are 100, 250, 190, 140, 220, and 110,
respectively. Production cost for window vari

Illustration of Analytical Verification of
Blocking
Simplex Iteration: O A, S1 = 6 2x2 , S2 = 4 4x2 ,
Suppose the move from O to A has a step of 1/3 (actual
step 0),
Increase x2 ,1 move 2to (0, 1/3) S= = 6 20 = 6 , S2 ,=S2 = 4 41/3
S1 1 6 21/3 = 16/3 4
A

Dr. Maddah
ENMG 500 Review Quiz 1
10/04/06
OR stands for
a) Operating Room
b) Ossama Rahbani
c) Operations Research
d) Operational Research
A model is
a) A good fellow
b) A map or blueprint
c) An abstract representation of the real world
d) Cindy Crawfo

Dr. Maddah
ENMG 500 Engineering Management I
10/17/06
The Big-M method starts with an initial solution,
a) which is feasible.
b) which is infeasible.
c) which corresponds to the origin O.
d) which is a pain in the neck.
How big should big M be?
a) M = 1

Dr. Maddah
ENMG 500 Engineering Management I
10/17/06
George Dantzig invented
a) The washing machine
b) The simplistic method
c) The method of the samurai
d) The simplex method
A corner point is
a) The intersection of exactly two constraints in a 2-vari

Dr. Maddah
ENMG 500 Engineering Management I
11/28/06
Duality (Continuous) Economic Interpretation of duality A resource allocation example. Dakota furniture company manufactures desks, tables and chairs. The manufacturing of each type of furniture requir

Dr. Maddah
ENMG 500 Engineering Management I
11/28/06
The Dual Simplex Method Underlying Theory Consider the LP (P) and its dual (D)
(P) min s.t. Z = cx Ax b x0 y (D) max s.t. w = by yA c y0
The primal (P) optimality conditions are
z j c j 0, for all vari

Dr. Maddah
ENMG 500 Engineering Management I
11/1/06
Duality Overview Every LP problem has a twin problem associated with it. One problem is known as the primal, and the other as the dual. The properties of the two problems are closely related, and they h

Dr. Maddah
ENMG 500 Engineering Management I
11/03/09
Simplex method in matrix form (revised simplex method) A LP with n decision variables and m constraints can be written as
max Z = cx s.t. Ax = b x0 x1 x c = ( c1 , c2 , c3 ,K, cn ) , x = 2 , M x n a11

Dr. Maddah
ENMG 500 Engineering Management I
10/21/07
Computational Procedure of the Simplex Method The optimal solution of a general LP problem is obtained in the following steps: Step 1. Express the problem in tableau form. Step 2. Select a starting ba