(Solution) IEOR 4601 Assignment 8 1. In Class We Considered A Network Problem With Two Resources And Three Itineraries, With Two Fares Per Itinerary And... | Snapessays.com

(Solution) IEOR 4601 Assignment 8 1. In class we considered a network problem with two resources and three itineraries, with two fares per itinerary and...

Need some help on dynamic pricing questions with network problems, deterministic linear programming, etcIEOR 4601 Assignment 8

1. In class we considered a network problem with two resources and three itineraries, with

two fares per itinerary and illustrated a variety of heuristics for that problem. Here

we will consider an expanded model with the same three itineraries but with Fve fares

per itinerary. Itinerary one, consumes one unit of resource one and has Fve fares:

185

,

160

,

150

,

135

,

100. Itinerary two, consumes one unit of resource two and has Fve

fares: 130

,

115

,

95

,

80

,

75. Itinerary three, consumes one unit of each resource and has

Fve fares: 260

,

240

,

220

,

195

,

170. Using the single index model the incidence matrix

A

is given by

A

=

?

111110000011111

000001111111111

?

and the fare vector by

p

=(185 160 150 135 100 130 115 95 80 75 260 240 220 195 170)

.

Assume a discrete time model with

T

=1

,

000 periods and time varying arrival rates

given by

?

t

=(

.

00

.

00

.

015

.

036

.

054

.

00

.

00

.

015

.

04

.

06

.

00

.

00

.

01

.

03

.

03 )

for 501

?

t

?

1000 and

?

t

=(

.

02

.

04

.

015

.

00

.

00

.

03

.

04

.

015

.

00

.

00

.

04

.

02

.

01

.

00

.

00 )

for 1

?

t

?

500. The initial vector of capacities is

c

=(100

,

120 )

.

All vectors should be interpreted as column vectors (although for convenience we write

them as row vectors).

a) ±ind the aggregate arrival rate

?

Tj

=

R

T

?

tj

dt, j

=1

,...,

15 for the 15 OD±s.

1

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