Shell Deutschland is processing crude oil in their refineries in Frankfurt and Berlin with a daily production of 800 barrels (BBL) and 900 barrels (BBL), respectively. The processed product, Petroleum, is distributed to the oil terminals in Munich, Dresden, and Hamburg. Because there was an estimate that the demand would be increased, Shell Deutschland plans to increase the capacity by constructing a new refinery in one or more of the following cities: Stuttgart, Leipzig, or Bonn. The estimated annual fixed cost (in thousands) for Stuttgart is $550,000, Leipzig is $760,000, and Bonn is $990,000. The three proposed refineries' daily capacity is 360 BBL, 650 BBL, and 760 BBL, respectively. The Shell Deutschland consultants predict that the estimated daily demand at the oil terminals is 670 BBL for Munich, 960 BBL for Dresden, and 550 BBL for Hamburg. The Shell Deutschland consultants are also aware of the flooding between Bonn and Dresden, which means the route is unavailable. The moving cost per barrel in dollars from each refinery to each oil terminal is shown below. Refinery Stuttgart Leipzig Bonn Frankfurt Berlin Munich 5 4 2 3 2 Dresden 8 11 5 7 10 a) Draw a network representation of this problem. b) Clearly define all decision variables. Hamburg 13 9 5 12 c) Formulate the objective function clearly. d) Clearly specify all the constraints such that only constants appear on the right- hand sides of constraints. e) Write a single constraint showing that if Shell Deutschland is constructing in
Shell Deutschland is processing crude oil in their refineries in Frankfurt and Berlin with a daily production of 800 barrels (BBL) and 900 barrels (BBL), respectively. The processed product, Petroleum, is distributed to the oil terminals in Munich, Dresden, and Hamburg. Because there was an estimate that the demand would be increased, Shell Deutschland plans to increase the capacity by constructing a new refinery in one or more of the following cities: Stuttgart, Leipzig, or Bonn. The estimated annual fixed cost (in thousands) for Stuttgart is $550,000, Leipzig is $760,000, and Bonn is $990,000. The three proposed refineries' daily capacity is 360 BBL, 650 BBL, and 760 BBL, respectively. The Shell Deutschland consultants predict that the estimated daily demand at the oil terminals is 670 BBL for Munich, 960 BBL for Dresden, and 550 BBL for Hamburg. The Shell Deutschland consultants are also aware of the flooding between Bonn and Dresden, which means the route is unavailable. The moving cost per barrel in dollars from each refinery to each oil terminal is shown below. Refinery Stuttgart Leipzig Bonn Frankfurt Berlin Munich 5 4 2 3 2 Dresden 8 11 5 7 10 a) Draw a network representation of this problem. b) Clearly define all decision variables. Hamburg 13 9 5 12 c) Formulate the objective function clearly. d) Clearly specify all the constraints such that only constants appear on the right- hand sides of constraints. e) Write a single constraint showing that if Shell Deutschland is constructing in
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
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Transcribed Image Text:Shell Deutschland is processing crude oil in their refineries in Frankfurt and Berlin with a
daily production of 800 barrels (BBL) and 900 barrels (BBL), respectively. The
processed product, Petroleum, is distributed to the oil terminals in Munich, Dresden,
and Hamburg. Because there was an estimate that the demand would be increased,
Shell Deutschland plans to increase the capacity by constructing a new refinery in one
or more of the following cities: Stuttgart, Leipzig, or Bonn. The estimated annual fixed
cost (in thousands) for Stuttgart is $550,000, Leipzig is $760,000, and Bonn is
$990,000. The three proposed refineries' daily capacity is 360 BBL, 650 BBL, and 760
BBL, respectively. The Shell Deutschland consultants predict that the estimated daily
demand at the oil terminals is 670 BBL for Munich, 960 BBL for Dresden, and 550 BBL
for Hamburg. The Shell Deutschland consultants are also aware of the flooding between
Bonn and Dresden, which means the route is unavailable.
The moving cost per barrel in dollars from each refinery to each oil terminal is shown
below.
Refinery
Stuttgart
Leipzig
Bonn
Frankfurt
Berlin
Munich
5
4
2
3
2
Dresden
8
11
5
7
10
a) Draw a network representation of this problem.
b) Clearly define all decision variables.
Hamburg
13
6
9
5
12
c) Formulate the objective function clearly.
d) Clearly specify all the constraints such that only constants appear on the right-
hand sides of constraints.
e) Write a single constraint showing that if Shell Deutschland is constructing in
Leipzig, then Shell Deutschland must also construct in Bonn or Stuttgart or
both.
f) Write a single constraint that Shell Deutschland can construct in Bonn if Shell
Deutschland is constructing in Leipzig.
g) Write constraint/s to make sure that Shell Deutschland constructs at least 1 but
not more than 2 refineries.
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