MIE376 Network Programming Formulation Problems
For each of the following probblems draw the appropriate network model, clearly marking the upper and lower bounds and the cost
per unit flow for each directed arc, and whether it is a minimization or maximization problem.
Priceler manufactures sedans and wagons. The number of vehicles that can be sold each of the next 3 months are shown below.
Each sedan sells for $8000 and each wagon for $9000. It costs $6000 to produce a
sedan and $7500 to produce a wagon. Every vehicle in inventory at the end of the
month incurs an inventory charge, $150 per sedan and $200 per wagon. During
each month at most 1500 vehicles can be produced. At the beginning of the first
month 1200 sedans and 100 wagons are available.
The ABC electric company owns 3 hydro-electric power generation stations: A, B and C. The stations are located at reservoirs
with dams across the Pristine River. Station A is located 10 Km upstream from station B, and station B is located 20 Km
upstream from station C. Water is measured in units of ML and electricity in units of MW. The only entry of water into the
Pristine River is at station A, 100 ML in each hour. Water travels down the river at an average speed of 10 Km/hr. For each
hour the station manager has to decide how much of the water arriving at the station is: a) “used” to generate electricity and
then allowed to proceed downstream, b) “spilled” to proceed downstream without producing electricity, and c) “stored” in the
reservoir for later use or spill. Each plant has a different generating efficiency determined by the drop in elevation at each
plant; the larger the drop, the larger the efficiency. The generating efficiencies at A, B, and C, are respectively 1.5, 4.2 and 8.5
MW/ML. Each plant also has a different maximum capacity determined by the size of the generating units at each plant. The
maximum capacities at A, B, and C are respectively 50, 100 and 150 MW of electricity for each hour. ABC’s hourly revenue is
calculated as the product of the hourly MW production at each plant times the hourly price of electricity (
). As a matter of
policy ABC always returns each reservoir by the end of the planning horizon to the same volume it had at the beginning of the
planning horizon. Formulate the problem of determining the generation and water release policy that maximizes the revenue
over an 8 hour planning horizon.
A catering company must meet it’s daily demand for clean napkins by either buying new napkins, using regular laundry
service which requires a full day turnaround, or special overnight service. Supplied with the demand for each of the next 5
days, and the costs for new napkins, regular laundry service, and overnight laundry service you have been asked to develop a
model which will minimize the cost of procuring the napkins over the next 5 days. The company currently has no napkins in
usable condition, clean or dirty, on the premises or at the laundry.