Please solve only mathematical model. Devision variable, objective functions and
ID: 469111 • Letter: P
Question
Please solve only mathematical model. Devision variable, objective functions and constraints using ILP Model only. Thanks! PLease include explanation and complete model
Every power Company has a base-load demand that is relauvely LULIDLaLLL. satisfy this base-load demand, a power company utilizes its most economical, -cost power generating assets and keeps them running continuously. To meet additional demands for power above the base-load, a power company must dis patch (or turn on) other generators. These other generators are sometimes called peakers" because they help the power company meet the highest demands or peak-loads. It costs different amounts of money to bring different types of peakers on-line. And because different peakers use different types of fuel (eg, coal, gas, bio-mass), their operating costs per megawatt MW) generated also differ. Thus, ispatchers for a power company continually have to decide which generator to bring on-line or turn off to meet their load profile in the least costly manner The Old Dominion Power (ODP) Company provides electrical power roughout Virginia and the Carolinas. Suppose ODP's peak-load profile (that is the estimated load above base-load) in MWs is currently estimated as follows: U Day Load (in MWs) 4,300 3,700 3,900 4,000 4,700 4,800 3,600 ODP currently has three peaking generators off-line that are available to help leet this load. The generators have the following operating characteristics: Generator Location Startup cost Cost per Day Maximum MW Capacity per Day New River Galax James River $800 $1,000 $700 $200 + $5 per MW $300 + $4 per MW $250 + $7 per MW 2,100 1,900 3,000 To get an off-line generator up and running, a startup cost must be paid. Once generator is running, it can continue to run indefinitely without having to pay this startup cost again. However, if the generator is turned off at any point, the etup cost must be paid again to get it back up and running. Each day that a gen rator runs, there is both a fixed and variable cost that must be paid. For example, iy day that the New River generator is on-line, it incurs a fixed cost of $200 plus per MW generated. So, even if this generator is not producing any MWs, it still sts $200 per day to keep it running (so as to avoid a restart. When they are run ning, each generator can supply up to the maximum daily MWs listed in the final slumn of the tableExplanation / Answer
Lets calculate the cost of every Generator Location .
Cost per day = Fixed Cost + Variable cost * Number of Units per day .
Cost at location New River = 200 + 5 * 2100 ( full capacity ) = 10700
Cost at Galax = 300 + 4 * 1900 ( Full capacity ) = 7900
Cost at James River = 250 + 7 * 3000 ( Full capacity ) = 21250
Below mentioned table shows the cost at maximum capacity at each location
Now as per the table above the cost at Galax will be less . So assume that generation starts with Galax , then New River and then at james river.
Now as per the given info, the load on 1st day is 4300. So if the production is done in Galax , then total units produced is 1900 and 2100 units will be produced at New River and Balance 300 units will be produced at James River.
So the startup cost at all the 3 location is included in cost= 1000 ( startup cost at Galax ) + 800 ( startup cost at New River) + 700 ( startup cost at Jsmes River ) = $ 2500
Fixed Cost = 300 + 200 + 250 = 750
Variable cost = 4 ( variable cost at galax ) * 1900 + 5 ( variable cost at New River ) * 2100 + 7 ( variable cost at James River) * 300 = 20200
Total cost on day 1 = 2500 ( Startup Cost ) + 750 ( Fixed Cost ) + 20200 ( Variable cost) = $ 23450
Similarly at Day 2 : Generators at Galax and New River are enough to satify the load . So Generator at James river will be shut down .
Generators at Galax and New river will be used to satify the load of all the days . Genrator at James River will be again started on Day 5 . So again startup cost is included to run the genrator on day 5 . Generator at James River will be stopped after day6 .
Please consider the minimum cost and units produced by genrators in each day as per the given load.
Generation Location Start up Fixed Cost Per Day variable cost Capacity Cost per day New River 800 200 5 2100 10700 Galax 1000 300 4 1900 7900 James River 700 250 7 3000 21250 Total 7000 39850