![]() They must equal integers (thus, this is an integer program), and in particular they can only equal the integers 0 or 1. yij = 1 if the closest truck to customer i∈I is at location j∈J (i.e., if i is assigned to j), and 0 otherwiseīoth xj and yij are binary decision variables.xj = 1 if we locate a truck at location j, and = 0 otherwise, for each j∈J.Our model also has decision variables. These are the unknowns, or the choices to be made by the decision maker (whether that’s Guroble planners or the optimization solver): f = fixed cost that Guroble has to pay for placing a truck at a potential location.This multiplier depends on the distance: the further a customer i is from a truck location j, the less willing the customer is to walk to the truck αij = demand multiplier for customer i∈I and truck j∈J.cij = travel distance from customer i∈I to truck j∈J.(These are the inputs, or data, for the model.) Let I denote the set of buildings (we’ll call them customers now) and let J denote the set of potential truck locations. Our IP uses the following notation for the parameters of the model. Now let’s get into some more detail about the IP itself, for those who have an appetite for the math. Sometimes these are symmetric, meaning the demand is equally likely to be greater than or less than the forecast. On some days during Round 2, you’ll see error bars telling you the range of values the actual demand will fall into. But since both solutions are evaluated based on actual demands, it’s possible that your solution can be better than Gurobi’s, if you get a lucky set of random demands. Note: Gurobi’s solution (like yours) is optimized using the demand forecasts. ![]() Your solution-and Gurobi’s-will be evaluated using the actual demands, but you won’t learn those until after you click Done. In Round 2, you won’t know the exact demands-the numbers inside the demand markers are only forecasts of the demands. Every day the map is empty of trucks and you have to start planning again. Each day brings a new wrinkle: for example, different customer locations, demand numbers, or cost parameters. The game is divided into rounds, and every round is divided into days.
0 Comments
Leave a Reply. |