OR Solver on the GPT Store

Introduction to OR Solver

GPT Description

GPT Prompt Starters

• In Kafka's "The Castle" novel, protagonist Mr. K must navigate through a town riddled with bureaucrats to reach the castle, with each bureaucrat demanding a specific bribe for passage. Your task is to formulate an Integer Programming (IP) model that maps out the most cost-effective route for Mr. K. This model should represent the town as a network of nodes (locations) and edges (paths), assign a bribe cost to each bureaucrat at these nodes or edges, and minimize the total amount of money spent on bribes, subject to the given constraints. The challenge is to balance the bribe costs with the need to reach the castle, reflecting the complex and obstructive bureaucracy depicted in Kafka's narrative.
• In the film "Taste of Cherry" by Abbas Kiarostami, Mr. Badii embarks on a critical journey in the outskirts of Tehran with the aim of finding someone to assist in ending his life. You are tasked with formulating an Integer Programming (IP) model to optimize Mr. Badii's route. Your task is to minimize the total distance he must travel while ensuring he visits all potential sites before nightfall. Each site represents a location he believes might provide a solution to his quest. Incorporate the varying distances between sites and the time constraint of completing the journey before nightfall. The model should help Mr. Badii efficiently plan his route under these sensitive and specific conditions. Consider and clearly define your assumptions, and formulate the objective function and constraints for the model.
• Each day, workers at the Gotham City Police Department work two 6-hour shifts chosen from 12 A.M. to 6 A.M., 6 A.M. to 12 P.M., 12 P.M. to 6 P.M., and 6 P.M. to 12 A.M. The following number of workers is needed during each shift. Workers whose two shifts are consecutive are paid $12 per hour; workers whose shifts are not consecutive are paid $18 per hour. Formulate an LP that can be used to minimize the cost of meeting the daily workforce demands of the Gotham City Police Department. (HINT: Think of all possible combinations of shifts). [Shifts : Required workers] (12 A.M. to 6 A.M.: 15 workers ,6 A.M. to 12 P.M: 5 workers, 12 P.M. to 6 P.M: 12 workers, 6 P.M. to 12 A.M: 6 workers)