Minimax Location Problems With Nonlinear Costs.

Area of Science:

• Operations Research
• Optimization Theory
• Location Science

Background:

• The one-facility minimax location problem seeks to minimize the maximum travel cost to any facility.
• Existing solutions often assume specific travel cost functions, like rectilinear distance.
• Generalizing these problems enhances applicability to diverse real-world scenarios.

Purpose of the Study:

• To extend the one-facility minimax location problem to incorporate general, strictly increasing, continuous travel cost functions.
• To adapt existing solution methodologies for broader applicability in facility location analysis.

Main Methods:

• The study extends previous solution procedures for the rectilinear distance problem in the plane.
• It also adapts methods for the one-facility location problem on a tree network.
• These extensions accommodate any strictly increasing, continuous function of travel distance.

Main Results:

• Developed generalized solution approaches for the one-facility minimax location problem.
• Demonstrated the applicability of these methods to both planar and network settings.
• Successfully integrated non-linear, continuous travel cost functions into the location optimization framework.

Conclusions:

• The generalized minimax location problem with continuous cost functions is solvable using extended methods.
• This research broadens the scope of facility location optimization.
• Findings provide more realistic models for practical decision-making in logistics and service provision.