The Application of mathematical programming to loop feeder allocation

Loop feeder allocation is the process of planning for economic use of the spare capacity in a feeder route, which supplies a central office. This paper presents a model of the feeder route for which a good allocation of feeder pairs is derived using a combination of heuristic and mathematical programming techniques. The model of the route reflects the factors relevant to making allocation decisions: subscriber growth, operating costs due to subscriber movement, transmission requirements, relief, and rearrangement costs. The model is flexible enough to handle allocation problems on routes with pair gain systems as well as conventional resistance design cable routes with multiple paths from some customers to the central office. An iterative separable linear programming algorithm is used to find the feasible allocation with the minimum expected operating expense. The need to reserve existing pairs in the feeder route to connect to the pairs placed in future relief jobs requires the solution of a multi-time period model. To save on computation time, a heuristic algorithm is used to solve the dynamic problem approximately.