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The purpose of this paper is to present a model to determine which roads to be built in each stage with limited budget.

A multistage network discrete expansion model with budget restriction is formulated and a heuristic algorithm is developed by the technique of comparing the original shortest paths and the sum of crossed shortest paths to avoid computing the shortest paths matrix repeatedly.

The optimal approach has a very significant effect in finding which roads to be built by the largest net benefit.

The paper discusses a new multistage network discrete expansion problem is the main research implications.

The optimal choice for road building schedule of new urban district when budgets were limited.

The paper presents a model and an algorithm for the optimization of road building schedule based on budget restriction.