We consider four tasks: three solvable and one perspective to minimize the cost (or time) of constructing a complex of buildings under given restriction on the time (cost) of this process.In other words, here is solved by optimal manner the problem of compromise between cost and time of construction of some bound set of buildings or only one building.

     The order of execution of different works on constructing a complex of buildings is described by a network graph (NG), which consists of a set of chains (ordinary and nested) of linked operations. Each such operation can be performed by several alternative options, which are characterized by two numerical parameters: cost and run-time.

     The object of optimizing is a NG, containing a set of chainsof operations which can be nested. The entire set of graph nodes, between which are placed its branches (operations), includes two main nodes: initial and final, as well a lot of intermediate nodes. Graph nodes have the following properties: from its initial node the chains of operations only come out, to the end node the chains only come in, and any intermediate node connects one or more of incoming operations and one outgoing, which will be executed provided that all incoming operations are executed.

Definition 1. Crucial is called such operation of any graph chain, that has only one option of its realization, i.e. one pair of possible values ​​of cost and time of its execution.

Definition 2. Common is called such resource that can be used exclusively (successively) to serve several operations from different chains of the graph. Individual is called a resource that can be used exclusively for serving operations of only any one chain ot the graph.

Optimizable network graph has the following property: its chains of operations are arranged in such a way that any of them have common nodes with only operations of previous chains of the graph.

   A task of minimizing the cost of constructing a complex of building allows to use temporarily unavailable resources (TUR), required to perform certain operations. For this are given several categories of TUR, which also can include a category of constantly available resources. For each such category are specified timeslots of resource accessibility, and in parameters of operations execution options — required categories numbers.

     TUR are quite frequently encounteredin construction. For example, during work stoppages on weekends and holidays, as well as while temporary employment in another places of teams of builders (subcontractors), which have to perform certain works on this construction site.

     Each element of a network graph can be either a real operation, that is characterized by a set of options for cost and time of its execution, or a nested network subgraph (NNSG). Optimizing NG is executed by subsequent optimization of NNSGs, selected in the graph, which successively are replaced in it by fictitious operations with found as a result of such optimization of sets of parameters of their execution.

     In the solvable tasks 1–3 common resources are absent. They are possible only in the perspective task 4.

     All these four tasks can be solved numerically by using the new science-intensive network technology called "Information technology of automation of control of discrete technological and information processes (in short — IT AC DTIP)", because optimizable process has all necessary properties for that. This process is discrete and is classified as a time-limited process. Its elements in terms of DTIP are:

• for solvable tasks 1–3:
  • a current (being optimized in this moment) graph chain of operations — a network demand (a chain of linked stages of service);
  • resource (individual) to perform a current operation of a current chain (team of builders with equipment) — a device of service;
• for perspective task 4, if it provides for common resources:
  • a current chain of operations that does not require the use of common resources and related to a current nested bunch of graph chains — a network demand;
  • a current group of chains of operations, using common resources and related to a current nested bunch of graph chains — also a network demand;
  • resource (common or individual) to perform a current operation of a current chain (team of builders with equipment) — a device of service.