Job-shop scheduling with resource-time models of operations

The job-shop problems with allocation of continuously-divisible nonrenewable resource is considered. The mathematical models of operations are linear, decreasing functions with respect to an amount of resource. The objective is sequencing operations and allocation of constrained resource such that the project duration is minimized. Thus, the problem considered is a generalization of the classical job-shop problem. Some properties of the optimal solution are presented. The algorithm of solving this problem is based on the disjunctive graphs theory and branch-and-bound technique. The theory of the algorithm is based on the critical path concept using the segment system approach. The special feature of the algorithm is that it gives a complete solution which is associated with each node of the enumeration tree. Possible generalizations of the results presented are indicated.