Bicriteria problem of discrete optimization in planning a multiunit construction project

The paper describes the bicriteria discrete optimization problem, that may occur during the scheduling of multiunit construction projects. The multiunit project involves the construction of many civil structures with the same sets of activities needed, but different in size. In the project the deadlines of activities in units are adopted. The missing of them by the contractor causes the payment of the disincentive penalty. The early completion of the activities in units is rewarded extra income for the construction contractor i.e. a incentive bonus. Changing the order of the execution of the units changes the value of the objective functions: the duration of the project and the cost (the sum of the disincentive penalties and incentive bonuses). The proposed model of the project is the bicriteria NP-hard flow shop problem with constraints characteristic for construction projects. The paper presents the method of determining the set of Paretooptimal solutions for small projects. The computational example of the model of the project is also included in the paper.

SINGLE MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING TIMES BY SUBMODULAR OPTIMIZATION

In scheduling with controllable processing times the actual processing time of each job is to be chosen from the interval between the smallest (compressed or fully crashed) value and the largest (decompressed or uncrashed) value. In the problems under consideration, the jobs are processed on a single machine and the quality of a schedule is measured by two functions: the maximum cost (that depends on job completion times) and the total compression cost. Our main model is bicriteria and is related to determining an optimal trade-off between these two objectives. Additionally, we consider a pair of associated single criterion problems, in which one of the objective functions is bounded while the other one is to be minimized. We reduce the bicriteria problem to a series of parametric linear programs defined over the intersection of a submodular polyhedron with a box. We demonstrate that the feasible region is represented by a so-called base polyhedron and the corresponding problem can be solved by the greedy algorithm that runs two orders of magnitude faster than known previously. For each of the associated single criterion problems, we develop algorithms that deliver the optimum faster than it can be deduced from a solution to the bicriteria problem.