Time-cost trade-off analysis of a priority based assignment problem

In this paper, a bi-objective priority based assignment problem (BPBAP) related to an industrial project, is considered in which, depending upon the work breakdown structure, the n tasks involved in the project are divided into two categories. One of the categories consists of m primary tasks and the other one consists of ( n - m) secondary tasks (for m < n). The project is such that the secondary tasks can be executed only after the primary tasks are finished, however, the tasks within each category may be executed simultaneously. This problem is a special case of categorized assignment scheduling problem, discussed extensively in literature. The BPBAP is studied with the objective of minimizing simultaneously, the two criteria namely, total execution time and total assignment cost of the project which are equal to the sum of execution times and assignment costs respectively, of primary and secondary tasks. Generally, it is not possible to optimize both the objectives simultaneously, therefore, there is a need to do time-cost trade-off analysis of the problem. Since, the present problem is based on two-stage execution of the project (one stage for each category of tasks), therefore, a criteria based iterative algorithm considering all the possible combinations of the parameters of both the categories, is developed that finds all the non-dominated points of BPBAP in a polynomial time. Numerical illustrations are provided in the support of theory.