This paper addresses two real-life assignment problems. In both cases, the number of employees to whom tasks should be assigned is significantly greater than the number of tasks. In the simple job assignment problem, at most one task (job) should be assigned to each employee; this constraint is relaxed in the multiple job assignment problem. In both cases, the goal is to minimize the time the last task is completed: these problems are known as Bottleneck Assignment Problems (BAPs for short). We show that the simple job assignment problem can be solved optimally using an iterative approach based on dichotomy. At each iteration, a linear programming problem is solved: in this case the solution is integer. We propose a fast heuristic to solve the multiple job assignment problem, as well as a branchand-bound approach which leads to an optimal solution. Numerical examples are presented. They show that the heuristic is satisfactory for the application at hand. The assignment problem consists of allocating renewable resources (construction equipment, crews, or contractors) of limited availability to a set of activities. The classical model for this problem minimizes the total time or cost of completing all activities with the assumption that each activity is assigned to one particular resource. This paper systematizes and describes extensions of these assumptions, considering the effects of task sequence: parallel, serial and hybrid (modeled by means of network methods). This study proposes algorithms for the solution of presented models, which can be used in construction project scheduling.

ANALYZE AND EXPLAIN IN YOUR OWN WORDS. I WILL CHECK PLAGIARISM. I WILL DOWNVOTE AND REPORT