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Projects are set of processes which aim to serve a unique product or a service in a time-bounded period. Pressure in terms of accelerating the time to market of the unique product or service has become the reality in every organization. Thus, companies need to search for new methodologies to schedule projects effectively. This paper presents a new mathematical model to schedule resource constrained projects in accordance with their logical relationships. Optimal solution of this complex model cannot be found in case of a high number of activities. Therefore, a new hybrid metaheuristic is proposed to find efficient solutions. Moreover, the proposed methodology is applied to schedule projects in a Turkish technology company. For 154 projects completed between 2018 and 2020, proposed methods finds on the average 3.91% better solution in 178 seconds compared to solutions obtained by CPLEX in 34,883 seconds. Proposed methods are also applied for 64 projects planned in 2021 and finds on the average 5% better results in 130 seconds compared to solutions found by CPLEX in 35,438 seconds. In brief, the proposed methodology provides efficient solutions with a very small number of delayed projects, reliable plans, better solution time and objective function value. [ABSTRACT FROM AUTHOR]

One of the important variants of the Traveling Salesman Problem (TSP) is the Minimum Latency Problem (LP). In the LP, the purpose is to find a Hamiltonian path or tour starting from the origin while minimizing the total latency (waiting time or delay time) of all customers. The latency of a customer is defined as the time passed from the beginning of the tour (or path) until the completing the service for that customer. Multiple LP with time windows (kLPTW) finds k tours or paths, each starting at the depot and visiting the nodes within their earliest and latest time (time windows) while minimizing total latency. If travel times between nodes do not depend on the traveler, it is named as homogeneous kLPTW, if travel times between nodes depend on the traveler, it is named as heterogeneous kLPTW. As far as we are aware, there is only one formulation for homogeneous and one formulation for heterogeneous case. In this paper, we proposed a new formulation for homogeneous and a new formulation for heterogeneous case with polynomial number of decision variables and constraints. Then, we solved benchmark instances with our formulations and existing formulations with different number of travelers. We compared the formulations in terms of CPU times and percentage deviation of linear programming relaxation values from the best values. We observed that, our formulations are superior than the existing formulations for all the problems for both kLPTW types with respect to each performance criteria. [ABSTRACT FROM AUTHOR]