This paper delves into a two-agent scheduling problem in which two agents are competing for a single resource. Each agent has a set of jobs to be processed by a single machine. The processing time, release time, weight, and the due dates of each job are known in advance. Both agents have their objectives, which are conflicting in nature. The first agent tries to minimize the total completion time, while the second agent tries to minimize the number of tardy jobs. (...) The two agents’ scheduling problem, an NP-hard problem, has a wide variety of applications ranging from the manufacturing industry to the cloud computing service provider. Due to the wide applicability, each variation of the problem requires a different algorithm, adapted according to the user’s requirements. This paper provides mathematical models, heuristic algorithms, and two nature-based metaheuristic algorithms to solve the problem. The algorithm’s performance was gauged against the optimal solution obtained from the AMPL-CPLEX solver for both solution quality and computational time. The outlined metaheuristics produce a solution that is comparable with a short computational time. The proposed metaheuristics even have a better solution than the CPLEX solver for medium-size problems, whereas the computation times are much less than the CPLEX solvers. (shrink)

Sports officials, players, and fans are concerned about overseas player rankings for the IPL auction. These rankings are becoming progressively essential to investors when premium leagues are commercialized. The decision-makers of the Indian Premier League choose cricketers based on their own experience in sports and based on performance statistics on several criteria. This paper presents a scientific way to rank the players. Our research examines and contrasts different multicriteria decision-making algorithms for ranking foreign players under various criteria to assess their (...) performance and efficiency. The paper uses three MCDM algorithms, TOPSIS, TODIM, and NR-TOPSIS, for foreign players ranking in the Indian Premier League. Our analysis is limited to the batsmen and bowlers only. We perform the analysis using Python language, a popular high-level programming language. Finally, we perform a sensitivity analysis to determine the stability of each method when the weights of the criterion or the value of a parameter was changed. Our analysis exhibits the superiority of TODIM over TOPSIS and NR-TOPSIS. (shrink)

The paper considers two-agent order acceptance scheduling problems with different scheduling criteria. Two agents have a set of jobs to be processed by a single machine. The processing time and due date of each job are known in advance. In the order accepting scheduling problem, jobs are allowed to be rejected. The objective of the problem is to maximize the net revenue while keeping the weighted number of tardy jobs for the second agent within a predetermined value. A mixed-integer linear (...) programming formulation is provided to obtain the optimal solution. The problem is considered as an NP-hard problem. Therefore, MILP can be used to solve small problem instances optimally. To solve the problem instances with realistic size, heuristic and metaheuristic algorithms have been proposed. A heuristic method is used to determine and secure a quick solution while the metaheuristic based on particle swarm optimization is designed to obtain the near-optimal solution. A numerical experiment is piloted and conducted on the benchmark instances that could be obtained from the literature. The performances of the proposed algorithms are tested through numerical experiments. The proposed PSO can obtain the solution within 0.1% of the optimal solution for problem instances up to 60 jobs. The performance of the proposed PSO is found to be significantly better than the performance of the heuristic. (shrink)