This study addresses a new single-item lot-sizing problem for flow-shop configurations by integrating the capacity contract selection problem with multiple energy sources. To the best of our knowledge, this problem has never been tackled before. We introduce a mathematical model which defines optimum production plan and energy contract option regarding the objectives and constraints of the production system and energy supplier contract conditions. Since the problem is NP-Hard, a Fix-and-Relax heuristic is introduced to solve the problem. Two different relaxation procedures are applied and the performance of the solution approach is tested on randomly generated instances. It is seen that the obtained results are quite promising. The applied heuristic approach produces solutions with the optimality gap $0.2\mathrm{\%}$ in average for the small problem sizes such as (N5_T5,N5_T7). For the larger instances, it allows to reach better results than the results obtained by commercial solvers within a shorter time.

Parallel machine scheduling problems are among the most studied scheduling problems in the literature. We study the unrelated parallel machine scheduling problem with release dates and machine-and sequence-dependent setup times to minimize the makespan. We introduce three heuristics, five local search methods and three metaheuristics for the problem: the Late Acceptance Hill Climbing and two variants of Simulated Annealing. Furthermore, we introduce a three-set 1620-instance benchmark in which the number of jobs and machines, release dates, processing and setup times are generated according to existing procedures. The proposed approaches are analyzed and compared on the proposed benchmark. We compare the proposed heuristics and derive the best heuristic to be used to generate the initial solution of the metaheuristics. Moreover, we show that the different metaheuristics are efficient, each performing best on one of the sets.