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Item A mixed integer programming formulation for Smashed Sums puzzle: Generating and solving problem instances(2021) Kececi, BarisPlaying mind games and puzzles has 2500 years of known history. Puzzles and games constitute a research domain that is attracting the interest of scientists from numerous disciplines such as artificial and computational intelligence, neural networks etc. All types of puzzles and games contain their own logic and mathematics. Able to know the science behind them and modelling the logic that a person uses to solve them would shed light to some decisional concepts. This is particularly true from the perspective of computational intelligence. In this paper a logic-based puzzle game called Smashed Sums is considered. The binary integer linear programming formulation is proposed to use in solving and generating the puzzles. Illustrative examples are given to show the validity of the formulation. Some experimental computations are conducted to analyze the puzzle and its complexity. And several open problems are concluded for the further researches.Item Order Acceptance and Scheduling Problem: A Proposed Formulation and the Comparison with the Literature(2020) Bicakci, Papatya S.; Kara, ImdatIn classical scheduling problem, it is assumed that all orders must be processed. In the order acceptance and scheduling (OAS) problem, some orders are rejected due to limited capacity. In make-to-order production environment, in which the OAS problem occurs, accepting all orders may cause overloads, delay in deliveries and unsatisfied customers. Oguz et al. (2010) introduced the OAS problem with sequence-dependent setup times and release dates. In this paper, we propose a new mixed integer programming formulation with O(n(2)) decision variables and O(n2) constraints for the same problem. We conduct a computational analysis comparing the performance of our formulation with Oguz et al. (2010) formulation. We use the benchmark instances, which are available in the literature. We observe that our formulation can solve all the instances up to 50 orders in a reasonable time, while Oguz et al. (2010) formulation can solve only the instances with 10 orders in the same time limit.Item Single-Machine Order Acceptance and Scheduling Problem Considering Setup Time and Release Date Relations(2020) Bicakci, Papatya S.; Kara, Imdat; Sagir, MujganThis paper focuses on a make-to-order production system, where rejection of some orders is inevitable due to limited production capacity. In such a system, accepting all orders may cause overloads, order delays, and customer dissatisfaction. For this reason, firms tend to reject some orders. The order acceptance and scheduling problem is defined as deciding simultaneously which orders to be selected and how to schedule these selected orders. An extension of this problem with sequence-dependent setup times and release dates has been rarely studied, and the existing studies suggest that setup activities wait for the release date to be performed. However, in real production environments this may not be the case. Therefore, this paper examines the relationships between setup times and release dates considering the overall scheduling literature. Previous scheduling studies define two different relationships concerning setup times and release dates. One of them considers setup time is completely dependent on release date, and the other one claims that they are completely independent. In this paper, a new relationship is addressed to propound that setup time may be partially dependent on the release date. The paper also proposes a new mixed integer linear programming formulation withO(n(2)) binary decision variables andO(n(2)) constraints. It includes a detailed computational analysis by solving available instances in the literature, which suggests that existing formulation can solve the test problems to optimality with up to 10 orders in a given time limit. Our proposed formulation, however, can solve the test problems to optimality with up to 50 orders within the same time limit. According to the findings, our approach seems to be more suitable for real-life applications, and the proposed formulation is extremely faster than the existing one.