Binary Integer Programming Method Research Articles

Virtual reality-based decision support model for interior design and decoration of an office building

Purpose The purpose of this paper is to develop a virtual reality (VR)-based and user-oriented decision support system for interior design and decoration. The four-phase decision-making process of the system is verified through a case study of an office building. Design/methodology/approach Different “spatial layouts” are presented by VR for users to decide their preference (Phase 1). According to the selected spatial layout, a “spatial scene” is constructed by VR and Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is used to determine the spatial scene preference (Phase 2). Based on the binary integer programming method, the system provides the optimal preliminary solution under a limited decoration budget (Phase 3). Finally, the consistency between the overall color scheme and pattern is fine-tuned by VR in order to obtain the final solution (Phase 4). Findings The questionnaire survey results show that decision makers generally affirm the operation and application of VR, and especially recognize the advantages in the improvement of VR-based interior design feasibility, communication efficiency and design decision-making speed. The optimization of the costs and benefits enables decision makers to effectively evaluate the impact of design decisions on subsequent project implementation during the preliminary design process. Originality/value The VR-based decision support system for interior design retains the original immersive experience of VR, and offers a systematic multiple criteria decision- making and operations research optimization method, thus, providing more complete decision-making assistance. Compared with traditional design communication, it can significantly reduce cognitive differences and improve decision-making quality and speed.

Examination Timetabling Problem: A Case Study

Background/Objectives: This paper presents a real-world examination-timetabling problem associated with Universiti Malaysia Terengganu (UMT) in Malaysia. We aim to develop a mathematical model that considers the main requirements to produce the examination timetable at UMT and attempts to optimize the assignment of exam into room and timeslot as preferred by the communities whilst satisfying the requirements mentioned. Methods/Analysis: The main requirements is modelled using Binary Integer Programming method and is validated using a self-develop dataset with two different preferences assignment and the computational results are reported and analyzed directly using the AIMMS Software with CPLEX 12.6.3 solver. Findings: The results shows that the newly developed models have successfully produce an examination timetable that completely solve all basic requirements addresses by the university and through the application of the models, we manage to maximize the preferences of the communities with the assignment of exam into the best preferred slots. Novelty/Improvement: These results will be used as reference for developing a more sophisticated examination-timetable model that will incorporate more demanding and challenging constraints as well as the preferences from community, which will be significantly better than those constructed using the existing manual system especially in terms of solving all requirements which cannot be easily done using the former system in UMT.

An objective approach of balanced cricket team selection using binary integer programming method

Selecting a balanced playing XI in the game of cricket with the right mix of players of different specialization is a difficult decision making problem for the team management. To make the process more objective, optimization techniques can be applied to the process of selection of players from a given squad. Such an exercise has two dimensions. First, a suitable tool for performance measurement of cricketers needs to be defined. Secondly, for selecting a balanced team of XI players, an appropriate objective function and some constraints need to be formulated. Since the captain gets an obvious inclusion in the cricket team, the area specialization of the captain influences the selection of other ten positions in the playing XI. This study attempts to select the optimum balanced playing XI from a squad of players given the specialization of the captain using binary integer programming. To validate the exercise, data from the fifth season of the Indian Premier League has been used.

Optimal placement of PMU and SCADA measurements for security constrained state estimation

This paper presents a method for the use of Supervisory Control and Data Acquisition (SCADA) and synchronized measurements for complete observability of a power system. Under normal operation, both Node Phasor Measurement Unit (NPMU) and SCADA measurements are optimally placed using integer programming and Genetic Algorithm (GA) respectively. The minimum condition number of the Jacobian matrix is used as a criteria in conjunction with GA to obtain a completely determined condition. Next, a triangular factorization approach is used to search for the necessary candidates for single branch outage and single/multiple measurement loss. These candidate measurements are optimized by the binary integer programming method. Numerical results on the IEEE test systems are demonstrated. The results clearly show the robustness of the method to obtain reliable measurements under both normal and contingency conditions.

An approximate scheduling policy for joint replenishment problem with transport capacity constraint

The joint replenishment problem (JRP) has been studied extensively, and many techniques have been applied to find the approximate solution of the minimum total costs and to determine the appropriate basic cycle time. In practice, joint replenishment is always limited by transport capacity. But few papers so far have incorporated the transport capacity constraint (TCC) with the optimal delivery schedule. In this article, the classical JRP model was extended to include TCC, and a model of JRP with TCC was developed. The model of JRP with TCC involves binary decision variables which need to be solved by binary integer programming (BIP). Since the available solution techniques of JRP cannot deal with the JRP with TCC, two algorithms have been proposed to solve this problem. One is the existing RAND method combined with the BIP algorithm (RAND + BIP) and the other is the modified RAND method for constraint problems combined with the BIP algorithm (MC_RAND + BIP). A numerical example solved by two algorithms demonstrates the approximate joint scheduling policy. Computational experiments with 1800 test problems were successfully performed by two algorithms and the results are compared. The MC_RAND + BIP method outperforms RAND + BIP on solution quality as well as running time for the large-size problems. The statistical estimating optimization technique was applied to evaluate the MC_RAND + BIP approximate solution quality, and the estimating optimal values of 18 groups of test problems all lie within the individual interval with 99% confidence. It indicates that the proposed algorithm can find the statistical optimal solution.