A two-dimensional strip packing problem is the process of packing a set of rectangular items of given dimensions into a strip of bounded width and infinite height so that the used height of the strip is minimized. In the case that only guillotine packing is permitted, the problem is called the guillotine strip packing problem (GSPP). Guillotine packing commonly arises in different industries such as glass, steel, paper and wood. Nevertheless, there is a lack of explicit mathematical models for GSPP that can globally solve the problem. In this paper, a new mixed-integer programming model inspired by a so-called sequence sub-tour elimination technique for the traveling salesman problem (TSP) is presented as a relaxation of (non-staged) GSPP with orthogonal rotation. The proposed model is able to find good solutions (good upper bounds) for the optimal objective value and more importantly, it is a polynomial model of order $O(n^2)$, i.e. the number of decision variables (and constraints, as well) is a polynomial of order $O(n^2)$ in the number of the rectangular items ($n$). Numerical results show that the solutions obtained from the proposed model are superior to several existing heuristic algorithms in the literature.

This study developed and validated a formalized and robust integer linear programming (ILP) model to optimize the lecturer-to-course assignment problem (concerning balancing workload) for a university department that offers engineering programs. Questionnaire surveys with 4 groups of a total of 159 informants (10 lecturers, 1 head of department, 1 program coordinator, and 147 mechanical engineering students) were conducted. Enumeration was used for lecturers, the head of the department, and the program coordinator, whilst convenience sampling was used for students, with a response rate of 60%. A binary integer linear programming (ILP) model was developed by considering workload-related constraints such as class capacity, course contact hours, course credits, and the number of courses per lecturer. The ILP model was implemented in optimization software and the results were validated using the Delphi method. The results demonstrate the robustness and efficiency of the model in balancing workload by objectively (reducing biases) assigning under-utilized lecturers to more courses and over-utilized lecturers to fewer courses, in terms of simultaneously considering other workload-related variables, unlike existing studies. These results were used to instill a timely, formal, and consistent assignment approach that is fair and free from biases. The proposed model contributes to enhancing fairness and hence collective satisfaction of lecturers, program coordinators, and students, given a formalized, consistent, and timesaving assignment approach that considers other workload-related variables other than the number of courses per lecturer. Another contribution lies in a deeper understanding of a comprehensive range of factors that play a role in lecturer-to-course assignments for higher education institutions. Moreover, this study has implications for practice, given that other academic institutions may benefit from this work, in terms of policy considerations.

This paper extends the proposed method by Jahanshahloo et al. (2004) (a method for generating all the efficient solutions of a 0–1 multi-objective linear programming problem, Asia-Pacific Journal of Operational Research). This paper considers the recession direction for a multi-objective integer linear programming (MOILP) problem and presents necessary and sufficient conditions to have unbounded feasible region and infinite optimal values for objective functions of MOILP problems. If the number of efficient solution is finite, the proposed method finds all of them without generating all feasible solutions of MOILP or concluding that there is no efficient solution. In any iteration of the proposed algorithm, a single objective integer linear programming problem, constrained problem, is solved. We will show that the optimal solutions of these single objective integer linear programming problems are efficient solutions of an MOILP problem. The algorithm can also give subsets of efficient solutions that can be useful for designing interactive procedures for large, real-life problems. The applicability of the proposed method is illustrated by using some numerical examples.

Electric vehicles (EVs) are new and growing loads in distribution networks. Increasing number of electric vehicles in a distribution network causes increase of electricity energy demand. Therefore, in the absence of any energy consumption management, some distribution system operation constraints (e.g. bus voltage magnitude) may be violated. Power electronic devices used for charging and discharging the batteries, are usually called chargers.The charger could be unidirectional (transfer the energy from network to the battery) or bidirectional. Bidirectional chargers work in four areas of PQ power plane. In this paper, firstly, the active and reactive power management of smart distribution network using electric vehicles as non-linear problem is presented. Then, the problem is converted to mixed integer linear programming (MILP) problem using specific linearization method and is solved by GAMS package. The proposed scheme has been tested on the 33-bus distribution network and its performance and capability have been evaluated by simulation results.

An integer linear programming model for university courses timetabling is proposed here. In order to reduce the number of decisive variables, a combination of a course, a professor schedule and the students ‘group was defined as an activity. In this context, the two integer programming models namely the activity-based model and a two-phase activity-based model were proposed. In the first model, all activities were scheduled based on the number of required weekly sessions in the weekdays intervals; however, in the second model, classes and training courses were determined according to the planned sessions considering their special restrictions. These models were formulated based on the process of assigning the university courses within specific intervals throughout the week considering fierce constraints for a given semester in the department of Economics at University of Isfahan. All regulation concerning the courses timetable of a semester were formulated in GAMS software. Then, 239 courses were successfully scheduled using the two-phase activity-based model in only 9 minutes and 16 seconds.

IntroductionFloods, droughts, water scarcity, water contaminants, and optimal use of water resources including reservoirs and aquifers are some of the many water problems present today. These will be even more noticeable in the future. The optimal operation of reservoirs is one of the best ways in water resources management to deal with such problems and other unwanted temporal and spatial distributions of water. Optimization techniques have become increasingly important in the management and operation of complex reservoir systems over the past three decades. Some researches have provided an extensive literature review and evaluation of various optimization methods and their corresponding models. Each optimization method has its advantages and disadvantages that make them suitable for some problems. Selection of each method depends on the characteristics of the system being considered, data availability, optimization objectives, and the problem constraints.