M-Convex Function Minimization Under L1-Distance Constraint and Its Application to Dock Reallocation in Bike-Sharing System

In this paper, we consider a problem of minimizing an M-convex function under an L1-distance constraint (MML1); the constraint is given by an upper bound for L1-distance between a feasible solution and a given “center.” This is motivated by a nonlinear integer programming problem for reallocation of dock capacity in a bike-sharing system discussed by Freund et al. (2017). The main aim of this paper is to better understand the combinatorial structure of the dock reallocation problem through the connection with M-convexity and show its polynomial-time solvability using this connection. For this, we first show that the dock reallocation problem and its generalizations can be reformulated in the form of (MML1). We then present a pseudo-polynomial-time algorithm for (MML1) based on the steepest descent approach. We also propose two polynomial-time algorithms for (MML1) by replacing the L1-distance constraint with a simple linear constraint. Finally, we apply the results for (MML1) to the dock reallocation problem to obtain a pseudo-polynomial-time steepest descent algorithm and also polynomial-time algorithms for this problem. For this purpose, we develop a polynomial-time algorithm for a relaxation of the dock reallocation problem by using a proximity-scaling approach, which is of interest in its own right.

Stochastic Coordination of the Wind and Solar Energy Using Energy Storage System Based on Real Time Pricing

In this paper, Stochastic synchronization of the Wind and Solar Energy Using Energy Storage system based on real-time pricing in the Day Ahead-Market Along with taking advantage of the potential of Demand Response programming, has been analyzed. Since renewables energies, loads and prices are uncertain, and planning is based on real-time pricing, the optimal biding proposition considers the wind power, solar system, and energy storage system. Uncertainty is addressed to solve the bidding strategy in a day-ahead market for optimal wind and PV power and optimal charging for energy storage. Batteries are the most promising device to compensate for the fluctuations of wind and photovoltaic power plants to mitigate their uncertainty. In general, using MILP is a suitable approach to address uncertainty as long as a linear formulation is acceptable for modeling either with continuous variables or integer ones. By setting some scenarios to formulate market prices, imbalance of energy, wind and solar system, the uncertainty problems could be easily solved by MILP solver. The model created enables the retailer to realize the potentials of the demand response program and exploit high technical and economic advantages. To ensure fair prices, a set of regulating constraints is considered for sales prices imposed by the regulation committees. A model is presented to optimize the electricity trading strategy in the electricity market, considering the uncertainty in the wholesale market price and the demand level. The retailer considered in this paper is a distribution company that is the owner and operator of the networks and operates under real-time pricing regulations. To model demand response, the elasticity coefficient is used. The proposed solution is implemented on a standard 144-bus sample network using a nonlinear integer programming method. The presented method results provide helpful and valuable information based on the optimal method proposed by the retailers considering the Demand response program and real-time pricing (RTP) system.

Mathematical experiment as a tool for modeling the freight transportation process

The process of multimodal freight transportation on a railway loop is investigated, for which a multicriteria optimization model with time indicators is created, which is a nonlinear integer programming problem. The developed approach is based on egalitarian and utilitarian principles in the welfare theory and allows (along with Pareto optimal transportation plans) to find other plans that can be considered rational from the point of view of maintaining the balance of interests of the transportation process participants. A mathematical experiment is an effective heuristic tool in research. The algorithm for solving the optimization problem is implemented in the environment of a computer algebra system and brought to numerical results.

Optimal Deployment of Cordon Sanitaire with Available Testing Capacity

During the COVID-19 pandemic, authorities in many places have implemented various countermeasures, including setting up a cordon sanitaire to restrict population movement. This paper proposes a bi-level programming model to deploy a limited number of parallel checkpoints at each entry link around the cordon sanitaire to achieve a minimum total waiting time for all travelers. At the lower level, it is a transportation network equilibrium with queuing for a fixed travel demand and given road network. The feedback process between trip distribution and trip assignment results in the predicted waiting time and traffic flow for each entry link. For the lower-level model, the method of successive averages is used to achieve a network equilibrium with queuing for any given allocation decision from the upper level, and the reduced gradient algorithm is used for traffic assignment with queuing. At the upper level, it is a queuing network optimization model. The objective is the minimization of the system’s total waiting time, which can be derived from the predicted traffic flow and queuing delay time at each entry link from the lower-level model. Since it is a nonlinear integer programming problem that is hard to solve, a genetic algorithm with elite strategy is designed. An experimental study using the Nguyen-Dupuis road network shows that the proposed methods effectively find a good heuristic optimal solution. Together with the findings from two additional sensitivity tests, the proposed methods are beneficial for policymakers to determine the optimal deployment of cordon sanitaire given limited resources.

Research on multi-objective optimal scheduling considering the balance of labor workload distribution

In order to solve the problem of unbalanced workload of employees in parallel flow shop scheduling, a method of job standard balance is proposed to describe the work balance of employees. The minimum delay time of completion and the imbalance of employee work are taken as the two goals of the model. A bi-objective nonlinear integer programming model is proposed. NSGA-II-EDSP, NSGA-II-KES, and NSGA-II-QKES heuristic rule algorithms are designed to solve the problem. A number of computational experiments of different sizes are conducted, and compared with solutions generated by NSGA-II. The experimental results show the advantages of the proposed model and method, which error is reduced 14.56%, 15.16% and 15.67%.

Stochastic Programming for Liner Ship Routing and Scheduling under Uncertain Sea Ice Conditions

It is anticipated that in the foreseeable future the Northern Sea Route (NSR) will be able to serve commercial shipping as an alternative transportation shortcut between East Asia and Europe, especially in the summer season. The sailing time, however, is heavily subject to the variation of sea ice conditions along this route. Any participating shipping company must consider how to mitigate the ill effects on itinerary planning caused by sailing time and cost uncertainty. Finding a good trade-off between the benefit from a tight schedule and the risk caused by an unexpected delay is a key element in relevant routing and scheduling decisions, and may be beyond the reach of traditional deterministic planning models. With the aim of maximizing profit over all possible shipping environment scenarios, this article proposes a two-stage stochastic nonlinear integer programming model for liner ship routing and scheduling with uncertain shipping time and cost, the nonlinearity of which arises from the coexistence of schedule-sensitive shipping demand and uncertain arrival time variables in the objective function. The model is converted into an equivalent linear integer programming counterpart by introducing a set of nominal delay variables, and Benders decomposition is applied to solve the linearized problem. Numerical experiments and sensitivity analyses are conducted to validate the efficacy and effectiveness of the model, the results of which suggest several managerial insights that can be used to guide liner ship route and schedule planning under uncertain shipping conditions.

Optimasi Tarif Kereta Bandara Soekarno-Hatta dengan Model Permintaan Berbasis Discrete Choice Experiment

Penelitian ini bertujuan menentukan tarif optimal Kereta Bandara Soekarno Hatta dengan fungsi permintaan yang diturunkan dengan pendekatan discrete-choice experiment. Fungsi permintaan diperoleh dengan memprediksi pilihan setiap individu pada beberapa tingkat harga yang berbeda, mengagregasikannya, dan kemudian menginterpolasikannya sehingga diperoleh fungsi yang kontinyu dan differentiable. Pilihan setiap individu diprediksi dari data utilitas individual menggunakan simulasi randomized first choice, sementara interpolasi fungsi permintaan dilakukan menggunakan cubic spline. Utilitas individual diestimasi dari data stated-preference berbentuk choice menggunakan pendekatan Bayesian. Dengan membatasi dua kelas tarif, harga ditentukan dengan mempertimbangkan kanibalisasi antar kelas tarif dan memperhatikan profitabilitas jangka panjang. Formulasi masalah optimasi yang diperoleh berbentuk nonlinear integer programming dengan fungsi tujuan polinomial orde empat yang parameternya dipengaruhi oleh nilai variabel keputusan. Ruang solusi yang tidak terlalu luas memungkinkan untuk memperoleh solusi dengan enumerasi, di mana diperoleh tarif optimal sebesar Rp67.000 untuk kelas tarif 1 di mana layanan Kereta Bandara dibundle dengan diskon angkutan taksi berbasis aplikasi, dan Rp57.000 untuk kelas tarif 2 yang berupa layanan Kereta Bandara saja. Dengan tarif tersebut diperkirakan akan diperoleh kontribusi total sebesar Rp274,68 milyar per tahun.

Planning of Aircraft Fleet Maintenance Teams

This paper addresses a support information system for the planning of aircraft maintenance teams, assisting maintenance managers in delivering an aircraft on time. The developed planning of aircraft maintenance teams is a computer application based on a mathematical programming problem written as a minimization one. The initial decision variables are positive integer variables specifying the allocation of available technicians by skills to maintenance teams. The objective function is a nonlinear function balancing the time spent and costs incurred with aircraft fleet maintenance. The data involve technicians’ skills, hours of work to perform maintenance tasks, costs related to facilities, and the aircraft downtime cost. The realism of this planning entails random possibilities associated with maintenance workload data, and the inference by a procedure of Monte Carlo simulation provides a proper set of workloads, instead of going through all the possibilities. The based formalization is a nonlinear integer programming problem, converted into an equivalent pure linear integer programming problem, using a transformation from initial positive integer variables to Boolean ones. A case study addresses the use of this support information system to plan a team for aircraft maintenance of three lines under the uncertainty of workloads, and a discussion of results shows the serviceableness of the proposed support information system.