Transformation and Linearization Techniques in Optimization: A State-of-the-Art Survey

A comparison among optimization software to solve bi-objective sectorization problem

In this study, we compare the performance of optimization software to solve the bi-objective sectorization problem. The used solution method is based on an approach that has not been used before in the literature on sectorization, in which, the bi-objective model is transformed into single-objective ones, whose results are regarded as ideal points for the objective functions in the bi-objective model. Anti-ideal points are also searched similarly. Then, using the ideal and anti-ideal points, the bi-objective model is redefined as a single-objective one and solved. The difficulties of solving the models, which are basically non-linear, are discussed. Furthermore, the models are linearized, in which case how the number of variables and constraints changes is discussed. Mathematical models are implemented in Python's Pulp library, Lingo, IBM ILOG CPLEX Optimization Studio, and GAMS software, and the obtained results are presented. Furthermore, metaheuristics available in Python's Pymoo library are utilized to solve the models' single- and bi-objective versions. In the experimental results section, benchmarks of different sizes are derived for the problem, and the results are presented. It is observed that the solvers do not perform satisfactorily in solving models; of all of them, GAMS achieves the best results. The utilized metaheuristics from the Pymoo library gain feasible results in reasonable times. In the conclusion section, suggestions are given for solving similar problems. Furthermore, this article summarizes the managerial applications of the sectorization problems.

A data-driven optimization model to response to COVID-19 pandemic: a case study

COVID-19 is a highly prevalent disease that has led to numerous predicaments for healthcare systems worldwide. Owing to the significant influx of patients and limited resources of health services, there have been several limitations associated with patients' hospitalization. These limitations can cause an increment in the COVID-19-related mortality due to the lack of appropriate medical services. They can also elevate the risk of infection in the rest of the population. The present study aims to investigate a two-phase approach to designing a supply chain network for hospitalizing patients in the existing and temporary hospitals, efficiently distributing medications and medical items needed by patients, and managing the waste created in hospitals. Since the number of future patients is uncertain, in the first phase, trained Artificial Neural Networks with historical data forecast the number of patients in future periods and generate scenarios. Through the use of the K-Means method, these scenarios are reduced. In the second phase, a multi-objective, multi-period, data-driven two-stage stochastic programming is developed using the acquired scenarios in the previous phase concerning the uncertainty and disruption in facilities. The objectives of the proposed model include maximizing the minimum allocation-to-demand ratio, minimizing the total risk of disease spread, and minimizing the total transportation time. Furthermore, a real case study is investigated in Tehran, the capital of Iran. The results showed that the areas with the highest population density and no facilities near them have been selected for the location of temporary facilities. Among temporary facilities, temporary hospitals can allocate up to 2.6% of the total demand, which puts pressure on the existing hospitals to be removed. Furthermore, the results indicated that the allocation-to-demand ratio can remain at an ideal level when disruptions occur by considering temporary facilities. Our analyses focus on: (1) Examining demand forecasting error and generated scenarios in the first phase, (2) exploring the impact of demand parameters on the allocation-to-demand ratio, total time and total risk, (3) investigating the strategy of utilizing temporary hospitals to address sudden changes in demand, (4) evaluating the effect of disruption to facilities on the supply chain network.

Combination of pricing and inventory policies for deteriorating products with sustainability considerations

Economic, environmental, and social criteria are all being taken into consideration simultaneously when determining pricing policies or inventory levels in sustainable production management. The combination of pricing and inventory policies is an important source of leverage for the efficient management of perishable products. This paper, among the first studies, proposes the problem of devising optimal pricing and inventory management decisions simultaneously where the environmental and social criteria are contributed for perishable complementary products replenished and sold by the same company. This study considers two interrelated price-sensitive linear demand functions to consider the possibility of shortage with both budget and warehouse capacity constraints. Another contribution of the proposed model is to consider an upper bound for environmental pollution and a lower bound for job opportunities as the constraints to the model. As a complex optimization model, the challenge of complexity is addressed by a heuristic algorithm for finding an optimal solution. After an extensive analysis using numerical examples, some managerial insights are concluded from the results. One finding from these analyses confirms that the total capacity of the warehouse, the total available budget, carbon emissions, and variable job opportunities have a high impact on the optimal solution to find a balance between sustainability criteria for making pricing and inventory policies.

A Comprehensive Approach for an Approximative Integration of Nonlinear-Bivariate Functions in Mixed-Integer Linear Programming Models

As decentralized energy supply units, microgrids can make a decisive contribution to achieving climate targets. In this context, it is particularly important to determine the optimal size of the energy components contained in the microgrids and their optimal operating schedule. Hence, mathematical optimization methods are often used in association with such tasks. In particular, mixed-integer linear programming (MILP) has proven to be a useful tool. Due to the versatility of the different energetic components (e.g., storages, solar modules) and their special technical characteristics, linear relationships can often only inadequately describe the real processes. In order to take advantage of linear solution techniques but at the same time better represent these real-world processes, accurate and efficient approximation techniques need to be applied in system modeling. In particular, nonlinear-bivariate functions represent a major challenge, which is why this paper derives and implements a method that addresses this issue. The advantage of this method is that any bivariate mixed-integer nonlinear programming (MINLP) formulation can be transformed into a MILP formulation using this comprehensive method. For a performance comparison, a mixed-integer quadratic constrained programming (MIQCP) model—as an MINLP special case—is applied and transformed into a MILP, and the solution of the transformed problem is compared with the one of the MIQCP. Since there are good off-the-shelf solvers for MIQCP problems available, the comparison is conservative. The results for an exemplary microgrid sizing task show that the method delivers a strong performance, both in terms of approximation error (0.08%) and computation time. The method and its implementation can serve as a general user-tool but also as a basis for further methodological developments and research.

A Smart Post-Processing System for Forecasting the Climate Precipitation Based on Machine Learning Computations

Although many meteorological prediction models have been developed recently, their accuracy is still unreliable. Post-processing is a task for improving meteorological predictions. This study proposes a post-processing method for the Climate Forecast System Version 2 (CFSV2) model. The applicability of the proposed method is shown in Iran for observation data from 1982 to 2017. This study designs software to perform post-processing in meteorological organizations automatically. From another point of view, this study presents a decision support system (DSS) for controlling precipitation-based natural side effects such as flood disasters or drought phenomena. It goes without saying that the proposed DSS model can meet sustainable development goals (SDGs) with regards to a grantee of human health and environmental protection issues. The present study, for the first time, implemented a platform based on a graphical user interface due to the prediction of precipitation with the application of machine learning computations. The present research developed an academic idea into an industrial tool. The final finding of this paper is to introduce a set of efficient machine learning computations where the random forest (RF) algorithm has a great level of accuracy with more than a 0.87 correlation coefficient compared with other machine learning methods.