A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: II. Probabilistic Guarantees on Constraint Satisfaction

Robust optimization and strategic analysis for agri-food supply chain under pandemic crisis: Case study from an emerging economy

Pandemic crises like the coronavirus disease 2019 (COVID-19) have severely influenced companies working in the Agri-food industry in different countries. Some companies could overcome this crisis by their elite managers, while many experienced massive financial losses due to a lack of the appropriate strategic planning. On the other hand, governments sought to provide food security to the people during the pandemic crisis, putting extreme pressure on companies operating in this field. Therefore, the aim of this study is to develop a model of the canned food supply chain under uncertain conditions in order to analyze it strategically during the COVID-19 pandemic. The problem uncertainty is addressed using robust optimization, and also the necessity of using a robust optimization approach compared to the nominal approach to the problem is indicated. Finally, to face the COVID-19 pandemic, after determining the strategies for the canned food supply chain, by solving a multi-criteria decision-making (MCDM) problem, the best strategy is specified considering the criteria of the company under study and its equivalent values are presented ​​as optimal values of a mathematical model of canned food supply chain network. The results demonstrated that "expanding the export of canned food to neighboring countries with economic justification" was the best strategy for the company under study during the COVID-19 pandemic. According to the quantitative results, implementing this strategy reduced by 8.03% supply chain costs and increased by 3.65% the human resources employed. Finally, the utilization of available vehicle capacity was 96%, and the utilization of available production throughput was 75.8% when using this strategy.

Data envelopment analysis and robust optimization: A review

This paper reviews the milestone approaches for handling uncertainty in data envelopment analysis (DEA). This paper presents the detailed classifications of robust data envelopment analysis (RDEA). RDEA is appropriate for measuring the efficiencies of decision‐making units in the presence of the data and distributional uncertainties. This paper reviews scenario‐based and uncertainty set of DEA models. It covers 73 studies from 2008 to 2019. The paper concludes with suggestions about the guidelines for future researches in the field of RDEA.

A Robust Fuzzy Optimization Model for Closed-Loop Supply Chain Networks Considering Sustainability

Supply chain network design (SCND) is an important strategic decision determining the structure of each entity in the supply chain, which has an important impact on the long-term development of a company. An efficient and effective supply chain network is of vital importance for improving customer satisfaction, optimizing the allocation of resources, and increasing profitability. The environmental concerns and social responsibility awareness of the whole society have spurred researchers and managers to design sustainable supply chains (SSCs) integrating the economic, environmental, and social factors. In addition, the innate uncertainty of the SCND problem requires an integrated method to cope. In this regard, this study develops a multi-echelon multi-objective robust fuzzy closed-loop supply chain network (CLSCN) design model under uncertainty including all three dimensions of sustainability. This model considers the total cost minimization, carbon caps, and social impact maximization concurrently to realize supply chain sustainability, and is able to make a balance between the conflicting multiple objectives. Meanwhile, the uncertainty of the parameters is divided into two categories and addressed with two approaches: the first category is missed working days related to social impact, which is solved by the fuzzy membership theory; the second category is the demand and remanufacturing rate, which is settled by a robust optimization method. To validate the ability and applicability of the model and solution approach, a numerical example is conducted and solved using ILOG CPLEX. The result shows that the supply chain network structure and the value of the optimization objectives will change when considering sustainability and different degrees of uncertainty. This will enable supply chain managers to reduce the environmental impact and enhance the social benefits of their supply chain activities, and design a more stable supply chain to better cope with the influence of uncertainty.

Chance-constrained optimization for nonconvex programs using scenario-based methods

This paper presents a scenario-based method to solve the chance-constrained optimization for the nonconvex program. The sample complexity is first developed to guarantee the probabilistic feasibility. Then through the sampling on uncertain parameters, many scenarios are generated to form a large-scale deterministic approximation for the original chance-constrained program. Solving the resulting scenario-based nonconvex optimization is usually time-consuming. To overcome this challenge, we propose a sequential approach to find the global optimum more efficiently. Moreover, two novel schemes: branching-and-sampling and branching-and-discarding are developed for the chance-constrained 0-1 program by refining the scenario set in order to find a less conservative solution. Finally, model predictive control and process scheduling problem are taken as examples to evaluate the effectiveness of proposed optimization approaches.

A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: III. Improving the Quality of Robust Solutions

In this paper, we study the solution quality of robust optimization problems when they are used to approximate probabilistic constraints and propose a novel method to improve the quality. Two solution frameworks are first compared: (1) the traditional robust optimization framework which only uses the a priori probability bounds and (3) the approximation framework which uses the a posteriori probability bound. We illustrate that the traditional robust optimization method is computationally efficient but its solution is in general conservative. On the other hand, the a posteriori probability bound based method provides less conservative solution but it is computationally more difficult because a nonconvex optimization problem is solved. Based on the comparative study of the two methods, we propose a novel iterative solution framework which combines the advantage of the a priori bound and the a posteriori probability bound. The proposed method can improve the solution quality of traditional robust optimization framework without significantly increasing the computational effort. The effectiveness of the proposed method is illustrated through numerical examples and applications in planning and scheduling problems.