Scenario-based Robust Optimization Research Articles

A New Robust Dynamic Data Envelopment Analysis Approach for Sustainable Supplier Evaluation

Supplier selection is one of the intricate decisions of managers in modern business era. There are different methods and techniques for supplier selection. Data envelopment analysis (DEA) is a popular decision-making method that can be used for this purpose. In this paper, a new dynamic DEA approach is proposed which is capable of evaluating the suppliers in consecutive periods based on their inputs, outputs, and the relationships between the periods classified as desirable relationships, undesirable relationships, and free relationships with positive and negative natures. To this aim various social, economic, and environmental criteria are taken into account. A new method for constructing an ideal decision-making unit (DMU) is proposed in this paper which differs from the existing ones in the literature according to its capability of considering periods with unit efficiencies which do not necessarily belong to a unique DMU. Furthermore, the new ideal DMU has the required ability to rank the suppliers with the same efficiency ratio. In the concerned problem, the supplier that has unit efficiency in each period is selected to construct an ideal supplier. Since it is possible to have more than one supplier with unit efficiency in each period, the ideal supplier can be made with different scenarios with a given probability. To deal with such uncertain condition, a new robust dynamic DEA model is elaborated based on a scenario-based robust optimization approach. Computational results indicate that the proposed robust optimization approach can evaluate and rank the suppliers with unit efficiencies which could not be ranked previously. Furthermore, the proposed ideal DMU can be appropriately used as a benchmark for other DMUs to adjust the probable improvement plans.

Robust Periodic Vehicle Routing Problem with Time Windows under Uncertainty: An Efficient Algorithm

In a competitive environment, distributors engage in intense rivalry to meet the customers’ demands and accordingly earn maximum profits. Due to changes in customers’ demands, changes in a planned combination of customers to be visited in various days, traffic changes, etc., a sequence of visiting customers by competitors will be changed. So, planning for serving customers ahead of competitors will be uncertain. On the other hand, total transportation costs are also of high importance in distribution of goods. By keeping this issue in mind, we develop a bi-objective mathematical model to evaluate a Periodic Vehicle Routing Problem (PVRP) with time windows under uncertainty for companies competing to provide services to customers. The model is established using an improved scenario-based robust optimization approach. Given that the PVRP is an NP-hard problem, an Improved Differential Evolution (IDE) algorithm is used to identify efficient solutions for the model. The results on small-scale problems were compared with those obtained using the CPLEX solver. To evaluate the performance of the proposed IDE algorithm, a few sample tests on large-scale problems are conducted, and the results are compared with those derived using two other differential evolution algorithms. The findings show that the IDE algorithm exhibits suitable accuracy and performance in solving the presented model.

Development of a scenario-based robust model for the optimal truck-shovel allocation in open-pit mining

We develop a scenario-based robust optimization (SBRO) approach to solve truck–shovel allocation (TSA) problem. To this end, we formulate the TSA problem in two phases by using the concepts of the SBRO approach, network analysis and the shortest path problem, and binary integer programming under uncertainties. We consider uncertainties in shovel output and crusher capacity from the first phase and number of available trucks from the second phase based on the SBRO approach. This TSA approach is applicable in all open-pit mines where trucks with different capacities are used, and different paths exist between loading and dumping points. We exemplify the applicability of the approach based on a copper mine data. We also compare the results of the SBRO approach with the current TSA of the studied mine. Then, we update the TSA formulation based on two new strategies of increasing shovel number and shovel capacity. Compared to the traditional strategy of the mine, the output of shovels increases to 6719, 10,000, and 12,500 tons/shift by the SBRO approach based on the strategies of the available equipment, increasing the number of shovels, and increasing the capacity of shovels, respectively. In addition, operational cost decreases to $1.1825, $0.8068, and $1.1238 per ton of ore based on the strategies, respectively.

A robust model for a humanitarian relief network with backup covering under disruptions: A real world application

In this paper a reliable and robust model for the humanitarian relief supply chain has been presented to deal with the risk of facility disruptions after an earthquake. Assignment of backup suppliers for affected population centers is considered in order to improve the reliability of the model. Employment of public local centers and defining a two-level structure for rescue centers was considered to raise the accessibility to population centers. A four-step methodology was suggested to define the input parameters of the model which were affected by the uncertainty associated with the magnitude of an earthquake. To investigate this uncertainty, the potential epicenters of probable earthquakes and their magnitudes were assumed as uncertain parameters and estimated with a set of scenarios. A scenario-based robust optimization approach was used to sweep over the uncertain parameters. In the proposed methodology, a practical three-factor function was described to determine the impact of an earthquake on rescue centers and demand points. A solution method was proposed based on Lagrangian relaxation method, whose computational efficiency was also examined. A case study in Tehran was used to show the performance of the model in addition to determine whether the proposed methodology was efficient and practical. The computational results revealed the efficiency of the proposed model and sensitivity analyses indicated that the proposed model could be useful in conditions where budget constraints exist.

Scenario-based robust optimization of water flooding in oil reservoirs enjoys probabilistic guarantees

Model-based optimization of the water-flooding process in oil reservoirs suffers from high levels of uncertainty arising from strongly varying economic conditions and limited knowledge of the reservoir model parameters. To handle uncertainty, diverse robust optimization approaches that use an ensemble of uncertain parameter realizations (i.e., scenarios), have been adopted. However, in scenario-based approaches, the effect of considering a finite set of scenarios on the constraint violation and/or the performance degradation with respect to the unseen scenarios have not been studied. In this paper, we provide probabilistic guarantees on the worst-case performance degradation of a scenario-based solution. By using statistical learning, we analyze the impact of the number of scenarios on the probabilistic guarantees for the worst-case solution subject to both economic and geological uncertainties. For the economic uncertainty, we derive an explicit a-priori relationship between the probabilistic guarantee and the number of considered scenarios, while for the geological uncertainty, a-posteriori probabilistic upper bounds on the worst-case solution are given.

A robust data envelopment analysis model with different scenarios

Input and output data, under uncertainty, must be taken into account as an essential part of data envelopment analysis (DEA) models in practice. Many researchers have dealt with this kind of problem using fuzzy approaches, DEA models with interval data or probabilistic models. This paper presents an approach to scenario-based robust optimization for conventional DEA models. To consider the uncertainty in DEA models, different scenarios are formulated with a specified probability for input and output data instead of using point estimates. The robust DEA model proposed is aimed at ranking decision-making units (DMUs) based on their sensitivity analysis within the given set of scenarios, considering both feasibility and optimality factors in the objective function. The model is based on the technique proposed by Mulvey et al. (1995) for solving stochastic optimization problems. The effect of DMUs on the product possibility set is calculated using the Monte Carlo method in order to extract weights for feasibility and optimality factors in the goal programming model. The approach proposed is illustrated and verified by a case study of an engineering company.

Designing an efficient supply chain network with uncertain data: a robust optimization—data envelopment analysis approach

Designing a supply chain network (SCN) is an important issue for organizations in competitive markets. In this paper, a novel robust SCN that considers the efficiencies and costs simultaneously is proposed. In order to estimate the efficiency of the producers and distributors, data envelopment analysis (DEA) model is incorporated into SCN. Moreover, to handle the uncertainty in data, a scenario-based robust optimization approach is applied. The proposed model finds out the efficient location of producers and distributors and determines the amount of purchases from each supplier in uncertain conditions. To illustrate the application of the proposed model, a numerical example is solved and results are analyzed.

A scenario-based robust optimization approach for batch processing scheduling

For years, there have been tremendous endeavors to reduce makespan in an attempt to decrease the production expenses. This investigation aims to develop a scenario-based robust optimization approach for a real-world flow shop with any number of batch processing machines. The study assumes there are some uncertainties associated with processing times as well as size of jobs. Each machine can process multiple jobs simultaneously as long as the machines’ capacities are not violated. In order to verify this developed model and to evaluate the performance of the proposed robust model, a number of test problems are prepared and a commercial optimization solver is adopted to solve these test problems. For the purpose of validating the results, the robust model and mean-value model are carried out by simulation, which confirmed the proposed model.

Scenario-based robust optimization of a water supply system under risk of facility failure

In this paper, we propose a scenario-based robust optimization model for the design of a water supply system considering the risk of facility failure, which is represented as an uncertainty set generated by a finite set of scenarios. New facilities are planned to be built to hedge against the possible failure of existing system facilities that would potentially damage the capacity of the system to meet given user demands. The goal is to build facilities that are both cost-effective and make the system robust. The system robustness is defined as the ability to satisfy user demands for every data realization in the uncertainty set. The proposed model is shown to be equivalent to a large-scale mixed-integer linear program that is solved by a Benders decomposition algorithm. Computational results demonstrate the efficiency of the proposed algorithm, and show that substantial improvement in system robustness can be achieved with minimal increase in system cost.

Scenario-Based Robust Optimization of Regional Water and Wastewater Infrastructure

AbstractUncertainties facing water planners and designers include changes in demand resulting from community growth (temporal and spatial), per capita water use, public perceptions, and regulations. One of the most powerful and intuitive ways to represent these uncertainties in the planning stage is to use scenarios. A scenario represents a realization of the system’s random parameters. Scenario-based analysis provides organizational flexibility by planning for multiple potential future scenarios, each of which may be, although is not necessarily, associated with a probability of occurrence. In this study, a scenario-based multiobjective optimization model for robust optimal design of regional-scale water and wastewater infrastructure is presented. The proposed methodology is demonstrated with an application to the planning of a decentralized water supply and reuse system for a new development area in metropolitan Tucson, where sustainable water supply is a significant issue.

A DECISION MODEL FOR REVERSE LOGISTICS SERVICE PROVIDERS IN DETERMINING ROBUST OPTIMAL PROCESSING QUANTITIES OF RETURNED PRODUCTS

ABSTRACT Reverse logistics covers a serial of activities in dealing with returned products from consumers, including collecting, reusing and recycling. Implementing reverse logistics is much more complicated and expensive than forward logistics to an enterprise. Meanwhile, the systematic patterns for handling transportation, storage, processing and management processes of these activities are still called for. Consequently, to reduce the reverse logistics cost and focus on its core business, an enterprise prefers outsourcing these activities in this manner. Previous studies focused on the selection of processing facilities and the infrastructure design of reverse logistics distribution channels for third-party reverse logistics service providers. In contrast, this research aims to deal with the issues of reverse logistics from different viewpoint. We propose a decision model for a reverse logistics service provider under the context of uncertain, multi-period, multi-type returned/recycled products and multiple processing facilities environment. The major focus of this model is on determining the robust optimal quantities of customer orders and robust optimal processing quantities of returned products for each processing facility. To deal with the issues of uncertainties, the model applies the scenario-based robust optimization approach. Further information on experiment results and implications can be found in this paper.

Planning the e-Scrap Reverse Production System Under Uncertainty in the State of Georgia: A Case Study

Due to legislative requirements, environmental concerns, and market image, the disposition of end-of-life e-scrap is attracting tremendous attention in many parts of the world today. Effective management of returned used product flows can have a great impact on the profitability and resulting financial viability of associated e-scrap reverse production systems. However, designing efficient e-scrap reverse production systems is complicated by the high degree of uncertainty surrounding several key factors. Very few examples of this complex design problem are documented in the academic literature. This paper contributes as analysis of a new, large-scale application that designs an infrastructure to process used televisions, monitors, and computer central processing units (CPUs) in the state of Georgia in the U.S. The case study employs a scenario-based robust optimization model for supporting strategic e-scrap reverse production infrastructure design decisions under uncertainty. A mixed integer linear programming (MILP) model is used to maximize the system net profit for specified deterministic parameter values in each scenario, and then a min-max robust optimization methodology finds a robust solution for all of the scenarios