A dynamic logistics coordination model for evacuation and support in disaster response activities

This paper describes an integrated location-distribution model for coordinating logistics support and evacuation operations in disaster response activities. Logistics planning in emergencies involves dispatching commodities (e.g., medical materials and personnel, specialised rescue equipment and rescue teams, food, etc.) to distribution centres in affected areas and evacuation and transfer of wounded people to emergency units. During the initial response time it is also necessary to set up temporary emergency centers and shelters in affected areas to speed up medical care for less heavily wounded survivors. In risk mitigation studies for natural disasters, possible sites where these units can be situated are specified according to risk based urban structural analysis. Logistics coordination in disasters involves the selection of sites that result in maximum coverage of medical need in affected areas. Another important issue that arises in such emergencies is that medical personnel who are on duty in nearby hospitals have to be re-shuffled to serve both temporary and permanent emergency units. Thus, an optimal medical personnel allocation must be determined among these units. The proposed model also considers this issue.     

Fuzzy and robust approach for decision-making in disaster situations

Central European Journal of Operations Research - The paper deals with the combination of multiple criteria decision making, fuzzy modelling, and robust optimization for shortest path planning...     

Location-allocation planning of stockpiles for effective disaster mitigation

In the existing framework for receiving and allocating Strategic National Stockpile (SNS) assistance, there are three noticeable delays: the delay by the state in requesting federal assets, the delay in the federal process which releases assets only upon the declaration of a disaster and lastly the time it takes to reach supplies rapidly from the SNS stockpile to where it is needed. The most efficient disaster preparedness plan is one that addresses all three delays taking into account the unique nature of each disaster. In this paper, we propose appropriate changes to the existing framework to address the first two delays and a generic model to address the third which determines the locations and capacities of stockpile sites that are optimal for a specific disaster. Specifically, our model takes into account the impact of disaster specific casualty characteristics, such as the severity and type of medical condition and the unique nature of each type of disaster, particularly with regard to advance warning and factors affecting damage. For disasters involving uncertainty (magnitude/severity) with regard to future occurrences, such as an earthquake, development of appropriate solution strategies involves an additional step using scenario planning and robust optimization. We illustrate the application of our model via case studies for hurricanes and earthquakes and are able to outline an appropriate response framework for each.     

A periodic testing model for a preparedness system with a defective state

This paper considers the periodic testing of a preparednesssystem where in addition to working and failed state recognition,a working but defective state also exists. Based upon the delaytime model, an expected availability model is derived and evaluatedas a function of the constant inspection period. The model enablesthe range of inspection periods which satisfy a pre-set availabilitycriterion to be established, and the optimal availability inspectionperiod to be identified. Variants of the basic model are considered including: wherea delay time period exists, but the technology to detect a defectis not available; where the delay time is zero, so that onlyfailures are detected; and where the system is replaced on aregular basis without any state testing. These variants enablethe value and effectiveness of the ability to detect defectsand to detect failures to be identified and quantified. The models are demonstrated in the context of a missile buffersystem, where the numerical example clarifies the value of modellingand the insight into the potential effectiveness of defect andfailure detection.     

A fuzzy-stochastic OWA model for robust multi-criteria decision making

All realistic Multi-Criteria Decision Making (MCDM) problems face various kinds of uncertainty. Since the evaluations of alternatives with respect to the criteria are uncertain they will be assumed to have stochastic nature. To obtain the uncertain optimism degree of the decision maker fuzzy linguistic quantifiers will be used. Then a new approach for fuzzy-stochastic modeling of MCDM problems will be introduced by merging the stochastic and fuzzy approaches into the OWA operator. The results of the new approach, entitled FSOWA, give the expected value and the variance of the combined goodness measure for each alternative. Robust decision depends on the combined goodness measures of alternatives and also on the variations of these measures under uncertainty. In order to combine these two characteristics a composite goodness measure will be defined. The theoretical results will be illustrated in a watershed management problem. By using this measure will give more sensitive decisions to the stakeholders whose optimism degrees are different than that of the decision maker. FSOWA can be used for robust decision making on the competitive alternatives under uncertainty.     

A two-stage stochastic programming framework for transportation planning in disaster response

This study proposes a two-stage stochastic programming model to plan the transportation of vital first-aid commodities to disaster-affected areas during emergency response. A multi-commodity, multi-modal network flow formulation is developed to describe the flow of material over an urban transportation network. Since it is difficult to predict the timing and magnitude of any disaster and its impact on the urban system, resource mobilization is treated in a random manner, and the resource requirements are represented as random variables. Furthermore, uncertainty arising from the vulnerability of the transportation system leads to random arc capacities and supply amounts. Randomness is represented by a finite sample of scenarios for capacity, supply and demand triplet. The two stages are defined with respect to information asymmetry, which discloses uncertainty during the progress of the response. The approach is validated by quantifying the expected value of perfect and stochastic information in problem instances generated out of actual data.     

A new robust DEA model and super-efficiency measure

Applications of traditional data envelopments analysis (DEA) models require knowledge of crisp input and output data. However, the real-world problems often deal with imprecise or ambiguous data. In this paper, the problem of considering uncertainty in the equality constraints is analyzed and by using the equivalent form of CCR model, a suitable robust DEA model is derived in order to analyze the efficiency of decision-making units (DMUs) under the assumption of uncertainty in both input and output spaces. The new model based on the robust optimization approach is suggested. Using the proposed model, it is possible to evaluate the efficiency of the DMUs in the presence of uncertainty in a fewer steps compared to other models. In addition, using the new proposed robust DEA model and envelopment form of CCR model, two linear robust super-efficiency models for complete ranking of DMUs are proposed. Two different case studies of different contexts are taken as numerical examples in order to compare the proposed model with other approaches. The examples also illustrate various possible applications of new models.     

A robust optimization model for production planning of perishable products

In this study, a robust optimization model is developed to solve production planning problems for perishable products in an uncertain environment in which the setup costs, production costs, labour costs, inventory costs, and workforce changing costs are minimized. Using the concept of postponement, the production process for perishable products is differentiated into two phases to better utilize the resources. By adjusting penalty parameters, decision-makers can determine an optimal production loading plan and better utilize resources while considering different economic growth scenarios. A case from a Hong Kong plush toy company is studied and the characteristics of perishable products are discussed. Numerical results demonstrate the robustness and effectiveness of the proposed model. An analysis of the trade-off between solution robustness and model robustness is also presented.     

A robust fuzzy k-means clustering model for interval valued data

Summary  In this paper a robust fuzzy k-means clustering model for interval valued data is introduced. The peculiarity of the proposed model is the capability to manage anomalous interval valued data by reducing the effects of such outliers in the clustering model. In the interval case, the concept of anomalous data involves both the center and the width (the radius) of an interval. In order to show how our model works the results of a simulation experiment and an application to real interval valued data are discussed.     

A robust optimization model for dynamic market with uncertain production cost

This article presents a robust optimization formulation for dealing with production cost uncertainty in an oligopolistic market scenario. It is not uncommon that players in the market face an equilibrium selling price but uncertain production costs. We show that, based on a nominal problem, the robust optimization formulation can be derived as a variational inequality with control and state variables. This convenient approach may be applied for computing optimal solutions efficiently, which help manufacturers dramatically and rapidly reform production and distribution schedules such that they can compete in the market successfully.     

A robust optimization model for agile and build-to-order supply chain planning under uncertainties

Supply chain planning as one of the most important processes within the supply chain management concept, has a great impact on firms’ success or failure. This paper considers a supply chain planning problem of an agile manufacturing company operating in a build-to-order environment under various kinds of uncertainty. An integrated optimization approach of procurement, production and distribution costs associated with the supply chain members has been taken into account. A robust optimization scenario-based approach is used to absorb the influence of uncertain parameters and variables. The formulation is a robust optimization model with the objective of minimizing the expected total supply chain cost while maintaining customer service level. The developed multi-product, multi-period, multi-echelon robust mixed-integer linear programming model is then solved using the CPLEX optimization studio and guidance related to future areas of research is given.     

A new robust mixed integer-valued model in DEA

The mixed integer linear programming (MILP) models are proposed to estimate the performance of decision making units (DMUs) including both integer and real values in data envelopment analysis (DEA). There are several studies to propose MILPs in the literature of DEA; however, they have some major shortcomings unfortunately. This study firstly mentioned the shortcomings in the previous researches and secondly suggests a robust MILP based on the Kourosh and Arash Method (KAM). The proposed linear model, integer-KAM (IKAM), has almost all capabilities of the linear KAM and significantly removes the shortcomings in the current MILPs. For instance, IKAM benchmarks and ranks all technically efficient and inefficient DMUs at the same time. It detects outliers, and estimates the production frontier significantly. A numerical example of 39 Spanish airports with four integer inputs and three outputs including two integer values and a real value also represents the validity of the statements.     

A distributionally robust area under curve maximization model

Area under ROC curve (AUC) is a performance measure for classification models. We propose new distributionally robust AUC models (DR-AUC) that rely on the Kantorovich metric and approximate AUC with the hinge loss function, and derive convex reformulations using duality. The DR-AUC models outperform deterministic AUC and support vector machine models and have superior worst-case out-of-sample performance, thereby showing their robustness. The results are encouraging since the numerical experiments are conducted with small-size training sets conducive to low out-of-sample performance.     

A linear regression model for imprecise response

A linear regression model with imprecise response and p real explanatory variables is analyzed. The imprecision of the response variable is functionally described by means of certain kinds of fuzzy sets, the LR fuzzy sets. The LR fuzzy random variables are introduced to model usual random experiments when the characteristic observed on each result can be described with fuzzy numbers of a particular class, determined by 3 random values: the center, the left spread and the right spread. In fact, these constitute a natural generalization of the interval data. To deal with the estimation problem the space of the LR fuzzy numbers is proved to be isometric to a closed and convex cone of R³ with respect to a generalization of the most used metric for LR fuzzy numbers. The expression of the estimators in terms of moments is established, their limit distribution and asymptotic properties are analyzed and applied to the determination of confidence regions and hypothesis testing procedures. The results are illustrated by means of some case-studies.     

A robust optimization model for multi-product two-stage capacitated production planning under uncertainty

Production planning (PP) is one of the most important issues carried out in manufacturing environments which seeks efficient planning, scheduling and coordination of all production activities that optimizes the company’s objectives. In this paper, we studied a two-stage real world capacitated production system with lead time and setup decisions in which some parameters such as production costs and customer demand are uncertain. A robust optimization model is developed to formulate the problem in which minimization of the total costs including the setup costs, production costs, labor costs, inventory costs, and workforce changing costs is considered as performance measure. The robust approach is used to reduce the effects of fluctuations of the uncertain parameters with regards to all the possible future scenarios. A mixed-integer programming (MIP) model is developed to formulate the related robust production planning problem. In fact the robust proposed model is presented to generate an initial robust schedule. The performance of this schedule could be improved against of any possible occurrences of uncertain parameters. A case from an Iran refrigerator factory is studied and the characteristics of factory and its products are discussed. The computational results display the robustness and effectiveness of the model and highlight the importance of using robust optimization approach in generating more robust production plans in the uncertain environments. The tradeoff between solution robustness and model robustness is also analyzed.     

A robust desirability function method for multi-response surface optimization considering model uncertainty

A robust desirability function approach to simultaneously optimizing multiple responses is proposed. The approach considers the uncertainty associated with the fitted response surface model. The uniqueness of the proposed method is that it takes account of all values in the confidence interval rather than a single predicted value for each response and then defines the robustness measure for the traditional desirability function using the worst case strategy. A hybrid genetic algorithm is developed to find the robust optima. The presented method is compared with its conventional counterpart through an illustrated example from the literature.     

A cardinality-constrained robust model for the assignment problem in Home Care services

Home Care includes medical, paramedical and social services which are delivered to patients at their domicile rather than in hospital. Managing human and material resources in Home Care services is a difficult task, as the provider has to deal with peculiar constraints (e.g., the continuity of care, which imposes that a patient is always cared for by the same nurse) and to manage the high variability of patients’ demands. One of the main issues encountered in planning Home Care services under continuity of care requirement is the nurse-to-patient assignment. Despite the importance of this topic, the problem is only marginally addressed in the literature, where continuity of care is usually treated as a soft-constraint rather than as a hard one. Uncertainty is another relevant feature of nurse-to-patient assignment problem, and it is usually managed adopting stochastic programming or analytical policies. However, both these approaches proved to be limited, even if they improve the quality of the assignments upon those actually provided in practice. In this paper, we develop a cardinality-constrained robust assignment model, which allows exploiting the potentialities of a mathematical programming model without the necessity of generating scenarios. The developed model is tested on real-life instances related to a relevant Home Care provider operating in Italy, in order to evaluate its capability of reducing the costs related to nurses’ overtimes.     

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.