Search

Hotelling's model—which is commonly referred to as the "linear city" model—is perhaps the most widely-used model of competition in differentiated products. However, pure-strategy Nash equilibria in prices do not exist unless the firms are located either sufficiently far apart from each other or at the same place. In fact, pure-strategy Nash equilibrium prices exist in only about 15 percent of all possible locations of firms in the linear city. This paper applies the undercut-proof equilibrium concept to solve for equilibrium prices for all possible locations of firms in the linear city. [ABSTRACT FROM AUTHOR]

The limited infrastructure of charging stations, which is crucial in route planning and total journey time and creates uncertainty in efficiency and operating costs, calls for new economic and statistical methods in sustainability development and environmental economics. This paper aims to examine the challenges of integrating electric vehicles into freight transport to improve distribution logistics’ environmental sustainability, which represents one of the pathways for reducing environmental risk. The analysis results underscore the inadequacy of the truck charging station network in the Czech Republic. This insufficiency presents an opportunity to enhance environmental sustainability and reduce carbon emissions through strategic analysis and optimizing charging station locations. The difficulty of identifying optimal locations for these stations, given truck availability, requires using multi-criteria decision-making techniques such as the Analytical Network Process (ANP). Municipalities with limited access to existing logistics facilities were considered during the simulation. This way, 15 new locations were identified for municipalities with insufficient distance to a charging station.By implementing the ANP method, the study contributes to a more environmentally sustainable transportation infrastructure, highlighting the potential for significant reductions in carbon emissions through improved charging station networks. These results apply to other countries and can provide novel insights on optimizing charging station locations for sustainable economic development and reducing freight transport’s carbon emissions and environmental risks.

In order to select the location of fire stations more scientifically and improve the efficiency of emergency management in chemical industry parks (CIPs), an improved risk calculation model for hazardous chemicals has been proposed by taking the domino effect and the identification of major hazardous installations for hazardous chemicals into account. In the analysis of the domino effect, the Monte Carlo simulation was used. Then, a location model of the fire stations was established with the optimization objectives of minimizing total cost and maximizing total risk coverage. The solving procedure of the location model is based on the augmented ε -constraint method combined with the TOPSIS method. Finally, a green chemical industry park was used as a case study for the validation and analysis of the location model. The results showed that the improved model could protect the high-risk areas, which is beneficial for the location decisions of fire stations. [ABSTRACT FROM AUTHOR]

Carsharing emerges as a flexible and sustainable transportation mode to deal with severe urban challenges. This paper addresses a joint design problem of carsharing systems by an integer linear programming (ILP) model. Strategic planning of stations' number, location and parking capacities and tactical planning of the fleet size and initial vehicle distribution are collaboratively optimized by considering all-day vehicle relocation and dynamic trip selection at the operational level. For the first time, vehicle relocation and demand selection are integrated with the joint optimization of strategic and tactical planning. We present a greedy heuristic algorithm embedding ILP to solve the problem. The case study of Chengdu demonstrates that the algorithm is computationally efficient when dealing with large-scale problems. The results identify how vehicle relocation and trip selection work in different scenes of travel time and demands and we conclude operators should target at medium-long trips by discount or promotion. [ABSTRACT FROM AUTHOR]

The transport system is one of the main bottlenecks of the world's largest producer and exporter of soybeans, Brazil. Long-distance truck transportation of grains increases costs, food waste, and CO 2 emissions. To handle these problems, the Brazilian government seeks to expand the transportation system through the national transport logistics plan (PNLT), promoting efficient operations. Collaborating on the environmental aspect, this paper proposes sustainable logistic infrastructure for soybean transportation. Investigating the largest grain-producing state in the world, Mato Grosso (Brazil), we show the optimal location for capacitated transshipment terminals untangling the relationship between logistics and sustainability. Besides handling cargo truck costs and CO 2 emission, the optimization model considers cities, road distances, transshipment terminals existents, terminals capacities, implementing costs, and locations near waterways and railways. In five scenarios with different combinations of waterways and railways, we contrast the cost of installing terminals and the total road distance traveled under different weights for the environmental components. The results indicate that it is possible to simultaneously obtain the minimum cost of installing transshipment terminals and to reduce emissions by 20% in all analyzed scenarios. We conclude that obtaining strategic solutions at lower costs can be combined with proper environmental responsibility. As contributions, the results allow for advances in the area of sustainable logistics, encouraging the development of new research in Brazil involving the dimensions of sustainability. In addition, the study supports the government's strategic decisions regarding ongoing discussions on expanding the intermodal soy transport network in the country. [ABSTRACT FROM AUTHOR]

The contradiction between logistics and distribution capacity and people's increasing demand has attracted more and more attention from all walks of life. At present, there are many problems and deficiencies in logistics in China. This paper establishes the location model of the national supply chain logistics center, taking the vegetable logistics distribution as an example. Based on the principle of maximum satisfaction and satisfying demand, a vegetable material flow location model with the ability to predict the annual yield of vegetables is proposed by using the advantages of Holt's linear trend method and immune algorithm in solving multi-objective optimization problems. Finally, the algorithm is applied to select the optimal logistics center in 31 provinces in China to maximize customer satisfaction. Thus, Chengdu, Guangzhou, Nanchang, Nanjing, Shijiazhuang, and Changchun re used as vegetable logistics centers. [ABSTRACT FROM AUTHOR]

In the event of oil spills in offshore oil and gas projects, containment and dispersion equipment must be sent to the affected areas within a critical time by vessels known as oil spill response vessels (OSRVs). Here, we developed an optimization tool, integrated with an oil spill trajectory simulation model, both in deterministic and stochastic alternatives, to support decision-making during the strategic planning of OSRV operations. The tool was constructed in Python using GNOME for oil spill simulations and the GUROBI to solve the optimization model. The tool was applied to a case study in Brazil and afforded relevant recommendations. In terms of research contributions, we proved the viability of the integration between oil spill simulation and mathematical modeling for OSRV strategic operation planning, we explored the stochasticity of the problem with an innovative strategy and we demonstrated flexibility and easy applicability of the framework on real operations. • We devised a deterministic optimization model for strategic planning of OSRVs. • The optimization model is integrated with an oil spill simulation model. • A stochastic alternative was also developed using a two-stage model. • The proposed models were tested using real data from southeast Brazil. • Reasonable computational time was achieved; stochastic model proved more beneficial. [ABSTRACT FROM AUTHOR]

Scientific planning, and the layout of the national level reserve base of emergency materials, will help improve the effectiveness of a country's overall emergency disaster reduction system. Based on the P-center location theory, this paper analyzes the factors affecting site selection at the national and state levels, determines the reasonable number of emergency material reserve bases at national and state levels, and then develops a national macro-level emergency supply reserve location planning model. In this study, the city of 28 states in a country were selected as alternative reserve cities and emergency demand city matrix, to conduct the research. The model is solved using a variable neighborhood search algorithm (VNS). The calculation results obtain the reasonable number of emergency material reserve bases set at the national level in this studied country, and the optimal solution of the base layout can be obtained if the number of emergency reserve bases set at the national level remains unchanged. The experimental results shows that the selected algorithm is reasonable. [ABSTRACT FROM AUTHOR]

For most companies, successful business operation is based on the location at the right place, in the right region, on the right plot. New investments in land, buildings and material handling equipment are carried out for the longer term. As the global business environment in which a company needs to decide on location is becoming more uncertain every day, it is of huge importance to make a thoughtful and ‘future-proof’ decision on the location for a new distribution site. Allocation can also be defined as a process that results in finding a position for a warehouse, company, production, people, things, and activities in a specific area. A newly built distribution site is impossible to be moved in a short period of time, so the decision on where to build a distribution site, warehouse, or manufacturing plant is of vital and strategic importance.

In order to select the location of fire stations more scientifically and improve the efficiency of emergency management in chemical industry parks (CIPs), an improved risk calculation model for hazardous chemicals has been proposed by taking the domino effect and the identification of major hazardous installations for hazardous chemicals into account. In the analysis of the domino effect, the Monte Carlo simulation was used. Then, a location model of the fire stations was established with the optimization objectives of minimizing total cost and maximizing total risk coverage. The solving procedure of the location model is based on the augmented ε-constraint method combined with the TOPSIS method. Finally, a green chemical industry park was used as a case study for the validation and analysis of the location model. The results showed that the improved model could protect the high-risk areas, which is beneficial for the location decisions of fire stations.

In this paper, a method of urban terminal network location based on cellular automaton and genetic algorithm is proposed for the lack of scientific and standardized evaluation system in urban terminal network location problem. In this method, on the basis of considering the influencing factors, location principles and location steps of network location, the location model of urban terminal based on cellular automaton is established. To evaluate layout of urban logistics terminal, an evaluation index of competitiveness is built up. Then, calculation method based on logic of the genetic algorithm is used to solve the optimization result of layout through the comparison of the evaluation index. Finally, the effectiveness of the proposed method is illustrated through the simulation based on the actual data from an express company. [ABSTRACT FROM AUTHOR]

To compete with online e-commerce, traditional retailing is implementing a new retail mode that combines online sales with physical stores, which may change the channel, transport mode and logistics cost of retail commodities from manufacturers to end consumers. In this context, it is necessary for physical retailers to relocate their shopping centers in order to maximize profits. This paper develops a location optimization model for physical shopping centers based on consumer shopping choices (platform choices and store choices), carbon tax policy and the economic scale of transport under the new retail mode. This model is applied to optimize the number and scale of physical shopping centers and corresponding locations with the objective of maximizing the retail profit under the new retail mode. The results show that under the new retail mode, the number of shopping centers, the scale of an individual physical store and the total retail logistics cost decrease, while the retail profit increases. This work lays a theoretical basis for retailers to build online and offline retail systems and rationally determines the spatial distribution of shopping centers in a city. [ABSTRACT FROM AUTHOR]

Improving customer satisfaction and shortening the manufacturing cycle have become common concerns of current manufacturers. This paper presents a multi-objective location model considering the maximization of collaborative manufacturing capabilities and service benefits. This method first uses the two dimensions of customer share and market consumption to segment customers, and identify the weight of various customer groups. Secondly, the space vector model (VSM) is used to calculate the matching between manufacturing capabilities and manufacturing requirements. Then build a multiobjective location model based on the two goals of collaborative manufacturing capabilities and service benefits. Finally, the model was tested with simulation data, which proved the validity and feasibility of the model. According to the simulation results, managers can accurately select the optimal manufacturing base from multiple candidate manufacturing bases with regard to less costs, shorter lead times, better manufacturing capabilities, better service benefits. In this paper, Fuzzy theory, Logit model and VSM are combined to salve the problem of manufacturing base location. Considering resources and service benefits of each manufacturing base, it is helpful to optimize the location of enterprises. From the academic and practical points, this study provides a new perspective for the location problem. [ABSTRACT FROM AUTHOR]

The insufficient charging infrastructure greatly obstructs the development of the electric vehicle(EV) industry. How to efficiently deploy charging stations in a city becomes an urgent problem for the local government. Previous refueling location models are not suitable for fulfilling the EVs' charging demand. This paper proposes a location model for charging stations based on the characteristics of travel behaviors of urban residents. The model consists of two parts: one for short distance commuters which utilize slow charging (SC) facilities, and the other for long distance travelers which utilize fast recharging (FR) facilities. It aims to harness limited resource to meet as much as possible charging demand for both parking vehicles and vehicles on long journeys. A typical city of China is used as an example to demonstrate the implementation and results of the model. We employed sensitive analyses to search for specific factors having strong impact on the number and location of charging stations. It is suggested that travel distance and locating capacity will greatly affect the final result. • A location model proposed for charging stations based on people travel behaviors. • The model combines short and long distance journeys together. • It is suggested that travel distance and locating capacity affect final results. [ABSTRACT FROM AUTHOR]

• Propose a wireless charging lane (WCL) location model considering the WCL adverse effect. • Linearize the model with minimum error. • Test the model and solution method on two networks. • Validate the necessity of considering the adverse effect of WCL. With the development of wireless charging technology, charging-while-driving now becomes possible. In this paper we propose a model to optimize the location of the wireless charging lanes (WCL) by taking into account their effects on road capacity and traveler's route choice. The model is formulated as a nonlinear programming problem and solved by a linearization method. A new method is developed to reduce the maximum error in the linearization process. The model and solution method are tested on Nguyen-Dupuis and Sioux Falls networks. The numerical results show that relatively high charging power and reasonable budget are necessary to recover the investment when charging lanes are deployed on road network. It is also demonstrated that the impacts of WCL on road capacity drop and travelers' route choice are not negligible, and should be considered in the determination of WCL location. [ABSTRACT FROM AUTHOR]

In this paper we consider regression models with centred errors, independent of the covariates. Given independent and identically distributed data and given an estimator of the regression function, which can be parametric or nonparametric in nature, we estimate the distribution of the error term by the empirical distribution of estimated residuals. To approximate the distribution of this estimator, Koul & Lahiri (1994) and Neumeyer (2009) proposed bootstrap procedures based on smoothing the residuals before drawing bootstrap samples. So far it has been an open question as to whether a classical nonsmooth residual bootstrap is asymptotically valid in this context. Here we solve this open problem and show that the nonsmooth residual bootstrap is consistent. We illustrate the theoretical result by means of simulations, which demonstrate the accuracy of this bootstrap procedure for various models, testing procedures and sample sizes. [ABSTRACT FROM AUTHOR]

Due to existence of certain conditions and developing forces at the level in the future wars, accuracy and velocity of the preparation procedure have special importance and is very vital and therefore it is very important to select optimal place/site as a preparation center. Thus this investigation tries to represent a practical model to select optimal places of preparation centers using mathematical models and location finding and using suggestions of elites and military experts in addition to considering the situations like minimizing the length of route and cost of operation. The current study’s purpose is applied and by nature it is descriptive-survey in which library and field research have been conducted for data collection as well as using targeted judgement method has been used in sampling. To achieve the goals in first stage, influential parameters have been identified and in the three phases: “velocity of preparation process”, “security of supportive routes”, and the possibility of establishment of equipment and sources will be calculated getting assistance from fuzzy hierarchal analysis and using elites’ opinions. Then the relative importance of the potential options of research is calculated by help of commanders and operational managers and at the next step the mathematical model of problem will be presented and designed through help obtained data and location models on the networks. Finally, using some designed scenarios and identifying fifteen options as selective candidates of supply center (network knots), the proposed model will be explained and the results will be analyzed.

Quantifying the effect of location on land values can be done by designing a location factor which considers the most relevant aspects that may influence this value such as proximity to large cities, the population living around the parcel or land to be valued, the distance from it to markets or logistic centres, or the existence of places of environmental or landscape interest. Considering these variables can be complicated by having to process large amounts of distinct data (distances, no. of inhabitants or population size, protected areas, etc.), which have to be processed and interpreted to be able to define the factor that summarises them, and can affect the land value from income, such as productive assets, to correct its value. The main proposal put forward in this research is to study the various location aspects that affect land values, and the possibilities that Geographic Information Systems (GIS) offer to design with free software tools that allow simple calculations of a location correction factor and, consequently, land values. Calculations were made for all the rural cadastral parcels (2.3 million) in the Valencian Region. Results can be integrated into a new online GIS portal and make these available to users in soil valuation studies. [ABSTRACT FROM AUTHOR]

Key to the mass adoption of electric vehicles (EV) is establishing a sufficient recharging infrastructure network, based on customer behavior and psychology. This study examines the battery charging station location problem, considering users’ range anxiety and distance deviations, two major barriers to the mass adoption of EV. The problem is formulated as a bi-level integer programming model based on a range anxiety function. Then, the problem is solved using an adaptive large-neighborhood search, combined with a k-shortest path algorithm and an iterative greedy heuristic. Finally, the effects of parameters are analyzed in the context of a real-world road network. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a location model of earthquake emergency service depot on the basis of hybrid multi-attribute decision-making method. The advantage of the proposed method is that practical mixed uncertainty of location decision information is considered, and the corresponding factors that affect the location of transfer stations are contained. To solve the location problem, a hybrid multi-attribute decision procedure without information transformation is developed. Besides, a novel weighting method and aggregation process is given. Finally, a numerical example is provided to show the feasibility and validity of the proposed method. [ABSTRACT FROM AUTHOR]

It is well known that with a parameter on the boundary of the parameter space, such as in the classic cases of testing for a zero location parameter or no autoregressive conditional heteroskedasticity (ARCH) effects, the classic nonparametric bootstrap - based on unrestricted parameter estimates - leads to inconsistent testing. In contrast, we show here that for the two aforementioned cases, a nonparametric bootstrap test based on parameter estimates obtained under the null - referred to as 'restricted bootstrap' - is indeed consistent. While the restricted bootstrap is simple to implement in practice, novel theoretical arguments are required in order to establish consistency. In particular, since the bootstrap is analysed both under the null hypothesis and under the alternative, non-standard asymptotic expansions are required to deal with parameters on the boundary. Detailed proofs of the asymptotic validity of the restricted bootstrap are given and, for the leading case of testing for no ARCH, a Monte Carlo study demonstrates that the bootstrap quasi-likelihood ratio statistic performs extremely well in terms of empirical size and power for even remarkably small samples, outperforming the standard and bootstrap Lagrange multiplier tests as well as the asymptotic quasi-likelihood ratio test. [ABSTRACT FROM AUTHOR]

In life-threatening situations where every second counts, the timely presence of firefighter services can make the difference between survival and death. Motivated by this, in collaboration with Fire Department Amsterdam-Amstelland in the Netherlands, we developed a mathematical programming model for determining the optimal locations of the vehicle base stations, and for optimally distributing firefighter vehicle types over the base stations. The model is driven by practical considerations. It (1) allows for fixing any subset of existing base locations that cannot be relocated (e.g., for historical reasons); (2) includes multiple vehicle types, each of which may have a type-dependent response-time target; and (3) includes crews that consist of arbitrary mixtures of professional (i.e., career) and volunteer firefighters. Extensive analysis of a large data set obtained from the Fire Department Amsterdam-Amstelland demonstrates: (1) that a reduction of over 50 percent in the fraction of firefighter late arrivals can be realized by relocating only three of the current 19 base locations; and (2) that adding new base locations to improve performance is unnecessary: optimization of the locations of the current base stations is as effective, and saves money. The results show an enormous potential for substantially reducing the fraction of late arrivals of firefighter services, with little investment in relocating a small number of stations. [ABSTRACT FROM AUTHOR]

Technical progress consists of improvements made upon the existing technology ( incremental innovation ) and innovative activities aiming at entirely new technology ( discrete innovation ). Incremental innovation is often of limited relevance to the new technology invented by successful discrete innovation. Previous theoretical studies have indicated that higher competitive pressure measured by product substitutability increases incremental innovation. In contrast, we find that intensified competition can decrease incremental innovation. A firm's market share upon its failure in discrete innovation decreases as competition intensifies. This effect decreases firms’ incentives for incremental innovation because the innovation outcome can be applied to a smaller amount of units. [ABSTRACT FROM AUTHOR]

The main objective of this research is to offer a model for determining the most proper location for investment in sugar industry. This model classifies the possible options for investment, taking into account several variables. The orientation of this research is an applied orientation and its objective is an explorative one. Therefore, no hypothesis is proposed to prove it. The required data for determining the parameters of the model is extracted from statistical yearbooks of the Iran Ministry of Agriculture during 1996 to 2006. According to the results obtained from this research, if new investments in sugar industry are carried out based on the offered classifications and pattern, the profitability will definitely increase.

A discrimination procedure, based on the location model is described and suggested for use in situation where the discriminating variables are mixtures of continuous and binary variables. Some procedures that have been previously employed, in a similar situation, like Fisher's linear discriminant function and the logistic regression were compared with this method using error rate (ER). Optimal ERs for these procedures are reported using real and simulated data for the case of varying sample size and number of continuous and binary variables and were used as a measure for assessing the performance of the various procedures. The suggested procedure performed considerably better in the cases considered and never did produce a result that is poor when compared with other procedures. Hence, the suggested procedure might be considered for such situations. [ABSTRACT FROM AUTHOR]

The traditional approach to origin–destination (OD) estimation based on data surveys is highly expensive. Therefore, researchers have attempted to develop reasonable low-cost approaches to estimating the OD vector, such as OD estimation based on traffic sensor data. In this estimation approach, the location problem for the sensors is critical. One type of sensor that can be used for this purpose, on which this paper focuses, is vehicle identification sensors. The information collected by these sensors that can be employed for OD estimation is discussed in this paper. We use data gathered by vehicle identification sensors that include an ID for each vehicle and the time at which the sensor detected it. Based on these data, the subset of sensors that detected a given vehicle and the order in which they detected it are available. In this paper, four location models are proposed, all of which consider the order of the sensors. The first model always yields the minimum number of sensors to ensure the uniqueness of path flows. The second model yields the maximum number of uniquely observed paths given a budget constraint on the sensors. The third model always yields the minimum number of sensors to ensure the uniqueness of OD flows. Finally, the fourth model yields the maximum number of uniquely observed OD flows given a budget constraint on the sensors. For several numerical examples, these four models were solved using the GAMS software. These numerical examples include several medium-sized examples, including an example of a real-world large-scale transportation network in Mashhad. [ABSTRACT FROM AUTHOR]

Evaluating crop suitability is usually based on traditional land approaches in many countries, using only agro-ecological zoning and soil data. However, land use is also controlled by socio-economic and other biophysical factors. It is actually unknown how coffee suitability is influenced by such socio-economic and biophysical factors. Therefore, here, we studied all known factors that influence coffee production in Rwanda using an inventory of small holder coffee fields, including at least 200 coffee trees. We identified 29 potential factors, including demography, and environmental factors such as climate, soil and topography. These factors were reduced to 17 variables explaining 86 % of the total dataset variability, by factor analysis. The dataset was subsequently stratified into ten agro-ecological zones, yielding regional models that explain regional variability of coffee field density up to 54 %. Regional models show that 60 % of the actual coffee farms are located in suitable locations. [ABSTRACT FROM AUTHOR]

In this paper, a moving monitoring procedure is proposed to detect potential variance change of the location model with dependent errors. The procedure is motivated by the problem that the existing square CUSUM test is insensitive to a late variance change of the location model. The asymptotic distribution of the statistics under the null hypothesis and the consistency under the alternative hypothesis are derived. Simulations show that our monitoring procedure compared to the square CUSUM test offers better power and can more quickly detect change. Moreover, the effectiveness of our procedure is illustrated by applying it to two data sets. [ABSTRACT FROM PUBLISHER]

Since the first modern shopping centre was built in the United States in the 1920s, shopping centres have gradually become representative patterns of economic growth and consumerism in the United States, and these patterns are now trending globally. Shopping centres have demonstrated tremendous development potential since their initial entry into China in the 1990s. Shanghai is the most economically prosperous city in China, and the development and evolution of its shopping centres reflect the trend in China's commercial real estate development. Therefore, based on the central-place and agglomeration economy theory, this paper quantitatively measures and analyses the spatial gravity, extending direction, agglomeration characteristics and hierarchical structure of Shanghai's shopping centres using GIS (Geographic Information Systems) and spatial analysis. Moreover, this paper analyses the dynamic mechanism of urban development and its patterns of centripetal and centrifugal movement. The results demonstrate the following. (1) The spatial gravity points are located in the districts of Huangpu, Luwan and Xuhui in the city centre and within the inner ring. In addition, there is a trend to be gradually near the middle ring, exhibiting an obvious tendency from the northeast to the southwest. (2) Shopping centres in Shanghai exhibit a clustered distribution in the centres of urban areas, which form numerous business districts that extend in the same direction. (3) The hot spot analysis is a very effective method for identifying the hierarchy of business circles. (4) Planning by the government is the most important external impetus, and commercial agglomeration is the internal force determining the spatial expansion of shopping centres. Additionally, urban transportation patterns have an obvious influence on the spatial morphology of shopping centres. (5) Over the last two decades, the spatial development of Shanghai's shopping centres has reached a balance between the centripetal and centrifugal forces. In other words, we have not observed a tendency towards suburbanization, which indicates that Shanghai's shopping centres are still in the early stages of development. Therefore, future shopping centres may be primarily located in the stretch or peripheral zones of the city. [ABSTRACT FROM AUTHOR]

Costumers and governments are pressuring companies to become more sustainable. However, the lack of research on how to incorporate these issues makes this a challenging task. To fill this gap a generic multi-objective mathematical programming model for the design and planning of supply chains, integrating the three dimensions of sustainability is presented. The economic pillar of sustainability is addressed in this work considering the costs of the supply chain. Then ReCiPe, an environmental assessment methodology, indicated in the literature and by the European Commission as the most developed one currently available, is for the first time applied to supply chain design optimization. Finally, a social indicator appropriate to assess strategic decisions is proposed. This social indicator considers the impact of social and political concerns on company's performance. The relevance of this model as a decision support system is highlighted with its application to a real case study of a Portuguese battery producer and distributor. A set of strategies to select the best solution among the obtained optimal ones is presented. Results show that the model allows improvements in all the three dimensions of sustainability and offers important managerial insights. [ABSTRACT FROM AUTHOR]

Covariate-specific time-dependent ROC curves are often used to evaluate the diagnostic accuracy of a biomarker with time-to-event outcomes, when certain covariates have an impact on the test accuracy. In many medical studies, measurements of biomarkers are subject to missingness due to high cost or limitation of technology. This article considers estimation of covariate-specific time-dependent ROC curves in the presence of missing biomarkers. To incorporate the covariate effect, we assume a proportional hazards model for the failure time given the biomarker and the covariates, and a semiparametric location model for the biomarker given the covariates. In the presence of missing biomarkers, we propose a simple weighted estimator for the ROC curves where the weights are inversely proportional to the selection probability. We also propose an augmented weighted estimator which utilizes information from the subjects with missing biomarkers. The augmented weighted estimator enjoys the double-robustness property in the sense that the estimator remains consistent if either the missing data process or the conditional distribution of the missing data given the observed data is correctly specified. We derive the large sample properties of the proposed estimators and evaluate their finite sample performance using numerical studies. The proposed approaches are illustrated using the US Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset. [ABSTRACT FROM AUTHOR]