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The purpose of this study is to develop a holistic optimization model for an integrated sustainable fleet planning and closed-loop supply chain (CLSC) network design problem under uncertainty.

A novel mixed-integer programming model that is able to consider interactions between vehicle fleet planning and CLSC network design problems is first developed. Uncertainties of the product demand and return fractions of the end-of-life products are handled by a chance-constrained stochastic program. Several Pareto optimal solutions are generated for the conflicting sustainability objectives via compromise and fuzzy goal programming (FGP) approaches.

The proposed model is tested on a real-life lead/acid battery recovery system. By using the proposed model, sustainable fleet plans that provide a smaller fleet size, fewer empty vehicle repositions, minimal CO₂ emissions, maximal vehicle safety ratings and minimal injury/illness incidence rate of transport accidents are generated. Furthermore, an environmentally and socially conscious CLSC network with maximal job creation in the less developed regions, minimal lost days resulting from the work's damages during manufacturing/recycling operations and maximal collection/recovery of end-of-life products is also designed.

Unlike the classical network design models, vehicle fleet planning decisions such as fleet sizing/composition, fleet assignment, vehicle inventory control, empty repositioning, etc. are also considered while designing a sustainable CLSC network. In addition to sustainability indicators in the network design, sustainability factors in fleet management are also handled. To the best of the authors' knowledge, there is no similar paper in the literature that proposes such a holistic optimization model for integrated sustainable fleet planning and CLSC network design.

Green supply chain management and new product innovation and diffusion have become quite popular and act as a rich source of providing competitive advantage for companies to trade without further deteriorating environmental quality. However, research on low-carbon footprint supply chain configuration for a new product represents a comparably new trend and needs to be explored further. Using relatively simple models, the purpose of this paper is to demonstrate how carbon emissions concerns, such as carbon emission caps and carbon tax scheme, could be integrated into an operational decision, such as product procurement, production, storage and transportation concerning new fast-moving consumer goods (FMCG) product introduction.

The situation titled “low-carbon footprint supply chain configuration problems” is mathematically formulated as a multi-objective optimization problem under the dynamic and stochastic phenomenon concerning receiver’s demand requirements and production plant capacity constraints. Further, the effects of demand and capacities’ uncertainties are modeled using the chance constraint approach proposed by Charnes and Cooper (1959, 1963).

Various cases have been validated using the case example of a new FMCG product manufacturer. To validate the proposed models, data are generated randomly and solved using optimization software LINGO 10.0.

The attempt is novel in the context of considering the dynamic and stochastic phenomenon with respect to demand center’s requirements and manufacturing plant’s capacity constraints with regard to the low-carbon footprints supply chain configuration of a new FMCG product.

The purpose of this paper is to set up a two‐stage stochastic integer‐programming model (TSM) for the multiperiod scheduling of multiproduct batch plants under demand uncertainty involving the constraints of material balances and inventory constraints, as well as the penalty for production shortfalls and excess.

Scheduling model is formulated as a discrete‐time State Task Network. Given a scheduling horizon consisting of several time‐periods in which product demands are placed, the objective is to select a schedule that maximizes the expected profit for a single and multiple product with a given probability level. The stochastic elements of the model are expressed with equivalent deterministic optimization models.

The TSM model not only allows for uncertain product demand correlations, but also gives different processing modes by a range of batch sizes and a task‐dependent processing time. The experimental results show that the TSM model is more appropriate than another model for multiperiod scheduling of multiproduct batch plants under correlated uncertain demand.

The choice of penalty parameter of demand uncertainty is the main limitation.

The paper provides very useful advice for multiperiod scheduling of multiproduct batch plants under demand uncertainty.

A stochastic model for the multiperiod scheduling of multiproduct batch plants under demand uncertainty was set up. A test problem involving 12 correlated uncertain product demands and two alternative models verified the availability of the TSM.

Supplier selection problem is the key process in decision making of supply chain management. An effective selection of vendors is heavily responsible for the success of any organization. Vendor selection problem (VSP) reflects a more practical view when the decision makers involved in the problem are present on different levels. Moreover, vendor selection consists of various random parameters to be dealt with in real life. The purpose of this paper is to present a decentralized bi-level VSP where demand and supply are normal random variables and objectives are fuzzy in nature. Decision makers are present at two levels and are called as leader and follower. As the next purpose, this paper extends and presents a solution approach for fuzzy bi-level multi-objective decision-making model with stochastic constraints. Different scenarios have been developed within a real-life case study based on different sets of controlling factors under the control of leader.

This study uses chance-constrained programming and fuzzy set theory to generate the results. Stochastic constraints are converted into deterministic constraints using chance-constrained programming. Decision variables in the bi-level VSP are partitioned between the two levels and considered as controlling factors. Membership functions based on fuzzy set theory are created for the goals and controlling factors and are used to obtain the overall satisfactory solutions. The model is tested on a real-life case study of a textile industry and different scenarios are constructed based on the choice of leader’s controlling factors.

Results showed that the approach is quite helpful as it generates efficient results producing a good level of satisfaction for the decision makers of both the levels. Results showed that on choosing the vendors that are associated with worst values in terms of associated costs, vendor ratings and quota flexibilities as controlling factors by the leaders, the level of satisfaction achieved is highest. The level of satisfaction of solution is lowest for the scenario when the leader chooses to control the decision variables associated with vendors that are profiled with minimum vendor ratings. Results also showed that higher availability of materials and budget with vendors proved helpful in obtaining quota allocations. Different scenarios generate different results along with different values of satisfaction degrees and objective values which shows the flexible feature of the approach based on leader’s choice of controlling factors. Numerical results showed that the leader’s control can be effectively incorporated maintaining satisfaction levels of the followers under various scenarios or conditions.

The paper makes a certain contribution toward the study of vendor selection existing in a hierarchical manner under uncertain environment. A wide set of data of different factors is needed which can be seen as a limitation when the available time is short for the supplier selection process.

VSP which is generally adopted by most of the large organizations is characterized with hierarchical decision making. Moreover, dealing with the real-life concern, the data available for some of the parameters are not complete, representing an uncertainty of parameters. This study is quite helpful for decentralized VSP under uncertain environment to reduce the costs, improve profit margins and to create long-term relationships with selected vendors. The proposed model also provides an avenue to explore the decision making when the leader has control over some of the decision variables.

Reviewing the literature available, this is the first attempt to present a multi-objective VSP where the decision makers are at hierarchical levels considering uncertain parameters such as demand and supply as per the best knowledge of authors. This research further provides an approach to construct scenarios or different cases based on the choice of leader’s choice of controlling factors.

The liquefied natural gas (LNG) business comprises a number of economic activities with inherent risks. The purpose of this paper is to propose an integrated modelling approach, as part of the investment decision‐making process, for optimising economic returns from LNG whilst taking into account uncertainty in various key input parameters.

Inter‐linked cash flow and pricing models of the LNG chain were constructed. Net present value was maximised based on selection of netback pricing variables and level of investment shareholding. Constraints were placed on the minimum acceptable returns. The risk affinity of the decision maker was captured in the form of a chance‐constrained optimisation problem. A genetic algorithm was applied for numerical optimisation, in combination with Monte Carlo simulations to account for the stochastic nature of the problem.

Based on the results of a case study, the deterministic solution, having no consideration to uncertainty, was found to be both sub‐optimal and provided an unsatisfactory risk outcome. The stochastic approach yielded an optimal solution with due consideration to risk. Various scenarios show that the choice of the decision variables significantly impacts the trade‐off between risk and returns along the LNG chain to government and investor.

The suitability of the methodology to the operational phase of the LNG business which incorporates different elements of risk, such as market dynamics and logistics, is as yet untested.

This framework may be useful in the formulation of optimal commercial structure of firms, investment portfolio and gas/LNG pricing arrangements for host governments involved in the LNG business.

The purpose of this paper is to present an efficient method for the numerical treatment of robust optimization problems with absolute reliability constraints.

Optimization with anti-optimization based on response surface techniques; polynomial chaos for approximation of the stochastic objective function.

The number of function calls is comparable to that of the corresponding deterministic problem. Thus, the method is well suited for complex technical systems. The performance of the method is demonstrated on an optimal design problem for turbochargers.

The highlights of this paper are: algorithms for robust and deterministic problems show comparable complexity; no derivatives required; good convergence properties because of special set up of optimization problem; application in complex industrial examples.

INTRODUCTION With the increasing importance of capital investment selection in modern business the field has attracted a large body of interest in the literature of the last two decades. It is the purpose of the survey to trace this development from the use of simple financial criteria for assessing investments to the use of more sophisticated financial measures, techniques for assessing risk in investments and finally complex models for selecting portfolios of investments.

The purpose of this paper deals with a capacitated multi-item dynamic lot-sizing problem with the simultaneous sequence-dependent setup scheduling of the parallel resource under complex uncertainty.

An improved chance-constrained method is developed, in which confidence level of uncertain parameters is used to process uncertainty, and based on this, the reliability of the constraints is measured. Then, this study proposes a robust reconstruction method to transform the chance-constrained model into a deterministic model that is easy to solve, in which the robust transformation methods are used to deal with constraints with uncertainty on the right/left. Then, experimental studies using a real-world production data set provided by a gearbox synchronizer factory of an automobile supplier is carried out.

This study has demonstrated the merits of the proposed approach where the inventory of products tends to increase with the increase of confidence level. Due to a larger confidence level may result in a more strict constraint, which means that the decision-maker becomes more conservative, and thus tends to satisfy more external demands at the cost of an increase of production and stocks.

Joint decisions of production lot-sizing and scheduling widely applied in industries can effectively avert the infeasibility of lot-size decisions, caused by capacity of lot-sing alone decision and complex uncertainty such as product demand and production cost. is also challenging.

This study provides more choices for the decision-makers and can also help production planners find bottleneck resources in the production system, thus developing a more feasible and reasonable production plan in a complex uncertain environment.

This paper aims to provide an integrated production-routing model in a three-echelon supply chain containing a two-layer transportation system to minimize the total costs of production, transportation, inventory holding and expired drugs treatment. In the proposed problem, some specifications such as multisite manufacturing, simultaneous pickup and delivery and uncertainty in parameters are considered.

At first, a mathematical model has been proposed for the problem. Then, one possibilistic model and one robust possibilistic model equivalent to the initial model are provided regarding the uncertain nature of the model parameters and the inaccessibility of their probability function. Finally, the performance of the proposed model is evaluated using the real data collected from a pharmaceutical production center in Iran. The results reveal the proper performance of the proposed models.

The results obtained from applying the proposed model to a real-life production center indicated that the number of expired drugs has decreased because of using this model, also the costs of the system were reduced owing to integrating simultaneous drug pickup and delivery operations. Moreover, regarding the results of simulations, the robust possibilistic model had the best performance among the proposed models.

This research considers a two-layer vehicle routing in a production-routing problem with inventory planning. Moreover, multisite manufacturing, simultaneous pickup of the expired drugs and delivery of the drugs to the distribution centers are considered. Providing a robust possibilistic model for tackling the uncertainty in demand, costs, production capacity and drug expiration costs is considered as another remarkable feature of the proposed model.

This paper studies the textile supply chain tactical planning under demand fuzziness through considering environmentally friendly and social responsibility. Hence, carbon emission in textile production and transportation is considered along with supply chain profitability.

The authors present a fuzzy multi-objective mathematical optimization model with credibilistic chance constraints to determine the fabric procurement quantities and production plan under uncertainty. The solution procedure makes use of credibility measure and fuzzy aggregation operator to attain compromise solutions.

A trade-off among carbon emissions, social performance and supply chain total profit is conducted. The analyses indicate the importance of transportation costs and carbon emission while determining the supply chain's tactical plan.

The textile supply chain's social sustainability alongside carbon emissions of textile operations is contemplated to provide apparel production and distribution logistics planning under uncertainty. In doing so, the authors propose a hybrid credibility-possibility mathematical optimization model to determine a compromise solution for textile managers.