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The paper examines the effect of uncertainty on the solution of mathematical programming problems, using Bayesian techniques. We show that the statistical inference of the unknown parameter lies in the solution vector itself. Uncertainty in the data is modeled using sampling models induced by constraints. In this context, the objective is used as prior, and the posterior is efficiently applied via Monte Carlo methods. The proposed techniques provide a new benchmark for robust solutions that are designed without solving mathematical programming problems. We illustrate the benefits of a problem with known solutions and their properties, while discussing the empirical aspects in a real-world portfolio selection problem. [ABSTRACT FROM AUTHOR]

In this paper, we address a two-stage hybrid flowshop scheduling problem with identical parallel machines in each stage. The problem assumes that the queue (Q)-time for each job, which represents the waiting time to be processed in the current stage, must be limited to a predetermined threshold due to quality concerns for the final product. This problem is motivated by one that occurs in the real field, especially in the diffusion workstation of a semiconductor fabrication. Our objective is to minimize the makespan of the jobs while considering product quality. To achieve this goal, we formulated mathematical programming, developed two dominance properties for this problem, and proposed three heuristics with the suggested dominance properties to solve the considered problem. We conducted simulation experiments to evaluate the performance of the proposed approaches using randomly generated problem instances that are created to closely resemble real production scenarios, and the results demonstrate their superiority over existing methods. Furthermore, we applied the proposed methods in a real-world setting within the semiconductor fabrication industry, where they have exhibited better performance compared to the dispatching rules commonly used in practical applications. These findings validate the effectiveness and applicability of our proposed methodologies in real-world scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we consider semi-infinite mathematical programming problems with equilibrium constraints (SIMPEC). By using the notion of convexificators, we establish sufficient optimality conditions for the SIMPEC. We formulate Wolfe and Mond-Weir type dual models for the SIMPEC under generalized convexity assumptions. Moreover, weak and strong duality theorems are established to relate the SIMPEC and two dual programs in the framework of convexificators. [ABSTRACT FROM AUTHOR]

Since its introduction in the early 2000s, robust optimization with budget uncertainty has received a lot of attention. This is due to the intuitive construction of the uncertainty sets and the existence of a compact robust reformulation for (mixed-integer) linear programs. However, despite its compactness, the reformulation performs poorly when solving robust integer problems due to its weak linear relaxation. To overcome the problems arising from the weak formulation, we propose a bilinear formulation for robust binary programming, which is as strong as theoretically possible. From this bilinear formulation, we derive strong linear formulations as well as structural properties for robust binary optimization problems, which we use within a tailored branch and bound algorithm. We test our algorithm's performance together with other approaches from the literature on a diverse set of "robustified" real-world instances from the MIPLIB 2017. Our computational study, which is the first to compare many sophisticated approaches on a broad set of instances, shows that our algorithm outperforms existing approaches by far. Furthermore, we show that the fundamental structural properties proven in this paper can be used to substantially improve the approaches from the literature. This highlights the relevance of our findings, not only for the tested algorithms, but also for future research on robust optimization. To encourage the use of our algorithms for solving robust optimization problems and our instances for benchmarking, we make all materials freely available online. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new approach to dynamic wireless charging that allows electric vehicles to charge wirelessly while in motion in both lanes on highways. The challenge is to locate the charging infrastructure on a highway between origin O and destination S (round trip) with heterogeneous battery vehicles, where each type of vehicle requires its allocation of charging segments on the road. We aim to ensure that each type of vehicle can complete a round trip without running out of battery charge while minimizing the number of charging segments and inverters on the road by studying both lanes simultaneously. We model the problem mathematically and validate it using a CPLEX optimizer for limited instances. Finally, we solve the problem using a hybrid approach that combines genetic algorithms and local search techniques to balance diversification and intensification. We have significantly improved the results found in the literature by reducing the number of inverters, which are expensive components in the charging infrastructure. Our approach takes advantage of utilizing a single inverter for both lanes of the highway, leading to cost savings and improved efficiency. [ABSTRACT FROM AUTHOR]

Motivated by recent investigations relating the sharpness of the Jensen inequality, this paper concerns with the sharpness of the converse of the Jensen inequality. For this reason, the Jensen inequality has become one of the most discussed developmental inequalities in the current literature on mathematical inequalities. In this Special Issue, we present new results related to classical inequalities, such as the Jensen inequality, Jensen-Steffensen inequality, Jessen inequality, Grüss inequality, Chebyshev inequality, etc. [Extracted from the article]

Decreasing greenhouse gas emissions plays a crucial role in the Europe energy transition and the production of hydrogen using electricity from renewable sources (green H 2) contributes significantly to this objective. As the renewable energy production capacity grows, the impact of green H 2 is likely to increase. In the case of the Iberian Electricity Market (MIBEL), no quantitative studies have so far tested the viability of the H 2 growth plans. This paper fills this gap through a novel mathematical programming model, which integrates H2 generation into the MIBEL. The model reveals a mismatch between the sustainability goals and the expansion plans of renewable and green H 2 for Spain and Portugal. [Display omitted] • Mathematical Programming to analyse green hydrogen production in the MIBEL. • Influence of the electricity market on hydrogen production and prices. • Generating green hydrogen is preferable to hydro pumping. • Green hydrogen integration might entail additional emissions. • MIBEL hydrogen strategy must be revised to achieve sustainability. [ABSTRACT FROM AUTHOR]

The paper deals with the mathematical programming problems with switching constraints that are defined with continuously differentiable functions. The main results are the upper approximations of the Frèchet normal cone of the feasible set for the problem. As applications of the main results, we present some stationary conditions of the considered problem. [ABSTRACT FROM AUTHOR]

This paper proposes a generalization of Markowitz model that incorporates skewness and kurtosis into the classical mean–variance allocation framework. The principal appeal of the present approach is that it provides the closed-form solution of the optimization problem. The four moments optimal portfolio is then decomposed into the sum of three portfolios: the mean–variance optimal portfolio plus two self-financing portfolios, respectively, accounting for skewness and kurtosis. Theoretical properties of the optimal solution are discussed together with the economic interpretation. Finally, an empirical exercise on real financial data shows the contribution of the two portfolios accounting for skewness and kurtosis when financial returns depart from Normal distribution. [ABSTRACT FROM AUTHOR]

The transition towards climate neutrality will result in an increase in electrical vehicles, as well as other electric loads, leading to higher loads on electrical distribution grids. This paper presents an optimisation algorithm that enables the integration of more loads into distribution grid infrastructure using information from smart meters and/or smart meter gateways. To achieve this, a mathematical programming formulation was developed and implemented. The algorithm determines the optimal charging schedule for all electric vehicles connected to the distribution grid, taking into account various criteria to avoid violating physical grid limitations and ensuring non-discriminatory charging of all electric vehicles on the grid while also optimising grid operation. Additionally, the expandability of the infrastructure and fail-safe operation are considered through the decentralisation of all components. Various scenarios are modelled and evaluated in a simulation environment. The results demonstrate that the developed optimisation algorithm allows for higher transformer loads compared to a P(U) control approach, without causing grid overload as observed in scenarios without optimisation or P(U) control. [ABSTRACT FROM AUTHOR]

In the academic year 2020-21 Middlesex University maths students accessed all learning sessions remotely. Each of these interactive sessions was live-streamed, recorded and uploaded to our Virtual Learning Environment, providing hundreds of hours of recorded, unedited maths lectures for students to review. This case study reports on a project (partially funded by an IMA Education Grant) in which we invited undergraduates to reflect on their remote learning experiences and curate these video lectures. Students were asked to identify the most engaging, useful and interesting segments, and categorise and explain their choices in free-text comments to help us develop our approach to remote lectures and video resources. A total of 33 video clips were identified by students across levels 4 to 6 on our specialist BSc Mathematics and BSc Mathematics with Computing programmes. In this paper we will discuss our findings, illustrate with example clips, identify themes in the student choices, and conclude with tips to produce engaging content. We will also discuss applications of video curation as a social pedagogic tool for the current Generation Z students. We will argue that sharing how students interact with digital learning resources can help address the significant digital divide in education. [ABSTRACT FROM AUTHOR]

One of the most common systems in non-automated warehouses, is drive-in pallet racking with a shared storage policy (which is usually based on the duration-of-stay). Such scheme targets towards an efficient use of storage space, since its operation costs are directly related to the size and layout of the warehouse. In this paper, two mathematical programming models and two greedy-randomised based heuristics for finding (nearly) optimal storage and retrieval operation sequences for this type of storage system are proposed. The computational effectiveness of the proposed approaches is measured by considering two sets of synthetic instances. The obtained results show that the proposed heuristics are not only able to compute high-quality solutions (as observed when being compared with the optimal solutions attained by the mathematical programming models), but it is also capable of providing solutions in very short running times even for large instances for which the mathematical programming model failed to find feasible solutions. At the light of these results, the best heuristic is also tested using a rolling-horizon planning strategy in a real-world case study, obtained from a Chilean company. It turns out that the attained results are more effective than the company's current storage policy. [ABSTRACT FROM AUTHOR]

In this paper, we point out some corrections needed in "Complexity of Stochastic Dual Dynamic Programming", a paper accepted to Mathematical Programming, 2020, online-first issue,. [ABSTRACT FROM AUTHOR]

In this paper, we study the quadratic assignment problem with a rank-one cost matrix (QAP-R1). Four integer-programming formulations are introduced of which three are assumed to have partial integer data. Unlike the standard quadratic assignment problem, some of our formulations can solve reasonably large instances of QAP-R1 with impressive running times and are faster than some metaheuristics. Pairwise relative strength of the LP relaxations of these formulations are also analyzed from theoretical and experimental points of view. Finally, we present a new metaheuristic algorithm to solve QAP-R1 along with its computational analysis. Our study offers the first systematic experimental analysis of integer-programming models and heuristics for QAP-R1. The benchmark instances with various characteristics generated for our study are made available to the public for future research work. Some new polynomially solvable special cases are also introduced. Summary of Contribution: This paper aims to advance our knowledge and ability in solving an important special case of the quadratic assignment problem. It shows how to exploit inherent properties of an optimization problem to achieve computational advantages, a strategy that was followed by researchers in model building and algorithm developments for decades. Our computational results attest to this time-tested general philosophy. The paper presents the first systematic computational study of the rank one quadratic assignment problem, along with new mathematical programming models and complexity analysis. We believe the theoretical and computational results of this paper will inspire further research on the topic and will be of significant value to practitioners using rank one quadratic assignment models. [ABSTRACT FROM AUTHOR]

Inference-based optimization via simulation, which substitutes Gaussian process (GP) learning for the structural properties exploited in mathematical programming, is a powerful paradigm that has been shown to be remarkably effective in problems of modest feasible-region size and decision-variable dimension. The limitation to "modest" problems is a result of the computational overhead and numerical challenges encountered in computing the GP conditional (posterior) distribution on each iteration. In this paper, we substantially expand the size of discrete-decision-variable optimization-via-simulation problems that can be attacked in this way by exploiting a particular GP—discrete Gaussian Markov random fields—and carefully tailored computational methods. The result is the rapid Gaussian Markov Improvement Algorithm (rGMIA), an algorithm that delivers both a global convergence guarantee and finite-sample optimality-gap inference for significantly larger problems. Between infrequent evaluations of the global conditional distribution, rGMIA applies the full power of GP learning to rapidly search smaller sets of promising feasible solutions that need not be spatially close. We carefully document the computational savings via complexity analysis and an extensive empirical study. Summary of Contribution: The broad topic of the paper is optimization via simulation, which means optimizing some performance measure of a system that may only be estimated by executing a stochastic, discrete-event simulation. Stochastic simulation is a core topic and method of operations research. The focus of this paper is on significantly speeding-up the computations underlying an existing method that is based on Gaussian process learning, where the underlying Gaussian process is a discrete Gaussian Markov Random Field. This speed-up is accomplished by employing smart computational linear algebra, state-of-the-art algorithms, and a careful divide-and-conquer evaluation strategy. Problems of significantly greater size than any other existing algorithm with similar guarantees can solve are solved as illustrations. [ABSTRACT FROM AUTHOR]

This paper investigates the selection of third-party logistics providers (3PLs) based on the best prices offered by them. The focus is on outbound logistics where 3PLs must have their own distribution centres for storage and picking activities. They must also have suitable trucks for distribution to different small-scale customers. The motivation for this paper is a case study from Germany in which a furniture company with hundreds of small customers in ten zones is seeking one or more 3PLs to do the distribution. A mathematical programming model was built based on integer programming where demand per order can be expressed using exponential distribution in each customer zone. The main contribution of this paper is that it finds the best 3PLs based on the different pricing methods of the various providers; this means including the location problem indirectly using the new integer programming model. The model takes into consideration three different methods of pricing based on the offers of five 3PLs. These different methods make it difficult for the decision makers to choose the best solution, especially if specific trends in demand are expected in the future for some customer zones. The results show that future increases in demand in terms of the number of orders or order size could affect the optimal solution. The best pricing method with the lowest variability in cost over time is selected. [ABSTRACT FROM AUTHOR]

Adaptive regularization with cubics (ARC) is an algorithm for unconstrained, non-convex optimization. Akin to the trust-region method, its iterations can be thought of as approximate, safe-guarded Newton steps. For cost functions with Lipschitz continuous Hessian, ARC has optimal iteration complexity, in the sense that it produces an iterate with gradient smaller than ε in O (1 / ε 1.5) iterations. For the same price, it can also guarantee a Hessian with smallest eigenvalue larger than - ε . In this paper, we study a generalization of ARC to optimization on Riemannian manifolds. In particular, we generalize the iteration complexity results to this richer framework. Our central contribution lies in the identification of appropriate manifold-specific assumptions that allow us to secure these complexity guarantees both when using the exponential map and when using a general retraction. A substantial part of the paper is devoted to studying these assumptions—relevant beyond ARC—and providing user-friendly sufficient conditions for them. Numerical experiments are encouraging. [ABSTRACT FROM AUTHOR]

Purpose: Repetitive projects play an important role in the construction industry. A crucial point in scheduling this type of project lies in enabling timely movement of crews from unit to unit so as to minimize the adverse effect of work interruptions on both time and cost. This paper aims to examine a repetitive scheduling problem with work continuity constraints, involving a tradeoff among project duration, work interruptions and total project cost (TPC). To enhance flexibility and practicability, multi-crew execution is considered and the logic relation between units is allowed to be changed arbitrarily. That is, soft logic is considered. Design/methodology/approach: This paper proposes a multi-objective mixed-integer linear programming model with the capability of yielding the optimal tradeoff among three conflicting objectives. An efficient version of the e-constraint algorithm is customized to solve the model. This model is validated based on two case studies involving a small-scale and a practical-scale project, and the influence of using soft logic on project duration and total cost is analyzed via computational experiments. Findings: Using soft logic provides more flexibility in minimizing project duration, work interruptions and TPC, especial for non-typical projects with a high percentage of non-typical activities. Research limitations/implications: The main limitation of the proposed model fails to consider the learning-forgetting phenomenon, which provides space for future research. Practical implications: This study assists practitioners in determining the "most preferred" schedule once additional information is provided. Originality/value: This paper presents a new soft logic-based mathematical programming model to schedule repetitive projects with the goal of optimizing three conflicting objectives simultaneously. [ABSTRACT FROM AUTHOR]

The development of customized service is an important way to transform and upgrade China's mining industry. However, in practice, there remain problems, such as the slow market response speed of service providers and the contradiction between the large-scale development of service providers and the personalized service needs of service demanders. This paper uses the theory and method of service modular design to solve these problems and explores the process-based service modular design method. Service modular design depends largely on the determination of the relationship between service activities and the reasonable division of modules. However, previous research has rarely made use of modular design methods and modeling tools in the mining service context. At the same time, evaluations of the relationship between service activities relying on knowledge and those relying on experience have been inconclusive. Therefore, this paper proposes a service modularization design method based on the fuzzy relation analysis of a design structure matrix (DSM) that solves the optimal module partition scheme. Triangular fuzzy number and fuzzy evidence theory are used to evaluate and fuse the multidimensional and heterogeneous relationship between service activities, and the quantitative processing of the comprehensive relationship between service activities is carried out. On this basis, the service module structure is divided, followed by the construction of the mathematical programming model with the maximum sum of the average cohesion degree in the module and the average coupling degree between modules as the driving goal. The genetic algorithm is used to solve the problem, and the optimal module division result is obtained. Finally, taking the service modular design of SHD coal production enterprises in China as an example, the feasibility of the proposed method is verified. [ABSTRACT FROM AUTHOR]

This research investigates the effectiveness of loops and paths as embedded in a modified pinch package (Aspen Energy Analyzer), that comprises a blend of traditional pinch technique with mathematical programming, in simultaneous optimization of total annual cost (TAC) in heat exchanger network synthesis (HENS). It uses composite curves, grand composites curves, supertargeting and looping system just as in pinch, as well as linear programming and mixed integer linear programming (MILP) in the design of HENs. The tool was adopted in solving some literature problems that had earlier been solved using pinch and mathematical programming techniques. The results obtained compared well with those of various authors that used different techniques as shown in the tables of cost comparison in this paper. The loop and path optimization technique adopted in this research obtained the least TAC in four out of five problems solved in this paper. This shows that loop and path optimization as available in a software-combining pinch and mathematical programming can be more effective than various other methods that have been adopted in the literature. It further demonstrated that no particular technique can return the lowest TAC for all HENS problems. [ABSTRACT FROM AUTHOR]

Process capacity and the associated notions of bottleneck activities and bottleneck resources—which are responsible for limiting process capacity to its present value—are fundamental concepts in the operations management literature. However, for processes that involve collaboration and multitasking, there is little clarity in the literature on what bottlenecks are, what they look like, and how they can be identified. In this paper, we formulate and analyze graph-theoretic optimization problems that determine bottleneck structures of activities and the associated bottleneck sets of resources in deterministic, single-product processes with possibly multiple copies of one or more resources and possibly multiple sets of resources that can perform each activity. In the presence of both collaboration and multitasking, sets of activities that are interconnected in a specific manner via shared resources form bottleneck structures that are responsible for limiting capacity. We use the collaboration graph of the process to either characterize bottleneck structures completely or identify graphical structures that must necessarily be part of any bottleneck structure. Our analysis reveals a natural hierarchy in the algorithmic approach for identifying bottleneck structures as processes become increasingly sophisticated, ranging from the "easy" case where the simple bottleneck formula correctly identifies bottlenecks to more complex cases where one needs to solve progressively complicated mathematical programs. In turn, this understanding helps us obtain prescriptive answers to several questions of interest to managers, for example, the budget-constrained procurement of resources to maximize capacity improvement and the design of processes to increase capacity without procuring additional resources. This paper was accepted by Jayashankar Swaminathan, operations management. [ABSTRACT FROM AUTHOR]

In this paper, we amend a multi-criteria methodology known as MURAME, to evaluate the creditworthiness of a large sample of Italian Small and Medium-sized Enterprises, using as input their balance sheet data. This methodology produces results in terms of scoring and of classification into homogeneous rating classes. A distinctive goal of this paper is to consider a preference disaggregation method to endogenously determine some parameters of MURAME, by solving a nonsmooth constrained optimization problem. Because of the complexity of the involved mathematical programming problem, for its solution we use an evolutionary metaheuristic, coupled with a specific efficient initialization. This is combined with an unconstrained reformulation of the problem, which provides a reasonable compromise between the quality of the solution and the computational burden. An extensive numerical experience is reported, comparing an exogenous choice of MURAME parameters with our approach. [ABSTRACT FROM AUTHOR]

This paper is dedicated to investigate the explicit Lagrangian topological optimization for stress-constrained problems with global and local volume constraints. In most of the works in the state of the art, the global volume constraints were chosen as the main constraint of the optimization formulation. However, in many of the industrial applications such as in automotive engineering, some packaging regulations may lead to local volume constraints which should be considered in optimization formulation. In this research, a low-dimensional explicit parametrization approach called moving morphable components is coupled with mathematical programming to solve the aforementioned problem. The large-scale stress constraint is handled with aggregation techniques. The results of this paper are presented in some famous benchmark problems with different local volume constraints. It is demonstrated that local volume constrained can be easily handled with this approach. The present approach can be more effective in solving real engineering problems with packaging constraints in comparison with the traditional methods. [ABSTRACT FROM AUTHOR]

Backrooms are an important echelon of the retail supply chain. However, research focus has been mostly targeted to optimise both distribution centres and stores' sales area. In this paper, we propose two mathematical programming formulations to solve the grocery backroom sizing problem. This problem consists of determining the dimension of each storage department in the backroom area to optimise its overall efficiency. The first formulation is a bottom-up approach that aims to reduce the backroom life-cycle costs by determining the optimum floor space and storage height for each department. The second is a top-down approach based on Data Envelopment Analysis (DEA), which determines the efficient level of storage floor space for each backroom department, based on a comparison with the benchmarks observed among existing stores. Each approach has distinct characteristics that turn the models suitable for different retail contexts. We also describe the application of the proposed approaches to a case study of a European retailer. The application of this methodology in the design process demonstrated substantial potential for space savings (6% for the bottom-up model and 16% for the top-down model). This space reduction should either allow higher revenues in the sales area and/or lower backroom-related costs. [ABSTRACT FROM AUTHOR]

Optimization is an important and decisive task in science. Many optimization problems in science are naturally too complicated and difficult to be modeled and solved by the conventional optimization methods such as mathematical programming problem solvers. Meta-heuristic algorithms that are inspired by nature have started a new era in computing theory to solve the optimization problems. The paper seeks to find an optimization algorithm that learns the expected quality of different places gradually and adapts its exploration-exploitation dilemma to the location of an individual. Using birds' classical conditioning learning behavior, in this paper, a new particle swarm optimization algorithm has been introduced where particles can learn to perform a natural conditioning behavior towards an unconditioned stimulus. Particles are divided into multiple categories in the problem space and if any of them finds the diversity of its category to be low, it will try to go towards its best personal experience. But if the diversity among the particles of its category is high, it will try to be inclined to the global optimum of its category. We have also used the idea of birds' sensitivity to the space in which they fly and we have tried to move the particles more quickly in improper spaces so that they would depart these spaces as fast as possible. On the contrary, we reduced the particles' speed in valuable spaces in order to let them explore those places more. In the initial population, the algorithm has used the instinctive behavior of birds to provide a population based on the particles' merits. The proposed method has been implemented in MATLAB and the results have been divided into several subpopulations or parts. The proposed method has been compared to the state-of-the-art methods. It has been shown that the proposed method is a consistent algorithm for solving the static optimization problems. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to extend the newly established a-feasibility and a-efficiently concept for grey flexible fuzzy linear programming, so as to present some important new concepts, models, methods, and a new framework of grey system theory in mathematical programming. In this paper, we concentrate on Grey Fuzzy Flexible Linear Programming (GFFLP) problems as a reasonable extension of GLP models that adapt more to real situations. For this aim, after defining the classical GFFLP model, we first introduce a new concept of a -feasibility and a - efficiency to these problems, and then we propose a two-phase approach to solve the mentioned problems. Furthermore, we give some fundamental theorems and constructive results to support and verify the proposed solving process. This approach will be open a new window to the modeling of the problems in the real world under flexibility conditions. A lot of successful practical applications of the new models to solve various problems have been found in many different areas and disciplines such as agriculture, decision sciences, diet problem, ecology, economy, geology, earthquake, industry, material science sports, medicine, management, transportation, and etc. Because of the ability to deal with poor, incomplete, or uncertain problems with grey systems, most real-world processes in decision problems are in the grey stage due to lack of information and uncertainty. However, the flexibility assumption in decision making is more comfortable for the Decision Maker (DM), hence in this paper, we concentrate on Grey Fuzzy Flexible Linear Programming (GFFLP) problems as a reasonable extension of GLP models in which is more adept with the real situations, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially when the available information is incomplete and the collected data is inaccurate. In this study, a general picture of grey mathematical programming under flexibility conditions is given as a new model and a new framework for various real problems where partial information is known; especially for uncertain decision systems with few data points and poor information. [ABSTRACT FROM AUTHOR]

[Display omitted] This paper presents an extended methodology for the design of flexible water network (FWN). In many water network systems, parameters of the water-using processes (e.g. flow rate, concentration, etc.) vary due to operational changes. Hence, it is important to synthesize a FWN that can absorb these changes, so to ensure business sustainability. In this paper, the recently established corner point method for FWN synthesis is extended to cater the discrete way of process parameters change. The newly proposed methodology ensures the synthesized FWN to achieve the intended objective, i.e. minimum fresh water intake and minimum total pipeline length, while satisfying the various process constraints (e.g. flow rate, concentration, etc.). To address the multiple-objective problem, a three-step optimization method has been developed. The corner point method is also extended to synthesize a FWN that achieves the minimum total annualized costs (TAC). A literature case study was used to show the usefulness of the proposed method. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to design an applied mathematical model to maximize the profits of maintenance activities in manufacturing organizations, also providing an efficient solution method for that. Design/methodology/approach: Reviewing published articles in the field of maintenance planning and then trying to model the problem to optimal decision making in this field. Findings: Maintenance optimization can be done more appropriately by the accurate use of mathematical programming. Research limitations/implications: The existence of probabilistic parameters in this problem leads to hard stochastic programming. Practical implications: Designing and organizing maintenance activities will increase productivity. This paper attempts to use mathematical models to optimize this matter. Originality/value: This paper highlights the importance of using optimization methods for maintenance planning. [ABSTRACT FROM AUTHOR]

Major manufactures are moving towards a sustainability goal. This paper introduces the results of collaboration with the leading company in the packaging and advertising industry in Germany and Poland. The problem addresses the manufacturing planning problem in terms of minimizing the total cost of production. The challenge was to bring a new production planning method into cardboard manufacturing and paper processing which minimizes waste, improves the return of expenses, and automates daily processes heavily dependent on the production planners' experience. The authors developed a module that minimizes the total cost, which reduces the overproduction and is used by the company's manufacturing planning team. The proposed approach incorporates planning allowances rules to compromise the manufacturing requirements and production cost minimization. [ABSTRACT FROM AUTHOR]

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Featured Application: This work considers a real-life problem posed by public institutions of Colombia responsible for the design and implementation of food supply master plans. As such, the results presented in this paper will likely have a direct impact in public policies that consider both ends of a fresh food supply chain: Farmers in the countryside and end consumers at the major demand centers. This paper investigates the problem of sustainable rural supply and urban distribution of fresh food products in central Colombia. Paradoxically, while farmers in the countryside suffer from poverty due to the low profitability of the agricultural activity, inhabitants at urban centers pay high prices for fresh and nutritious foods. In this work, we propose a supply chain system and a business model based on food hubs located on existing (and often abandoned) public facilities in the central region of Colombia. There are many examples in which the hub strategy has facilitated trade and logistics in supply chains. However, few studies consider the particularities of the presented case. We study a business strategy through a mathematical model which considers both the sustainable and efficient operation of the food hubs and better trading conditions for farmers. We propose a variant of the competitive hub location problem adapted to this case study. We tested the model under different scenarios such as changes in the attractiveness parameters, operation costs, and profit margins. The results suggest that if hubs are able to attract farmers, the model can be both sustainable for the hub concessionaires and for the farmers. [ABSTRACT FROM AUTHOR]

Project management is a process that schemes and controls the project life cycle via the easiest and the best way to achieve project goals. Project managers always aim to simultaneously handle conflicting goals in the organization. In this paper, a new mathematical model is proposed that simultaneously minimizes total cost and completion time and maximizes the quality in the project management decision problem. Contractual penalty cost and contractual reward cost with a new method are the other consideration in the proposed model. In the projects, the relation between time and direct cost is a nonlinear function. Hence, a linearization technique is presented with attention to variable change and piecewise linearization, in which nonlinear function is converted to the linear programming model. On the other hand, in real conditions according to uncertainty in environmental situations and incomplete information, there can be ambiguity in parameters and variables of the problem. The uncertainty of the parameters and variables is expressed with fuzzy sets theory and fuzzy mathematical programming. The other aim of this paper is to introduce a modified version of fully fuzzy multi-objective linear programming for the problem. For analyzing a fully fuzzy time–cost–quality project management model, a practical example of the literature is provided. By examining the results of the model with conflicting objectives, two scenarios are presented to explore the interactions of conflicting objectives on the project, and the results are reported. [ABSTRACT FROM AUTHOR]

A multi-mode resource-constrained project scheduling problem (MRCPSP) with multiple skills is investigated in this paper. Unlike the traditional form of this problem, and considering the real-world project circumstances, project activities can be preempted. In this paper, a new multi-objective mixed-integer linear programming (MILP) model with three objective functions is extended. These objectives are: (1) minimizing the project makespan, (2) minimizing the total resource costs, and (3) minimizing the total project risk. Based on real-life projects, non-renewable resources are represented as an uncertain stochastic parameter. To cope with the uncertain environment, chance-constrained programming with a confidence level is considered. A real-world construction project of a sports center in Tehran is utilized to demonstrate the applicability of the presented formulation. A well-known lexicographic optimization method, namely AUGMECON2, is applied to solve the proposed formulation with three objectives. Ultimately, for the case study and two datasets J30 and MM50, the proposed lexicographic optimization algorithm is compared with an efficient multi-objective mathematical programming technique known as the AUGMECON method. The comparison is based on performance metrics (i.e., IGD and HV) commonly used in multi-objective optimization. The results show the relative dominance of the proposed lexicographic optimization algorithm over the AUGMECON method in all sizes of the problem instances. [Display omitted] • Considering a multi-skill multi-mode resource-constrained project scheduling problem with preemption. • Presenting a new multi-objective mixed-integer linear programming model for problem with a time lag between activities. • Minimizing three objectives: the total project risk, project makespan, and total project cost simultaneously. • Investigating the real project of building a sports center in a prominent engineering company to validate the model. • Proposing chance-constrained programming with the stochastic parameter and AUGMECON2 method for the first time. [ABSTRACT FROM AUTHOR]

This paper considers the design and balancing of mixed-model disassembly lines with multi-robotic workstations under uncertainty. Tasks of different models are performed simultaneously by the robots which have different capacities for disassembly. The robots have unidentical task times and energy consumption respectively. Task precedence diagrams are used to model the precedence relations among tasks. Considering uncertainties in disassembly process, the task processing times are assumed to be interval numbers. A mixed-integer mathematical programming model is proposed to minimise the cycle time, peak workstation energy consumption, and total energy consumption. This model has a significant managerial implication in real-life disassembly line systems. Since the studied problem is known as NP-hard, a metaheuristic approach based on an evolutionary simulated annealing algorithm is developed. Computational experiments are conducted and the results demonstrate the proposed algorithm outperforms other multi-objective algorithms on optimisation quality and computational efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we propose the concepts of the composition of possibilistic variables and state functions. While in conventional compositional data analysis, the interdependent components of a deterministic vector must add up to a specific quantity, we consider such components as possibilistic variables. The concept of state function is intended to describe the state of a dynamic variable over time. If a state function is used to model decay in time, it is called the ageing function. We present a practical implementation of our concepts through the development of a model for a supply chain planning problem, specifically the order promising process for perishables. We use the composition of possibilistic variables to model the existence of different non-homogeneous products in a lot (sub-lots with lack of homogeneity in the product), and the ageing function to establish a shelf life-based pricing policy. To maintain a reasonable complexity and computational efficiency, we propose the procedure to obtain an equivalent interval representation based on α-cuts, allowing to include both concepts by means of linear mathematical programming. Practical experiments were conducted based on data of a Spanish supply chain dedicated to pack and distribute oranges and tangerines. The results validated the functionality of both, the compositions of possibilistic variables and ageing functions, showing also a very good performance in terms of the interpretation of a real problem with a good computational performance. [ABSTRACT FROM AUTHOR]

This paper proposes a robust possibilistic and multi-objective mixed-integer linear programming mathematical model to concurrently plan part quality inspection and Preventive Maintenance (PM) activities for a serial multi-stage production system. This system contains the deteriorating stages and faces the uncertainty about estimated cost components and demand amount. The integrated model reaches two significant decisions which are the right time and place for performing the part quality inspection and PM. These decisions are made while the model is to simultaneously optimise the implied system productivity and total cost. To measure the implied system productivity, a new piecewise utility function for the ratio of produced conforming products to input workpieces is developed. A real case study and a numerical example are explored to validate and verify the developed model. The results prove the significance and effectiveness of considering the uncertainty and conflicting practical objectives for the problem. [ABSTRACT FROM AUTHOR]

This Note points out a minor error in a technique developed by Soyster and Lev [1] for determining if a linear goal can be substituted for a fractional goal in a goal programming problem. A revised formulation is provided. [ABSTRACT FROM AUTHOR]

This article presents a response to comments made by writer Roger C. Vergin on the author's article "Lot Size Scheduling on a Single Machine for Machine for Stochastic Demand," published in the November 1973 issue. The author points out that the assumptions challenged by Vergin are not important to the overall results of the author's model. Furthermore, he shows that the need for cyclical scheduling process for a multi-product single machine system arises as a result of the interference caused by batches of products because of different time intervals between production runs.

The article presents the author's comments on criticisms of the management science paper "On Sequencing n Jobs on One Machine to Minimize the Number of Late Jobs," by William L. Maxwell. Maxwell presented an integer programming formulation for a one-machine job shop problem. The author contends that Maxwell's formulation was erroneous due to the intermediate steps leading from the original problem. He explains that the steps are not adequately described and therefore problematic. The author also explains that the counterexample to Maxwell's assessment is unable to be proven.

In the emerging modern technology of additive manufacturing, the need for optimization can be found in literature in many places. Additive manufacturing (AM) is making an object layer by layer directly from digital data. Previous works of literature have classified additive manufacturing processes into seven types. However, there is a lack of comprehensive review describing the optimization challenges and opportunities in the material extrusion process (polymer technology) and also the need for FDM polymer materials application in impeller making. In this review paper, a specific optimization method called multicriteria decision-making (MCDM) from the mathematical programming technique used in additive manufacturing polymer technology (AMPT) is discussed. The other topics such as different types of optimization techniques, applications of different MCDM tools and their applications in different fields including AM, and the optimization challenges and opportunities in AMPT particularly impeller application are discussed. [ABSTRACT FROM AUTHOR]

Airport gates are the main places for aircraft to receive ground services. With the increased number of flights, limited gate resources near to the terminal make the gate assignment work more complex. Traditional solution methods based on mathematical programming models and iterative algorithms are usually used to solve these static situations, lacking learning and real-time decision-making abilities. In this paper, a two-stage hybrid algorithm based on imitation learning and genetic algorithm (IL-GA) is proposed to solve the gate assignment problem. First of all, the problem is defined from a mathematical model to a Markov decision process (MDP), with the goal of maximizing the number of flights assigned to contact gates and the total gate preferences. In the first stage of the algorithm, a deep policy network is created to obtain the gate selection probability of each flight. This policy network is trained by imitating and learning the assignment trajectory data of human experts, and this process is offline. In the second stage of the algorithm, the policy network is used to generate a good initial population for the genetic algorithm to calculate the optimal solution for an online instance. The experimental results show that the genetic algorithm combined with imitation learning can greatly shorten the iterations and improve the population convergence speed. The flight rate allocated to the contact gates is 14.9% higher than the manual allocation result and 4% higher than the traditional genetic algorithm. Learning the expert assignment data also makes the allocation scheme more consistent with the preference of the airport, which is helpful for the practical application of the algorithm. [ABSTRACT FROM AUTHOR]

This paper studies the convergence and error estimates of approximate solutions to an optimal control problem governed by semilinear elliptic equations with non-convex cost function and non-convex mixed pointwise constraints, and unbounded constraint set. We discretize the optimal control problems by the finite element method in order to obtain a sequence of mathematical programming problems in finite-dimensional spaces. We show that under certain conditions, the optimal solutions of the obtained mathematical programming problems converge to an optimal solution of the original problem. In particular, if the original problem satisfies the so-called no-gap second-order conditions, then some error estimates of approximate solutions are obtained. [ABSTRACT FROM AUTHOR]

Product recovery, accompanied by cradle to cradle policies from the contemporary supply chain, becomes an essential element in meeting environmental compliance and waste management policies. Incorporation of reverse logistics into the traditional supply chains becomes a complementary factor for efficient product recovery. To begin with product recovery, consumers are encouraged to return their end-of-use/end-of-life products, and the steps of collecting and planning the movement of returned products are crucial decisions. The efficient planning of a cost effective recovery process in reverse logistics requires dealing with the uncertainty underlying in the quantity and quality of the returned products. In this paper, we propose establishing an initial collection point within a permissible radius of the customer zones to overcome some of the issues of uncertainty. The uncertainty in the quantity and quality of the returned products are modelled using fuzzy triangular numbers. To capture the real world conditions of the proposed problem, our model aims at maximizing the profit incurred in the recovery process in an uncertain environment. The model was solved with the help of fuzzy mathematical programming. The model is validated by a company case belonging to the manufacturing of electronic products. To increase the applicability of the product recovery process in the industry, we propose a recovery process for the planning horizon consisting of multi periods and multi products. The outcomes of the proposed model indicate that for the successful realisation of such network, customers need to be legally enforced to return their end of used products in the channels established for value recovery. [ABSTRACT FROM AUTHOR]

This paper discusses the optimization of emergency resource scheduling for major railway emergencies under multiple uncertainties while considering the uncertainties in demand, reserve, and transportation costs of resources. We introduce a novel approach that integrates stochastic mathematical programming, interval parameter programming, and fuzzy mathematical programming to study uncertain parameter interactions and coupling. A two-stage interval fuzzy credibility-constrained model is established and solved using an interval interactive algorithm. Finally, through a case study on China Railway Nanchang Group Co., Ltd., the novelty and effectiveness of the proposed method for optimizing emergency resource scheduling strategies under multiple uncertainties are demonstrated. [ABSTRACT FROM AUTHOR]

Topology optimization is gaining popularity as a primary tool for engineers in the initial stages of design. Essentially, the design domain is broken down into individual pixels, with the material density of each element or mesh point serving as a design variable. The optimization problem is then tackled through mathematical programming and optimization methods that rely on analytical gradient calculation. In this study, topology optimization using honeycomb tessellation elements is explored. Hexagonal elements have the ability to flexibly connect two adjacent elements. The use of the hexagonal element limits the occurrence of the checkerboard pattern to the finite elements of the quadrilateral standard Lagrangian type. A mathematical model is developed with the objective function being the minimum compliance value of the design domain. The element stiffness matrix is constructed using the strain-displacement matrix and the constitutive matrix, assuming a unit Young’s modulus. Additionally, optimal conditions are established using Lagrangian multipliers. Two sensitivity and density filtering filters are employed to increase optimization efficiency, prevent the algorithm from reaching a local optimal state, and speed up convergence. If the suggested filter is employed, the objective function achieves a value of c=173,0293 and convergence is attained after 200 iterations. In contrast, without using the filter, the objective function has a larger value (c=186,7922) and convergence occurs at the 27th iteration. The results are significant for optimizing topology to meet specific boundary condition requirements. This paper proposes a novel approach using a combination of filters to advance topology optimization using hexagonal elements in future applications. [ABSTRACT FROM AUTHOR]

Economic, technological, and environmental causes are moving energy toward smart distribution networks. The change from fossil fuels to renewable energy sources is extremely environmentally friendly in both the building and transport sectors. Microgrids could be efficiently used in remote areas utilizing renewable energy resources for supplying different energy demands namely power, heat and cold. This paper presents a mixed-integer linear programming (MILP) model for optimizing planning and sizing decisions in microgrids connected to main grid. Planning decisions the amount of generation of each distributed generation (DG) technology and the amount of power transmission to other nodes. Also, sizing of different DGs including photovoltaic and combined heat and power facilities are performed by the proposed model. According to the results, the model is able to optimize sizing and planning decisions in grid-connected microgrids. [ABSTRACT FROM AUTHOR]