Single Linear Programming Research Articles

EVALUATION OF THE PRODUCTION PLANNING POLICY ALTERNATIVES IN A PET RESIN PRODUCTION PLANT: A CASE STUDY FROM TURKEY

Goal: The main purpose of this work is to develop several production planning models for one of bottle grade PET production plants (in Turkey) under different scenarios by considering different levels of inventory (no stock and different levels of safety stocks), different energy sourcing alternatives (natural gas/coal or both) and production throughput (different lot sizes).
 Design/Methodology/Approach: Deterministic multi-product multi-period single level mixed integer linear programming model is presented. The model is implemented for the above defined scenarios. We have also considered the total emission produced for different energy alternatives.
 Results: The models for the different scenarios have shown that significant performance improvements can be achieved by changing the parameters/policies of the production. The best model obtained has yielded 6.6% of profit improvement and 6.9% of cost reduction.
 Limitations of the investigation: Planning horizon of this work could cover the data of years 2014 to 2018. However, the actual data employed for this study is limited with one year due to unavailability of further data. In addition to this, improvement of current production planning approach of the plant by implementation of proposed model is one of the objectives of this study to see success rate of model. Though, this couldn’t be realized. We hypothetically tested the improvement provided by the proposed model, therefore we can’t analyze the actual improvement.
 Practical implications: Interactions among optimal results obtained by running model with different scenarios and their effect on selected performance variables are the main contribution of this work. Similar methodology could be used at other PET resin manufacturing plants or alternatively the production facilities having similar type of continuous manufacturing processes to find their optimal levels of inventory, production throughput and proper choice for energy sourcing alternative.
 Originality/Value: The research on the production planning for PET resin industry by considering the different scenarios (levels of inventory / energy sourcing alternatives/ production throughput) is novel as far as we know, and therefore the approach used in this study is expected to be useful for other similar plants.

Computing Controlled Invariant Sets from Data Using Convex Optimization

This work presents a data-driven method for approximation of the maximum positively invariant (MPI) set and the maximum controlled invariant (MCI) set for nonlinear dynamical systems. The method only requires the knowledge of a finite collection of one-step transitions of the discrete-time dynamics, without the requirement of segments of trajectories or the control inputs that effected the transitions to be available. The approach uses a novel characterization of the MPI and MCI sets as the solution to an infinite-dimensional linear programming (LP) problem in the space of continuous functions, with the optimum being attained by a (Lipschitz) continuous function under mild assumptions. The infinite-dimensional LP is then approximated by restricting the decision variable to a finite-dimensional subspace and by imposing the non-negativity constraint of this LP only on the available data samples. This leads to a single finite-dimensional LP that can be easily solved using off-the-shelf solvers. We analyze the convergence rate and sample complexity, proving probabilistic as well as hard guarantees on the volume error of the approximations. The approach is very general, requiring minimal underlying assumptions. In particular, the dynamics is not required to be polynomial or even continuous (forgoing some of the theoretical results). Detailed numerical examples up to state-space dimension ten with code available online demonstrate the method.

Backtracking based Joint-Sparse Signal Recovery for Distributed Compressive Sensing

In Distributed Compressive Sensing (DCS), the Joint Sparsity Model (JSM) refers to an ensemble of signals being jointly sparse. In [4], a joint reconstruction scheme was proposed using a single linear program. However, for reconstruction of any individual sparse signal using that scheme, the computational complexity is high. In this paper, we propose a dual-sparse signal reconstruction method. In the proposed method, if one signal is known apriori, then any other signal in the ensemble can be efficiently estimated using the proposed method, exploiting the dual-sparsity. Simulation results show that the proposed method provides fast and efficient recovery.

Common set of weights and efficiency improvement on the basis of separation vector in two-stage network data envelopment analysis

Common set of weights (CSWs) method is one of the popular ranking methods in DEA which can rank efficient and inefficient units. Based on an identical criterion, the method selects the most favorable weight set for all units. An important issue is that in most common DEA models, the internal structure of the production units is ignored and the units are often considered as black boxes. In this paper, in order to evaluate the units and subunits in the two-stage NDEA based on an identical criterion, it is suggested to use CSWs method on the basis of separation vector. Our research contribution in this paper includes: (1) CSWs method is formulated in two-stage NDEA as a multiple objective fractional programming (MOFP) problem. (2) A method is suggested based on separation vector to change MOFP problem into single objective linear programming (SOLP) problem in two-stage NDEA. In the theorem, it is shown that the obtained solutions from MOFP and SOLP in two-stage NDEA are identical. (3) In the framework of the new models of two-stage NDEA, a process is introduced to improve efficiency evaluation by CSWs on the basis of separation vector which is based on the radial improvement of inputs and final outputs. Finally, an enlightening application is presented.

Finding all solution sets of piecewise-linear interval equations using an integer programming solver

This paper presents an efficient and easily implementable method for finding all solution sets of piecewise-linear interval equations using integer programming. In this method, the problem of finding all solution sets is formulated as a mixed integer programming problem, and it is solved by a high-performance integer programming solver such as CPLEX. It is shown that all solution sets are obtained by solving a single mixed integer programming problem and related linear programming problems. Numerical examples are given to confirm the effectiveness of the proposed method.

A solution approach to fully fuzzy linear fractional programming problems

In this paper, we propose a method of solving the fully fuzzy linear fractional programming problems, Express all the parameters and variables are triangular fuzzy numbers. Convert all the triangular fuzzy numbers in their parametric form, we convert the fractional programming problem in to a single objective linear programming problem in parametric form. We put new fuzzy arithmetic and fuzzy ranking, we obtain the optimal solution the given fully fuzzy linear fractional programming problem without converting to its equivalent crisp linear programming problem. A numerical example is provided to illustrate the efficiency of the proposed method.

A 1-norm regularized linear programming nonparallel hyperplane support vector machine for binary classification problems

This research proposes a 1-norm regularized linear programming nonparallel hyperplane support vector machine (LNSVM) model to solve binary classification problems and enhance the robustness performance. Numerous nonparallel support vector machine (SVM) models have been studied with outstanding performance on classification tasks. However, most nonparallel SVM models require two independent models to determine hyperplanes. In addition, due to the involvement of the 2-norm terms, traditional SVM models may suffer from the lack of robustness to outliers and irrelevant features. Therefore, the LNSVM model is proposed by reformulating a typical nonparallel SVM model through the 1-norm regularization. By applying the exterior penalty theory, the proposed LNSVM model is converted to the dual exterior penalty problem, which is solved by the Newton–Armijo algorithm. The essential differences that distinguish the LNSVM model from other nonparallel SVM models are: (1) Different from typical nonparallel SVM models, which solve two quadratic programming (QP) problems, the proposed LNSVM model determines two nonparallel hyperplanes simultaneously by solving a single linear programming (LP) model; (2) The robustness performance of the proposed LNSVM model has been enhanced to tolerate noisy data through the involvement of 1-norm loss function, which can also eliminate redundant features by generating sparse solution during the training procedure. The performance of the proposed LNSVM model is tested through a comparison with state-of-art SVM-based classifiers using a synthetic dataset and 11 practical benchmark datasets. The experimental results show the superiority of the proposed LNSVM model, by achieving better classification performance regarding accuracy, sensitivity, specificity, and removing redundant features synchronously.

Scheduling surgery groups considering multiple downstream resources

Surgery groups are clustered surgery procedure types that share comparable characteristics (e.g. expected duration). Scheduling OR blocks leaves many options for operational surgery scheduling and this increases the variation in usage of both the OR and downstream beds. Therefore, we schedule surgery groups to reduce the options for operational scheduling, ultimately bridging the gap between tactical and operational scheduling. We propose a single step mixed integer linear programming (MILP) approach that approximates the bed and OR usage and a simulated annealing approach. Both approaches are compared on a real-life data set and results show that the MILP performs best in terms of solution quality and computation time. Furthermore, the results show that our model may improve the OR utilization from 71% to 85% and decrease the bed usage variation from 53 beds to 11 beds compared to historical data. To show the potential and robustness of our model, we discuss several variants of the model requiring minor modifications. The use of surgery groups makes it easier to implementation our model in practice and, for operational planners, it is instantly clear where to schedule different types of surgery.

A multi-component enhanced Russell measure of efficiency: With application to water supply plans

Public water providers aim at developing a water supply plan (WSP) that not only provides a reliable and satisfactory level of service but also is efficient in terms of performance. This paper deals with evaluating the performance of WSPs within the framework of multi-component data envelopment analysis. Specifically, we consider the overall performance of each WSP as a decision making unit (DMU) so that economic, social, hygienic, technological, managerial and environmental performances of the WSP make up independent components of the defined DMU. To assess the performance of a set of WPSs, we propose a multi-component enhanced Russell measure of efficiency that takes all sources of inefficiency into account. We show that the proposed measure can be decomposed into individual efficiency measures at component level. This decomposition much enhances the efficiency of computing the proposed measure, noting the fact that this measure is obtained by solving a single linear program. It also guarantees the proposed measure to inherit two important—unit invariance and strong monotonicity—properties of the conventional enhanced Russell measure. In our empirical study, we apply our model to evaluate the efficiency of 10 urban WSPs in Qom city of Iran. In line with experts’ practical opinions, our findings reveal that the (relatively) most efficient WSP is to construct a potable water network and separation of non-drinking water network for urban usage.

Two-stage robust planning-operation co-optimization of energy hub considering precise energy storage economic model

The increasing penetration of renewable energy resources in integrated energy system makes it necessary to consider uncertainty, appropriate investment and scientific operation for energy storage systems, including battery energy storage systems and thermal energy storage systems. In this paper, we propose a two-stage robust planning-operation co-optimization method for Energy Hub considering uncertainties from renewable energy resources as well as multi-load demands, the sizing problem and precise economic model of energy storage systems, in which lifetime loss cost of battery energy storage systems and static loss of thermal energy storage systems are mainly included. Integer variables exist in both stages, thus in the proposed method, dual norms are used to transform uncertain constraints into robust counterparts with which the worst cases are calculated directly, then the problem is merged into a single stage mixed integer linear program. In case studies, optimal planning strategies including multiple storages in Energy Hub are explored under the consideration of sizing problem and uncertainties, and it’s found that simultaneously constructing multiple energy storages can have mutually beneficial relationships and propose more economic planning/operation strategies. Then it’s validated that precise energy storage model can better improve economics and flexibility of Energy Hub both in longer term and short term planning optimization. Meanwhile, convergence speed of the model and solution algorithm in this paper is acceptable for practical planning problem.

Exact and Practical Modulo Scheduling for High-Level Synthesis

Loop pipelining is an essential technique in high-level synthesis to increase the throughput and resource utilisation of field-programmable gate array--based accelerators. It relies on modulo schedulers to compute an operator schedule that allows subsequent loop iterations to overlap partially when executed while still honouring all precedence and resource constraints. Modulo schedulers face a bi-criteria problem: minimise the initiation interval (II; i.e., the number of timesteps after which new iterations are started) and minimise the schedule length. We present Moovac, a novel exact formulation that models all aspects (including the II minimisation) of the modulo scheduling problem as a single integer linear program, and discuss simple measures to prevent excessive runtimes, to challenge the old preconception that exact modulo scheduling is impractical. We substantiate this claim by conducting an experimental study covering 188 loops from two established high-level synthesis benchmark suites, four different time limits, and three bounds for the schedule length, to compare our approach against a highly tuned exact formulation and a state-of-the-art heuristic algorithm. In the fastest configuration, an accumulated runtime of under 16 minutes is spent on scheduling all loops, and proven optimal IIs are found for 179 test instances.

Integrated PV Charging of EV Fleet Based on Energy Prices, V2G, and Offer of Reserves

Workplace charging of electric vehicles (EVs) from photovoltaic (PV) panels installed on an office building can provide several benefits. This includes the local production and use of PV energy for charging the EV and making use of dynamic tariffs from the grid to schedule the energy exchange with the grid. The long parking time at the workplace provides the chance for the EV to support the grid via vehicle-to-grid technology, the use of a single EV charger for charging several EVs by multiplexing and the offer of ancillary services to the grid for up and down regulation. Further, distribution network constraints can be considered to limit the power and prevent the overloading of the grid. A single mixed integer linear programming (MILP) formulation that considers all the above applications has been proposed in this paper for a charging a fleet of EVs from PV. The MILP is implemented as a receding-horizon model predictive energy management system. Numerical simulations based on market and PV data in Austin, TX, USA, have shown 32% to 651% reduction in the net cost of EV charging from PV when compared to immediate and average rate charging policies.

A diurnal flux balance model of Synechocystis sp. PCC 6803 metabolism.

Phototrophic organisms such as cyanobacteria utilize the sun’s energy to convert atmospheric carbon dioxide into organic carbon, resulting in diurnal variations in the cell’s metabolism. Flux balance analysis is a widely accepted constraint-based optimization tool for analyzing growth and metabolism, but it is generally used in a time-invariant manner with no provisions for sequestering different biomass components at different time periods. Here we present CycleSyn, a periodic model of Synechocystis sp. PCC 6803 metabolism that spans a 12-hr light/12-hr dark cycle by segmenting it into 12 Time Point Models (TPMs) with a uniform duration of two hours. The developed framework allows for the flow of metabolites across TPMs while inventorying metabolite levels and only allowing for the utilization of currently or previously produced compounds. The 12 TPMs allow for the incorporation of time-dependent constraints that capture the cyclic nature of cellular processes. Imposing bounds on reactions informed by temporally-segmented transcriptomic data enables simulation of phototrophic growth as a single linear programming (LP) problem. The solution provides the time varying reaction fluxes over a 24-hour cycle and the accumulation/consumption of metabolites. The diurnal rhythm of metabolic gene expression driven by the circadian clock and its metabolic consequences is explored. Predicted flux and metabolite pools are in line with published studies regarding the temporal organization of phototrophic growth in Synechocystis PCC 6803 paving the way for constructing time-resolved genome-scale models (GSMs) for organisms with a circadian clock. In addition, the metabolic reorganization that would be required to enable Synechocystis PCC 6803 to temporally separate photosynthesis from oxygen-sensitive nitrogen fixation is also explored using the developed model formalism.

Multilevel Programming-Based Coordinated Cyber Physical Attacks and Countermeasures in Smart Grid

Since the Ukraine blackout in 2015, coordinated cyber-physical attacks (CCPAs) have been emerging and are used to mask line outages in the smart grid. In this paper, we investigate the features of CCPAs and constitute the mathematic formulation with respect to topologies and electric parameters of a power grid before and after attacks. With the objective of maximizing the number of overloaded lines, a bilevel programming model is developed to describe the interaction between the adversary and the control center. The most damaging CCPA can be determined by transforming the developed bilevel model to a single mixed-integer linear programming problem using the Karush-Kuhn-Tucker conditions. Based on the features of the bilevel model, the countermeasure is expressed as a trilevel model with one leader and multiple followers. The implicit enumeration-based searching strategy is proposed to solve the trilevel model to identify the protected meters. Both the implementation of CCPAs and the effectiveness of the developed countermeasure are verified on the modified IEEE 14-bus system.

On Technique for Generating Pareto Optimal Solutions of Multi-objective Linear Programming Problems

Subjective selection of weights in method of combining objective functions in a multi – objective programming problem may favour some objective functions and thus suppressing the impact of others in the overall analysis of the system. It may not be possible to generate all possible Pareto optimal solution as required in some cases. In this paper we develop a technique for selecting weights for converting a multi-objective linear programming problem into a single objective linear programming problem. The weights selected by our technique do not require interaction with the decision makers as is commonly the case. Also, we develop a technique to generate all possible Pareto optimal solutions in a multi-objective linear programming problem. Our technique is illustrated with two and three objective function problems.

Linear fractional programming based on triangular neutrosophic numbers

In this paper, a solution procedure is proposed to solve neutrosophic linear fractional programming problem (NLFP) where cost of the objective function, the resources and the technological coefficients are triangular neutrosophic numbers. Here, the NLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using proposed approach, the transformed MOLFP problem is reduced to a single objective linear programming (LP) problem which can be solved easily by suitable linear programming technique. The proposed procedure illustrated through a numerical example.

IGDT‐based economic dispatch considering the uncertainty of wind and demand response

Integration of wind generation and demand response (DR) poses challenges for the power system operation due to their uncertain characteristics. In this study, an economic dispatching method considering the uncertainties of wind and DR is proposed. The method based on the information gap decision theory (IGDT) can be used to evaluate risks associated with uncertainties from risk averse (RA) and risk-seeking (RS) perspectives. The RA IGDT-based model can provide maximum tolerable robustness region for the required cost target. The RS IGDT-based model can help achieve the lowest operation costs with desired uncertainties. The proposed model is bi-level. The upper level subproblem aims to maximise (minimise) the allowable uncertainty level to satisfy the pre-determined cost target, while the lower level subproblem is to maximise (minimise) possible cost considering the uncertainties. The bi-level model is then transformed into a single level mixed integer linear programming problem that can be solved through commercial solves. Finally, the authors evaluate the performance of the IGDT-based approach by simulations on the modified 6-bus and IEEE 118-bus systems. The results show that the proposed approach can provide suggestions for system operators to make appropriate scheduling plan based on the expected cost targets and risk preferences.

Green Procurement Relationships Development under Carbon Emissions Regulations: A Bi-Level Programming Approach.

A multi-period Stackelberg game is adopted to study a green procurement relationship between manufacturers and suppliers in a supply chain. The manufacturers are considered as leaders, while the suppliers are modelled as followers in this Stackelberg game. Accordingly, a mixed binary linear bi-level programming model is developed to elaborate the game in consideration of carbon tax scheme. The upper level (the leader) aims at selecting a proper number of suitable suppliers to provide heterogeneous raw materials at the lowest operational cost. The objective of the lower level (the follower) is to find optimal purchasing quantities of raw materials. In addition, two lemmas are introduced to transform the mixed linear bi-level programming model into a single level linear programming model. The numerical example illustrates that: (1) the manufacturer prefers to adopt the multiple sourcing strategy due to the flexibility; (2) keeping stable supplies and large order volumes could effectively reduce carbon emissions for the suppliers and make the supply chain greener.

An Approach for Solving Fuzzy Multi-Objective Linear Fractional Programming Problems

In this paper, an attempt has been taken to develop a method for solving fuzzy multi-objective linear fractional programming (FMOLFP) problem. Here, at first the FMOLFP problem is converted into (crisp) multi-objective linear fractional programming (MOLFP) problem using the graded mean integration representation (GMIR) method proposed by Chen and Hsieh. That is, all the fuzzy parameters of FMOLFP problem are converted into crisp values. Then the MOLFP problem is transformed into a single objective linear programming (LP) problem using a proposal given by Nuran Guzel. Finally the single objective LP problem is solved by regular simplex method which yields an efficient solution of the original FMOLFP problem. To show the efficiency of our proposed method, three numerical examples are illustrated and also for each example, a comparison is drawn between our proposed method and the respected existing method.

Efficiency evaluation in two-stage data envelopment analysis under a fuzzy environment: A common-weights approach

Data envelopment analysis (DEA) has been genuinely known as an impeccable technique for efficiency measurement. In practice, since many production systems such as broadcasting companies, banking institutions and R&D organisations include two processes connected in series, we have need of utilising two-stage DEA models to identify the sources of inefficiency and explore in turn appropriate options for improving performance. The lack of the ability to generate the actual weights is not only an ongoing challenge in traditional DEA models, it can also have serious repercussion for the contemporary DEA models (e.g., two-stage DEA). This paper presents a common-weights method for two-stage structures that allows us to consider equality of opportunity in a fuzzy environment when evaluating the system efficiency and the component process efficiencies. The proposed approach first seeks upper bounds on factor weights and then determines a set of common weights by a single linear programming problem. We illustrate the developed approach with a data set taken from the literature.