Industrial Instances Research Articles

Mixed integer linear programming models for Flow Shop Scheduling with a demand plan of job types

This paper presents two mixed integer linear programming (MILP) models that extend two basic Flow Shop Scheduling problems: $$ {\text{Fm}} $$/$$ {\text{prmu}} $$/$$ {\text{C}}_{ \hbox{max} } $$ and $$ {\text{Fm}} $$/$$ {\text{block}} $$/$$ {\text{C}}_{ \hbox{max} } $$. This extension incorporates the concept of an overall demand plan for types of jobs or products. After using an example to illustrate the new problems under study, we evaluated the new models and analyzed their behaviors when applied to instances found in the literature and industrial instances of a case study from Nissan’s plant in Barcelona. CPLEX solver was used as a solution tool and obtained acceptable results, allowing us to conclude that MILP can be used as a method for solving Flow Shop Scheduling problems with an overall demand plan.

Heuristic Algorithm for a WIP Projection Problem at Finite Capacity in Semiconductor Manufacturing

In this paper, we propose a heuristic approach for fixing work-in-progress (WIP) projection issues in the semiconductor industry especially for high mix low volume facilities. The considered problem consists of estimating the start and end dates for each remaining process step of the production lots in the WIP and anticipating the fab loading taking into account the constraints of the maximum throughput of machines considered as capacity constraints and customer delivery commitments. The objective being to guarantee on-time delivery, we focus on minimizing the total weighted tardiness. We have formulated the problem into a mixed-integer programming and we have empirically shown its computational intractability. Due to the computational intractability using actual production data, a heuristic algorithm is proposed. It is an iterative finite capacity planning system that considers as inputs lots due dates and equipment capabilities and capacities. The performance of the heuristic is assessed using industrial instances. It turns out that it achieves targeted objectives with satisfactory results in terms of quality of the solution and computation time.

Investigation of poly(\u03b3-glutamic acid) production via online determination of viscosity and oxygen transfer rate in shake flasks

BackgroundPoly(γ-glutamic acid) (γ-PGA) is a biopolymer with many useful properties making it applicable for instance in food and skin care industries, in wastewater treatment, in biodegradable plastics or in the pharmaceutical industry. γ-PGA is usually produced microbially by different Bacillus spp. The produced γ-PGA increases the viscosity of the fermentation broth. In case of shake flask fermentations, this results in an increase of the volumetric power input. The power input in shake flasks can be determined by measuring the torque of an orbitally rotating lab shaker. The online measurement of the volumetric power input enables to continuously monitor the formation or degradation of viscous products like γ-PGA. Combined with the online measurement of the oxygen transfer rate (OTR), the respiration activity of the organisms can be observed at the same time.ResultsTwo different Bacillus licheniformis strains and three medium compositions were investigated using online volumetric power input and OTR measurements as well as thorough offline analysis. The online volumetric power input measurement clearly depicted changes in γ-PGA formation due to different medium compositions as well as differences in the production behavior of the two investigated strains. A higher citric acid concentration and the addition of trace elements to the standard medium showed a positive influence on γ-PGA production. The online power input signal was used to derive an online viscosity signal which was validated with offline determined viscosity values. The online measurement of the OTR proved to be a valuable tool to follow the respiration activity of the cultivated strains and to determine its reproducibility under different cultivation conditions.ConclusionsThe combination of the volumetric power input and the OTR allows for an easy and reliable investigation of new strains, cultivation conditions and medium compositions for their potential in γ-PGA production. The power input signal and the derived online viscosity directly reflect changes in γ-PGA molecular weight and concentration, respectively, due to different cultivation conditions or production strains.

Revisiting Exchange Concept: A Rationale for Marketing Mix in Islamic Marketing

Marketing mix has been the cornerstone of the discipline and dominating marketing early thought. This concept has been the focal point in the development of conventional managerial paradigm with strong adherence to its normative pillars of ‘4 Ps’. History has shown that a new paradigm constantly shifting the status quo of such concept into more advance findings. The objective of this paper is to present the rationale of marketing mix in Islamic marketing. Despite the evolution of marketing mix paradigm over more than 40 years, it is undeniable that such classical marketing canon has its root from concept of exchange. By using both qualitative and quantitative approaches in the development of instruments has led to the development of the 5Cs model. It is aimed to proposed a more advance finding derived from an Islamic perspective towards the concept. In depth literature review and survey has found a distinct set of marketing mix variables catering to Muslim consumer that are in line with Islamic principles. 5Cs models of Commitment, Characteristics, Conformity, Conscience, Customer centric offers a new way of marketing to Muslim consumers governed by Islamic principles and injunctions. Therefore, 5Cs model can be applied in many areas, for instance in Halal industry. It is recommended that business and academia will apply and further develop the model as it will enrich the framework and as to remain relevant.

A methodology for the large-scale multi-period precedence-constrained knapsack problem: an application in the mining industry

This paper considers a generalization of the precedence-constrained knapsack problem known as multi-period precedence-constrained knapsack, in which the decision maker faces a horizon of several periods. Associated with each period is a capacity limit that cannot be exceeded by items chosen in that specific period. The motivation for studying this problem comes from a recognized problem in the mining industry, known as open pit mine production scheduling. An old, yet fast sequencing heuristic has been used in the literature to tackle similar combinatorial problems with precedence constraints. In this study, we first strengthen the LP relaxation formulation of the problem by adding inequalities derived from both precedence and knapsack constraints, and then use the LP solutions to generate efficient weights for the sequencing heuristic. Generating the heuristic's weights in this way significantly improves its output. Using this methodology, extremely large instances can be solved to near-optimum levels in minutes. The performance of this methodology is tested on a set of benchmark instances in the mining industry, where this problem is a major application.

WPM3: An (in)complete algorithm for weighted partial MaxSAT

Maximum Satisfiability (MaxSAT) has been used to solve efficiently many combinatorial optimization problems. At recent editions of international MaxSAT Evaluation (MSE), the best performing solvers for real world (industrial) problems were those implementing SAT-based algorithms. These algorithms reformulate the MaxSAT optimization problem into a sequence of SAT decision problems where Pseudo-Boolean (PB) constraints may be introduced. In order to identify the most suitable PB constraints, some algorithms (core-guided) analyze the unsatisfiable cores retrieved from the previous SAT problems in the sequence while refining the lower bound. In this paper, we first conduct a comprehensive study on the complete core-guided algorithms Eva and OLL, that inspired the best performing solvers on industrial instances at MSE-2014. Despite of its apparently different foundations, we show how they are intimately related and identify how to improve them. In this sense, we present our complete core-guided algorithm WPM3. We show how to further exploit the analysis of unsatisfiable cores by being aware of their global structure, i.e., how the cores are interrelated. This is used to encode more efficient PB constraints and enables the algorithm to obtain assignments and refine also the upper bound. Therefore, WPM3 can also work as an incomplete algorithm. At MSE-2015, it showed a competitive performance on industrial instances. It got one out of three gold medals at the complete track and dominated at the incomplete track.

Using Global Constraints to Automate Regression Testing

Nowadays, any communicating or autonomous systems rely on high-quality software-based components. To ensure a sufficient level of quality, these components must be thoroughly verified before being released and being deployed in operational settings. Regression testing is a crucial verification process that executes any new release of a software-based component against previous versions of the component, with existing test cases. However, the selection of test cases in regression testing is challenging as the time available for testing is limited and some selection criteria must be respected. This problem, coined as Test Suite Reduction (TSR), is usually addressed by validation engineers through manual analysis or by using approximation techniques. Even if the underlying optimization problem is untractable in theory, solving it in practice is crucial when there are pressing needs to release high-quality components while at the same time reducing the time-to-market of new software releases. In this paper, we address the TSR problem with sound Artificial intelligence techniques such as Constraint Programming (CP) and global constraints. By associating each test case a cost-value aggregating distinct criteria, such as execution time, priority or importance due to the error-proneness of each test case, we propose several constraint optimization models to find a subset of test cases covering all the test requirements and optimizing the overall cost of selected test cases. Our models are based on a combination of NVALUE, GLOBALCARDINALITY, and SCALAR_PRODUCT, three well-known global constraints that can faithfully encode the coverage relation between test cases and test requirements. Our contribution includes the reuse of existing preprocessing rules to simplify the problem before solving it and the design of structure-aware heuristics, which take into account the notion of costs, associated with test cases. The work presented in this paper has been motivated by an industrial application in the communication domain. Our overall goal is to develop a constraint-based approach of test suite reduction that can be deployed to test a complete product line of conferencing systems in continuous delivery mode. By implementing this approach in a software prototype tool and experimentally evaluated it on both randomly generated instances and industrial instances, we hope to foster a quick adoption of the technology.

Phase Transitions for Scale-Free SAT Formulas

Recently, a number of non-uniform random satisfiability models have been proposed that are closer to practical satisfiability problems in some characteristics. In contrast to uniform random Boolean formulas, scale-free formulas have a variable occurrence distribution that follows a power law. It has been conjectured that such a distribution is a more accurate model for some industrial instances than the uniform random model. Though it seems that there is already an awareness of a threshold phenomenon in such models, there is still a complete picture lacking. In contrast to the uniform model, the critical density threshold does not lie at a single point, but instead exhibits a functional dependency on the power-law exponent. For scale-free formulas with clauses of length k=2, we give a lower bound on the phase transition threshold as a function of the scaling parameter. We also perform computational studies that suggest our bound is tight and investigate the critical density for formulas with higher clause lengths. Similar to the uniform model, on formulas with k>=3, we find that the phase transition regime corresponds to a set of formulas that are difficult to solve by backtracking search.

New local search methods for partial MaxSAT

Maximum Satisfiability (MaxSAT) is the optimization version of the Satisfiability (SAT) problem. Partial Maximum Satisfiability (PMS) is a generalization of MaxSAT which involves hard and soft clauses and has important real world applications. Local search is a popular approach to solving SAT and MaxSAT and has witnessed great success in these two problems. However, unfortunately, local search algorithms for PMS do not benefit much from local search techniques for SAT and MaxSAT, mainly due to the fact that it contains both hard and soft clauses. This feature makes it more challenging to design efficient local search algorithms for PMS, which is likely the reason of the stagnation of this direction in more than one decade.In this paper, we propose a number of new ideas for local search for PMS, which mainly rely on the distinction between hard and soft clauses. The first three ideas, including weighting for hard clauses, separating hard and soft score, and a variable selection heuristic based on hard and soft score, are used to develop a local search algorithm for PMS called Dist. The fourth idea, which uses unit propagation with priority on hard unit clauses to generate the initial assignment, is used to improve Dist on industrial instances, leading to the DistUP algorithm.The effectiveness of our solvers and ideas is illustrated through experimental evaluations on all PMS benchmarks from the MaxSAT Evaluation 2014. According to our experimental results, Dist shows a significant improvement over previous local search solvers on all benchmarks. We also compare our solvers with state-of-the-art complete PMS solvers and a state-of-the-art portfolio solver, and the results show that our solvers have better performance in random and crafted instances but worse in industrial instances. The good performance of Dist has also been confirmed by the fact that Dist won all random and crafted categories of PMS and Weighted PMS in the incomplete solvers track of the MaxSAT Evaluation 2014.

Generating SAT instances with community structure

Nowadays, modern SAT solvers are able to efficiently solve many industrial, or real-world, SAT instances. However, the process of development and testing of new SAT solving techniques is conditioned to the finite and reduced number of known industrial benchmarks. Therefore, new models of random SAT instances generation that capture realistically the features of real-world problems can be beneficial to the SAT community. In many works, the structure of industrial instances has been analyzed representing them as graphs and studying some of their properties, like modularity.In this work, we use the notion of modularity to define a new model of generation of random SAT instances with community structure, called Community Attachment. For high values of modularity (i.e., clear community structure), we realistically model pseudo-industrial random SAT formulas. This model also generates SAT instances very similar to classical random formulas using a low value of modularity. We also prove that the phase transition point, if exists, is independent on the modularity. We evaluate the adequacy of this model to real industrial SAT problems in terms of SAT solvers performance, and show that modern solvers do actually exploit this community structure. Finally, we use this generator to observe the connections between the modularity of the instance and some components of the solver, such as the variable branching heuristics or the clause learning mechanism.

Perspective and potential of CO2: A focus on potentials for renewable energy conversion in the Mediterranean basin

Figures commonly quoted on the soon shortage of generating energy from fossil sources which may give the impression that it will be possible to switch to renewable energies conversion as foundations for the future of industrial instances in the Mediterranean basin. In this study, CO2 energy potential and perspectives in the Mediterranean basin have been investigated in terms of efficiency, feasibility, geographical patterns and savings. Two conjoint mathematical protocols have been carried out in order to yield a simplified extracted scheme for prototype CO2 trapping/storage plants.

On Using Incremental Encodings in Unsatisfiability-based MaxSAT Solving

In recent years, unsatisfiability-based algorithms have become prevalent as state of the art for solving industrial instances of Maximum Satisfiability (MaxSAT). These algorithms perform a succession of unsatisfiable SAT solver calls until an optimal solution is found. In several of these algorithms, cardinality or pseudo-Boolean constraints are extended between iterations. However, in most cases, the formula provided to the SAT solver in each iteration must be rebuilt and no knowledge is reused from one iteration to the next. This paper describes how to implement incremental unsatisfiability-based algorithms for MaxSAT. In particular, we detail and analyze our implementation of the MSU3 algorithm in the OPENWBO framework that performed remarkably well in the MaxSAT Evaluation of 2014. Furthermore, we also propose to extend incrementality to weighted MaxSAT through an incremental encoding of pseudo-Boolean constraints. The experimental results show that the performance of MaxSAT algorithms can be greatly improved by exploiting the learned information and maintaining the internal state of the SAT solver between iterations. Finally, the proposed incremental encodings of cardinality and pseudo-Boolean constraints are not exclusive for MaxSAT usage and can be used in other domains.

A hybrid differential evolution algorithm for multiple container loading problem with heterogeneous containers

We consider a multiple container loading problem, commonly known as the three-dimensional bin packing problem (3D-BPP), which deals with maximizing container space utilization while the containers available for packing are heterogeneous, i.e., varying in size. The problem has wide applications in cargo transportation, warehouse management, medical packaging, and so on. We develop a differential evolution (DE) algorithm hybridized with a novel packing heuristic strategy, best-match-first (BMF), which generates a compact packing solution based on a given box packing sequence and a container loading sequence. The effectiveness of the proposed algorithm is evaluated on a set of industrial instances and randomly generated instances. The results show that the proposed algorithm outperforms existing solution approaches in terms of solution quality.

Exploiting subproblem optimization in SAT-based MaxSAT algorithms

The Maximum Satisfiability (MaxSAT) problem is an optimization variant of the Satisfiability (SAT) problem. Several combinatorial optimization problems can be translated into a MaxSAT formula. Among exact MaxSAT algorithms, SAT-based MaxSAT algorithms are the best performing approaches for real-world problems. We have extended the WPM2 algorithm by adding several improvements. In particular, we show that by solving some subproblems of the original MaxSAT instance we can dramatically increase the efficiency of WPM2. This led WPM2 to achieve the best overall results at the international MaxSAT Evaluation 2013 (MSE13) on industrial instances. Then, we present additional techniques and heuristics to further exploit the information retrieved from the resolution of the subproblems. We exhaustively analyze the impact of each improvement what contributes to our understanding of why they work. This architecture allows to convert exact algorithms into efficient incomplete algorithms. The resulting solver had the best results on industrial instances at the incomplete track of the latest international MSE.

An exact algorithm for wirelength optimal placements in VLSI design

We present a new algorithm designed to solve floorplanning problems optimally. More precisely, the algorithm finds solutions to rectangle packing problems which globally minimize wirelength and avoid given sets of blocked regions. We present the first optimal floorplans for 3 of the 5 intensely studied MCNC block packing instances and a significantly larger industrial instance with 27 rectangles and thousands of nets. Moreover, we show how to use the algorithm to place larger instances that cannot be solved optimally in reasonable runtime.

Logic-based Benders decomposition for an inventory-location problem with service constraints

We study an integrated inventory-location problem with service requirements faced by an aerospace company in designing its service parts logistics network. Customer demand is Poisson distributed and the service levels are time-based leading to highly non-linear, stochastic service constraints and a nonlinear, mixed-integer optimization problem. Unlike previous work in the literature, which propose approximations for the nonlinear constraints, we present an exact solution methodology using logic-based Benders decomposition. We decompose the problem to separate the location decisions in the master problem from the inventory decisions in the subproblem. We propose a new family of valid cuts and prove that the algorithm is guaranteed to converge to optimality. This is the first attempt to solve this type of problem exactly. Then, we present a new restrict-and-decompose scheme to further decompose the Benders master problem by part. We test on industry instances as well as random instances. Using the exact algorithm and restrict-and-decompose scheme we are able to solve industry instances with up to 60 parts within reasonable time, while the maximum number of parts attempted in the literature is 5.

A graph partitioning strategy for solving large-scale crew scheduling problems

Railway crew scheduling deals with generating driver duties for a given train timetable such that all work regulations are met and the resulting schedule has minimal cost. Typical problem instances in the freight railway industry require the generation of duties for thousands of drivers operating tens of thousands of trains per week. Due to short runtime requirements, common solution approaches decompose the optimization problem into smaller subproblems that are solved separately. Several studies have shown that the way of decomposing the problem significantly affects the solution quality. An overall best decomposition strategy for a freight railway crew scheduling problem, though, is not known. In this paper, we present general considerations on when to assign two scheduled train movements to separate subproblems (and when to rather assign them to the same subproblem) and deduct a graph partitioning based decomposition algorithm with several variations. Using a set of real-world problem instances from a major European railway freight carrier, we evaluate our strategy and benchmark the performance of the decomposition algorithm both against a common non-decomposition algorithm and a lower bound on the optimal solution schedule. The test runs show that our decomposition algorithm is capable of producing high-quality solution schedules while significantly cutting runtimes compared to the non-decomposition solution algorithm. We are following a "greenfield" approach, where no information on previous schedules is needed. Hence, our approach is applicable to any railway crew scheduling setting, including network enlargement, integration of new customers, etc.

The robust crew pairing problem: model and solution methodology

We present a new robust formulation for the crew pairing problem where flight and connection times are random and vary within an interval. The model protects against infeasibility with a specified level of uncertainty and minimizes crew cost in the worst case. The resulting robust terms in the objective function and in the resource constraints are nonlinear. We apply Lagrangian relaxation to separate the nonlinear terms in the subproblem leading to a new robust formulation of the shortest path problem with resource constraints. We show that the nonlinear subproblem can be solved as a series of linear auxiliary problems. The proposed solution methodology was successful to solve industry instances in very competitive times and led to more robust crew pairing solutions as shown by simulation experiments.

Validation of nominations in gas network optimization: models, methods, and solutions

In this article, we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult nonconvex mixedinteger nonlinear feasibility problem. The first phase consists of four distinct algorithms applying mixedinteger linear, mixedinteger nonlinear, nonlinear, and methods for complementarity constraints to compute possible settings for the discrete decisions. The second phase employs a precise continuous nonlinear programming model of the gas network. Using this setup, we are able to compute high-quality solutions to real-world industrial instances that are significantly larger than networks that have appeared in the mathematical programming literature before.

Solving tri-objective multistage hybrid flow shop scheduling problems using a discrete firefly algorithm

Hybrid flow shop (HFS) scheduling problems turn into a fascinating area of research for the past several decades. However, most of the researchers consider only single objective and makespan is the most vital objective function. The real industrial scheduling problems involve multiple conflicting objectives. The HFS scheduling problems were proved to be NP-hard (non-deterministic polynomial time hard) problems. In this paper, we present a discrete firefly algorithm (DFA) to minimise the makespan, total flow time and machine idle time in a multistage HFS environment consisting of n jobs and k stages with identical parallel machines. The performance of the proposed algorithm is tested with a real industrial case study data and random problem instances. Computational results proved the effectiveness of the proposed algorithm.