Formulations and heuristics for the multi-item uncapacitated lot-sizing problem with inventory bounds

We consider the multi-item uncapacitated lot-sizing problem with inventory bounds, in which a production plan for multiple items has to be determined considering that they share a storage capacity. We present (a) a shortest path formulation and (b) a formulation based on the a priori addition of valid inequalities, which are compared with a facility location formulation available in the literature. Two easy-to-implement mixed integer programming heuristic frameworks are also presented, (a) a rounding scheme and (b) a relax-and-fix approach performed in a time partitioning fashion. Computational experiments are performed to evaluate the different approaches. The numerical results show that the proposed relax-and-fix heuristic outperforms all other approaches. Its solutions are within 4.0% of optimality in less than 10 minutes of running time for all tested instances, with mean gaps in the order of 2.1 and 1.8% for instances with more relaxed and tighter capacities, respectively. The obtained solutions were always better than those obtained by a commercial MIP solver running for one hour using any of the available formulations.     

A novel integer programming formulation with logic cuts for the U-shaped assembly line balancing problem

U-shaped assembly lines are regarded as an efficient configuration in Just-In-Time manufacturing. Balancing the workload in these lines is an unsolved problem that attracted significant research within the past two decades. We present a novel integer programming formulation for U-shaped line balancing problems, where cycle time, the interval between two consecutive outputs, is known and the aim is to minimize the number of workstations. To enhance the efficiency of the LP relaxation of the new formulation, we present three types of logic cuts (assignable-station-cuts, task-assignment-cuts and knapsack-cuts) that exploit the inherent logic of the problem structure. The new formulation and logic cuts are tested on an extensive set of benchmark problems to provide a comparative analysis with the existing models in the literature. The results show that our novel formulation augmented by assignable-station-cuts is significantly better than the previous formulations.     

Efficient formulation and heuristics for multi-item single source ordering problem with transportation cost

Integrated inventory and transportation decisions are critical in the supply chain, providing significant gains for all parties. In this paper, we present a mathematical formulation for the dynamic demand multi-item single source replenishment problem with a piecewise linear transportation cost. Through an extensive experimental study, we find that the new formulation provides a tighter LP relaxation of the problem, while requiring fewer computational resources to optimally solve the problem when compared with existing model in the literature. We also present a new metaheuristic for this general class of coordinated capacitated replenishment problems. On average, the solutions from heuristics are within 1.23% of the optimal solution for the comprehensive set of test problems.     

A note on upper bound formulations in limit analysis

In this paper, we study some recent formulations for the computation of upper bounds in limit analysis. We show that a previous formulation presented by the authors does not guarantee the strictness of the upper bound, nor does it provide a velocity field that satisfies the normality rule everywhere. We show that these deficiencies are related to the quadrature employed for the evaluation of the dissipation power. We derive a formulation that furnishes a strict upper bound of the load factor, which in fact coincides with a formulation reported in the literature. From the analysis of these formulations, we propose a post‐process, which consists in computing exactly the dissipation power for the optimum upper bound velocity field. This post‐process may further reduce the strict upper bound of the load factor in particular situations. Finally, we also determine the quadratures that must be used in the elemental and edge gap contributions, so that they are always positive and their addition equals the global bound gap. Copyright © 2012 John Wiley & Sons, Ltd.     

A fuzzy set theory approach to national composite S&;T indices

Summary Composite science and technology (S&T) indices are essential to overall understanding and evaluation of national S&T status, and to formulation of S&T policy. However, only a few studies on making these indices have been conducted so far since a number of complications and uncertainties are involved in the work. Therefore, this study proposes a new approach to employ fuzzy set theory and to make composite S&T indices, and applies it. The approach appears to successfully integrate various S&T indicators into three indices: R&D input, R&D output, and economic output. We also compare Koreas S&T indices with those of five developed countries (France, Germany, Japan, the United Kingdom, and the United States) to obtain some implications of the results for Koreas S&T.     

Application of statistical physics methods and conceptsto the study of science & technology systems

We apply methods and concepts of statistical physics to the study of science & technology(S&T) systems. Specifically, our research is motivated by two concepts of fundamentalimportance in modern statistical physics: scaling and universality. We try to identify robust,universal, characteristics of the evolution of S&T systems that can provide guidance to forecastingthe impact of changes in funding. We quantify the production of research in a novel fashioninspired by our previous study of the growth dynamics of business firms. We study the productionof research from the point of view both of inputs (R&D funding) and of outputs (publications andpatents) and find the existence of scaling laws describing the growth of these quantities.We also analyze R&D systems of different countries to test the "universality" of our results.We hypothesize that the proposed methods may be particularly useful for fields of S&T (or forlevels of aggregation) for which either not enough information is available, or for which evolutionis so fast that there is not enough time to collect enough data to make an informed decision.     

Delineating development trends of nanotechnology in the semiconductor industry: Focusing on the relationship between science and technology by employing structural topic model

The bibliometrics research on nanotechnology highlights close interrelationships between scientific and technological activities (S&T) in the field of nanotechnology. Notwithstanding abundant empirical evidence on the mutual relations between S&T, the dynamics of the relationship from a contextual perspective have gained relatively little attention. Accordingly, our understanding of how science- and technology-oriented nanotechnology identifies development opportunities from each other is still at a nascent stage. To address this gap, by focusing on nanotechnology in the semiconductor industry, we use structural topic model to empirically explore the dynamic interrelationships between science- and technology-oriented nanotechnology. We empirically delineate the dynamic development trends in the context of the interrelationships between S&T and demonstrate how development opportunities are identified from each other. These findings show a new window of opportunities for how state-of-the-art models for semantic analysis can be used in the literature on S&T interrelationships.     

Solving elementary shortest-path problems as mixed-integer programs

Ibrahim et al. (Int Trans Oper Res 16:361–369, 2009) presented and analyzed two integer programming formulations for the elementary shortest-path problem (ESPP), which is known to be NP-hard if the underlying digraph contains negative cycles. In fact, the authors showed that a formulation based on multi-commodity flows possesses a significantly stronger LP relaxation than a formulation based on arc flow variables. Since the ESPP is essentially an integer problem, the contribution of our paper lies in extending this research by comparing the formulations with regard to the computation time and memory requirements required for their integer solution. Moreover, we assess the quality of the lower bounds provided by an integer relaxation of the multi-commodity flow formulation.     

A new decomposition algorithm for a liquefied natural gas inventory routing problem

We consider an inventory routing problem (IRP) in the liquefied natural gas (LNG) supply chain, called the LNG-IRP. Here, an actor is responsible for the LNG production and inventory management at the liquefaction plants, the routing and scheduling of a heterogeneous fleet of LNG ships, as well as the inventories and sales at the regasification terminals. Furthermore, all ports have a limited number of berths available for loading and unloading. The LNG-IRP is more complicated than many other maritime inventory routing problems because a constant rate of the cargo evaporates in the tanks each day and is used as fuel during transportation. In addition, a variable number of tanks are unloaded at the regasification terminals. We introduce a new path flow formulation for this problem arising from a novel decomposition scheme based on parts of a ship schedule, called duties. A ship schedule for the entire planning horizon can be divided into duties consisting of a visit to a liquefaction plant, then one or two visits to a regasification terminal before ending in a liquefaction plant. The solution method suggested is based on a priori generation of duties, and the formulation is strengthened by valid inequalities. The same problem was previously solved by a branch-price-and-cut algorithm for a schedule-based formulation. Computational results show that the new formulation provides tighter bounds than the previous schedule-based formulation. Furthermore, on a set of 27 benchmark instances, the proposed algorithm clearly outperforms the previous branch-price-and-cut algorithm both with regard to computational time and the number of problems solved within a 10-h time limit.     

The Stochastic Uncapacitated Facility Location Problem: A New Formulation and Extensions to the Capacitated Problem

This note presents an alternative formulation of the deterministic location model which Tcha and Yoon have recently developed to approximate the stochastic uncapacitated facility location problem. The model, besides being more compact and easier to handle than their model, has the distinct advantage of having a tighter LP relaxation. Also suggested is how the new formulation can be implemented in Van Roy's Cross Decomposition method for solving a more general stochastic capacitated problem.     

Science and technology policies: A tale of political use,misuse and abuse of traditional R&;D indicators

Future political priorities for science and technology (S&T) policy formulation usually rest on a rather simplistic interpretation of past events. This can lead to serious errors and distortions and can negatively affect the innovation system. In this article we try to highlight the riskiness involved in policy making based on traditional R&D indicators and trends. We would emphasise that this approach does not take account of structural aspects crucial for the analysis of the innovation system. We examine the implications for science, technical and human resources policies of the political challenge of R&D convergence in a peripheral EU region. Three scenarios are developed based on application of the same criteria to the trends observed in traditional R&D input indicators.     

Structural changes in S&T research in India

Before India became an independent country, its scientists and policy makers could foreseethe importance of science in its development, and accordingly a number of research anddevelopment (R&D) institutions were established. However during these five decades ofindependence, the choice between basic sciences and technology was always a subject of debate.It will be appropriate now to examine the changing patterns of Science and Technology (S&T)manpower growth to find out the ground truth reality. The present study pertains to the analysis ofS&T outturn data in various fields of scientific research that can provide a base for S&T planningand policy making. These S&T indicators will be helpful in estimating future requirements, whichin turn can be useful to a great extent in science and technology policy formulation. Theseestimates and future projections are based on mathematical modelling of the data pertaining to theoutturn of highly qualified Scientific and Technical (S&T) personnel in India from differentfaculties over the period 1990-1998. From the trend analysis it is evident that research is no moreperceived as an interesting career except in the field of engineering and medicine. The findingsfurther suggest that there is a noticeable shift from basic sciences to technology.     

A novel branch-and-bound algorithm for the chance-constrained resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) has been widely studied during the last few decades. In real-world projects, however, not all information is known in advance and uncertainty is an inevitable part of these projects. The chance-constrained resource-constrained project scheduling problem (CC-RCPSP) has been recently introduced to deal with uncertainty in the RCPSP. In this paper, we propose a branch-and-bound (B&B) algorithm and a mixed integer linear programming (MILP) formulation that solve a sample average approximation of the CC-RCPSP. We introduce two different branching schemes and eight different priority rules for the proposed B&B algorithm. The computational results suggest that the proposed B&B procedure clearly outperforms both a proposed MILP formulation and a branch-and-cut algorithm from the literature.     

The European perspective on S&T indicators

The S&T indicators activity is first described as a complex process involving a variety of functions, capabilities and institutions; this provides a framework to assess the S&T indicators activity in a country or, more generally, in a research system. Then, the main features of the S&T indicators scene in Europe are presented: regarding the countries, the diversity of the institutional settings and the growing potentials is stressed; among countries, at European level, the important and original role of the European Commission in the dynamics of the S&T indicators activites in Europe is presented; finally, it is argued that the European scene consists of a diversity of research groups which are in competition and collaboration, sharing a number of intellectual concerns and orientations. The perspectives for S&T indicators activity in the EU countries are defined by the greater quantity of source data, by the conceptual advances regarding the S&T system and by the new needs of the decision-makers. In conclusion, some alternative scenarios are suggested.     

Exploiting group symmetry in truss topology optimization

We consider semidefinite programming (SDP) formulations of certain truss topology optimization problems, where a lower bound is imposed on the fundamental frequency of vibration of the truss structure. These SDP formulations were introduced in Ohsaki et al. (Comp. Meth. Appl. Mech. Eng. 180:203–217, 1999). We show how one may automatically obtain symmetric designs, by eliminating the ‘redundant’ symmetry in the SDP problem formulation. This has the advantage that the original SDP problem is substantially reduced in size for trusses with large symmetry groups.     

The impact of sales and operations planning practices on manufacturing operational performance

There is a lack of rigorous empirical studies directly examining the impact of sales and operations planning (S&OP) practices on manufacturing operational performance. This paper aims to fill this gap by analysing a sample of 725 manufacturers from 34 countries. Hypotheses relate internal S&OP, integration with suppliers (IS) and integration with customers with manufacturing operational performance (delivery, quality and flexibility). The constructs were validated with structural equation modelling and the hypotheses were tested using multiple stepwise regression. Our findings showed a positive and moderate-to-large effect of internal S&OP on manufacturing performance, controlling for firm size, country economic development and market dynamics. There was no significant impact of supply chain integration on manufacturing performance. However, we found that IS positively moderated the relationship between internal S&OP and performance, suggesting that firms with mature IS amplify the effect of internal S&OP on performance. The study is among the first to empirically and rigorously establish the impacts of S&OP practices on manufacturing performance, using a large sample of manufacturers spanning different countries, markets and firm sizes. Results show that S&OP practices have a broad impact across several performance dimensions and are a powerful lever for generating manufacturing performance.     

Scheduling parallel processors: An integer linear programming based heuristic for minimizing setup time

The problem of scheduling parallel processors in a make-to-stock environment with sequence setup costs is considered. A new algorithm which formulates a series of 0-1 integer sub problems is proposed and contrasted with an earlier formulation (Dearing and Henderson 1982,1984). Parallels between the sub problem formulations and generalized networks are discussed. The efficiency and quality of the solutions provided were tested using previously published data for a loom assignment problem. The heuristic solution was evaluated against the optimal integer linear programming (ILP) solution, and a rounded linear program (LP) approximation to the optimal solution for several sample problems. Results indicate that the heuristic is efficient, provides near optimal solutions to production planning problems and requires significantly less computing capability than previously reported LP, TLP approaches.     

A trial of general indicator of science and technology: Methodological study of overall estimation of national S&T activity

This paper presents methods using a large number of quantitative indicators of the overall estimation of national S&T activity. The methods collected here apply multivariate analysis techniques to a set of S&T indicators to investigate its structure and extract a single or a small number of indicators of S&T activity. We perform structural analysis and integration of 14 main S&T indicators in 5 countries, the U.S., Japan, Germany, France and the U.K. Latent variables underlying this set of indicators naturally emerge from this analysis, and from these we were able to extract valuable information concerning the nature of S&T activity in each country. This method was also useful for investigating the nature and interpretation, as well as the reliability, of previous S&T indicators.     

Basic research is overshadowed by applied research in China: a policy perspective

This paper demonstrates that basic research has been overshadowed by applied research in China for decades, from the perspective of S&T policy. The data involves 4,707 Chinese S&T policies during the period between 1949 and 2010, which are grouped into five phases, based on the process of S&T system reform in China. We also found that S&T policies in China are leaning more towards basic research, and the gap between basic research and applied research is shrinking.     

Comparison of fully implicit and IMPES formulations for simulation of water injection in fractured and unfractured media

In this work, we compare the fully implicit (FI) and implicit pressure‐explicit saturation (IMPES) formulations for the simulation of water injection in fractured media. The system of partial differential equations is discretized within the discrete‐fracture framework using a control‐volume method. A unique feature of the methodology is that there is no need for the computation of matrix–fracture transfer terms. The non‐linear system of equations resulting from the FI formulation is solved with state‐of‐the‐art Newton and tensor methods. Direct and Krylov iterative methods are employed to solve the system resulting from the Newton linearization. The performance of the FI and IMPES formulations is compared with numerical testing. Results show that the contrast between matrix and fracture properties affects the performance of both IMPES and FI formulations and that the tensor method outperforms all the Newton solvers for the near‐singular Jacobian matrix. Copyright © 2006 John Wiley & Sons, Ltd.