PCB assembly line assignment:a genetic algorithm approach

Purpose – This paper sets out to study a production-planning problem for printed circuit board (PCB) assembly. A PCB assembly company may have a number of assembly lines for production of several product types in large volume. Design/methodology/approach – Pure integer linear programming models are formulated for assigning the product types to assembly lines, which is the line assignment problem, with the objective of minimizing the total production cost. In this approach, unrealistic assignment, which was suffered by previous researchers, is avoided by incorporating several constraints into the model. In this paper, a genetic algorithm is developed to solve the line assignment problem. Findings – The procedure of the genetic algorithm to the problem and a numerical example for illustrating the models are provided. It is also proved that the algorithm is effective and efficient in dealing with the problem. Originality/value – This paper studies the line assignment problem arising in a PCB manufacturing company in which the production volume is high.

A genetic algorithm for the generalised transportation problem

The generalised transportation problem (GTP) is an extension of the linear Hitchcock transportation problem. However, it does not have the unimodularity property, which means the linear programming solution (like the simplex method) cannot guarantee to be integer. This is a major difference between the GTP and the Hitchcock transportation problem. Although some special algorithms, such as the generalised stepping-stone method, have been developed, but they are based on the linear programming model and the integer solution requirement of the GTP is relaxed. This paper proposes a genetic algorithm (GA) to solve the GTP and a numerical example is presented to show the algorithm and its efficiency.

SAS/OWA:ordered weighted averaging in SAS optimization

This paper explores the use of the optimization procedures in SAS/OR software with application to the ordered weight averaging (OWA) operators of decision-making units (DMUs). OWA was originally introduced by Yager (IEEE Trans Syst Man Cybern 18(1):183-190, 1988) has gained much interest among researchers, hence many applications such as in the areas of decision making, expert systems, data mining, approximate reasoning, fuzzy system and control have been proposed. On the other hand, the SAS is powerful software and it is capable of running various optimization tools such as linear and non-linear programming with all type of constraints. To facilitate the use of OWA operator by SAS users, a code was implemented. The SAS macro developed in this paper selects the criteria and alternatives from a SAS dataset and calculates a set of OWA weights. An example is given to illustrate the features of SAS/OWA software. © Springer-Verlag 2009.

The development of a solid waste management strategy

This research is concerned with the application of operational research techniques in the development of a long- term waste management policy by an English waste disposal authority. The main aspects which have been considered are the estimation of future waste production and the assessment of the effects of proposed systems. Only household and commercial wastes have been dealt with in detail, though suggestions are made for the extension of the effect assessment to cover industrial and other wastes. Similarly, the only effects considered in detail have been costs, but possible extensions are discussed. An important feature of the study is that it was conducted in close collaboration with a waste disposal authority, and so pays more attention to the actual needs of the authority than is usual in such research. A critical examination of previous waste forecasting work leads to the use of simple trend extrapolation methods, with some consideration of seasonal effects. The possibility of relating waste production to other social and economic indicators is discussed. It is concluded that, at present, large uncertainties in predictions are inevitable; waste management systems must therefore be designed to cope with this uncertainty. Linear programming is used to assess the overall costs of proposals. Two alternative linear programming formulations of this problem are used and discussed. The first is a straightforward approach, which has been .implemented as an interactive computer program. The second is more sophisticated and represents the behaviour of incineration plants more realistically. Careful attention is paid to the choice of appropriate data and the interpretation of the results. Recommendations are made on methods for immediate use, on the choice of data to be collected for future plans, and on the most useful lines for further research and development.

Determination of muscle fatigue in clinical practices using dynamically embedded signals

This paper explores a new method of analysing muscle fatigue within the muscles predominantly used during microsurgery. The captured electromyographic (EMG) data retrieved from these muscles are analysed for any defining patterns relating to muscle fatigue. The analysis consists of dynamically embedding the EMG signals from a single muscle channel into an embedded matrix. The muscle fatigue is determined by defining its entropy characterized by the singular values of the dynamically embedded (DE) matrix. The paper compares this new method with the traditional method of using mean frequency shifts in the EMG signal's power spectral density. Linear regressions are fitted to the results from both methods, and the coefficients of variation of both their slope and point of intercept are determined. It is shown that the complexity method is slightly more robust in that the coefficient of variation for the DE method has lower variability than the conventional method of mean frequency analysis.

Evaluating productive efficiency:comparative study of commercial banks in Gulf countries

Financial institutes are an integral part of any modern economy. In the 1970s and 1980s, Gulf Cooperation Council (GCC) countries made significant progress in financial deepening and in building a modern financial infrastructure. This study aims to evaluate the performance (efficiency) of financial institutes (banking sector) in GCC countries. Since, the selected variables include negative data for some banks and positive for others, and the available evaluation methods are not helpful in this case, so we developed a Semi Oriented Radial Model to perform this evaluation. Furthermore, since the SORM evaluation result provides a limited information for any decision maker (bankers, investors, etc...), we proposed a second stage analysis using classification and regression (C&R) method to get further results combining SORM results with other environmental data (Financial, economical and political) to set rules for the efficient banks, hence, the results will be useful for bankers in order to improve their bank performance and to the investors, maximize their returns. Mainly there are two approaches to evaluate the performance of Decision Making Units (DMUs), under each of them there are different methods with different assumptions. Parametric approach is based on the econometric regression theory and nonparametric approach is based on a mathematical linear programming theory. Under the nonparametric approaches, there are two methods: Data Envelopment Analysis (DEA) and Free Disposal Hull (FDH). While there are three methods under the parametric approach: Stochastic Frontier Analysis (SFA); Thick Frontier Analysis (TFA) and Distribution-Free Analysis (DFA). The result shows that DEA and SFA are the most applicable methods in banking sector, but DEA is seem to be most popular between researchers. However DEA as SFA still facing many challenges, one of these challenges is how to deal with negative data, since it requires the assumption that all the input and output values are non-negative, while in many applications negative outputs could appear e.g. losses in contrast with profit. Although there are few developed Models under DEA to deal with negative data but we believe that each of them has it is own limitations, therefore we developed a Semi-Oriented-Radial-Model (SORM) that could handle the negativity issue in DEA. The application result using SORM shows that the overall performance of GCC banking is relatively high (85.6%). Although, the efficiency score is fluctuated over the study period (1998-2007) due to the second Gulf War and to the international financial crisis, but still higher than the efficiency score of their counterpart in other countries. Banks operating in Saudi Arabia seem to be the highest efficient banks followed by UAE, Omani and Bahraini banks, while banks operating in Qatar and Kuwait seem to be the lowest efficient banks; this is because these two countries are the most affected country in the second Gulf War. Also, the result shows that there is no statistical relationship between the operating style (Islamic or Conventional) and bank efficiency. Even though there is no statistical differences due to the operational style, but Islamic bank seem to be more efficient than the Conventional bank, since on average their efficiency score is 86.33% compare to 85.38% for Conventional banks. Furthermore, the Islamic banks seem to be more affected by the political crisis (second Gulf War), whereas Conventional banks seem to be more affected by the financial crisis.

Multi-criteria logistics distribution network design using SAS/OR

This paper explores the use of the optimization procedures in SAS/OR software with application to the contemporary logistics distribution network design using an integrated multiple criteria decision making approach. Unlike the traditional optimization techniques, the proposed approach, combining analytic hierarchy process (AHP) and goal programming (GP), considers both quantitative and qualitative factors. In the integrated approach, AHP is used to determine the relative importance weightings or priorities of alternative warehouses with respect to both deliverer oriented and customer oriented criteria. Then, a GP model incorporating the constraints of system, resource, and AHP priority is formulated to select the best set of warehouses without exceeding the limited available resources. To facilitate the use of integrated multiple criteria decision making approach by SAS users, an ORMCDM code was implemented in the SAS programming language. The SAS macro developed in this paper selects the chosen variables from a SAS data file and constructs sets of linear programming models based on the selected GP model. An example is given to illustrate how one could use the code to design the logistics distribution network.

Fuzzy data envelopment analysis:a discrete approach

Data envelopment analysis (DEA) as introduced by Charnes, Cooper, and Rhodes (1978) is a linear programming technique that has widely been used to evaluate the relative efficiency of a set of homogenous decision making units (DMUs). In many real applications, the input-output variables cannot be precisely measured. This is particularly important in assessing efficiency of DMUs using DEA, since the efficiency score of inefficient DMUs are very sensitive to possible data errors. Hence, several approaches have been proposed to deal with imprecise data. Perhaps the most popular fuzzy DEA model is based on a-cut. One drawback of the a-cut approach is that it cannot include all information about uncertainty. This paper aims to introduce an alternative linear programming model that can include some uncertainty information from the intervals within the a-cut approach. We introduce the concept of "local a-level" to develop a multi-objective linear programming to measure the efficiency of DMUs under uncertainty. An example is given to illustrate the use of this method.

An integer-valued data envelopment analysis model with bounded outputs

Integer-valued data envelopment analysis (DEA) with alternative returns to scale technology has been introduced and developed recently by Kuosmanen and Kazemi Matin. The proportionality assumption of their introduced "natural augmentability" axiom in constant and nondecreasing returns to scale technologies makes it possible to achieve feasible decision-making units (DMUs) of arbitrary large size. In many real world applications it is not possible to achieve such production plans since some of the input and output variables are bounded above. In this paper, we extend the axiomatic foundation of integer-valuedDEAmodels for including bounded output variables. Some model variants are achieved by introducing a new axiom of "boundedness" over the selected output variables. A mixed integer linear programming (MILP) formulation is also introduced for computing efficiency scores in the associated production set. © 2011 The Authors. International Transactions in Operational Research © 2011 International Federation of Operational Research Societies.

An aggregate measure of financial ratios using a multiplicative DEA model

This paper examines the problems in the definition of the General Non-Parametric Corporate Performance (GNCP) and introduces a multiplicative linear programming as an alternative model for corporate performance. We verified and tested a statistically significant difference between the two models based on the application of 27 UK industries using six performance ratios. Our new model is found to be a more robust performance model than the previous standard Data Envelopment Analysis (DEA) model.

CAPS in Z(2,n)

We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. For the determination of caps with maximum cardinality and complete caps with minimum cardinality we provide integer linear programming formulations and identify some values for small n.

New Upper Bounds for Some Spherical Codes

The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, y ∈ W, x 6= y, is denoted by A(n, s). We use two methods for obtaining new upper bounds on A(n, s) for some values of n and s. We find new linear programming bounds by suitable polynomials of degrees which are higher than the degrees of the previously known good polynomials due to Levenshtein [11, 12]. Also we investigate the possibilities for attaining the Levenshtein bounds [11, 12]. In such cases we find the distance distributions of the corresponding feasible maximal spherical codes. Usually this leads to a contradiction showing that such codes do not exist.

Exact Discriminant Function Design Using Some Optimization Techniques

Some aspects of design of the discriminant functions that in the best way separate points of predefined final sets are considered. The concept is introduced of the nested discriminant functions which allow to separate correctly points of any of the final sets. It is proposed to apply some methods of non-smooth optimization to solve arising extremal problems efficiently.

A spatiotemporal Data Envelopment Analysis (S-T DEA) approach:the need to assess evolving units

One of the major challenges in measuring efficiency in terms of resources and outcomes is the assessment of the evolution of units over time. Although Data Envelopment Analysis (DEA) has been applied for time series datasets, DEA models, by construction, form the reference set for inefficient units (lambda values) based on their distance from the efficient frontier, that is, in a spatial manner. However, when dealing with temporal datasets, the proximity in time between units should also be taken into account, since it reflects the structural resemblance among time periods of a unit that evolves. In this paper, we propose a two-stage spatiotemporal DEA approach, which captures both the spatial and temporal dimension through a multi-objective programming model. In the first stage, DEA is solved iteratively extracting for each unit only previous DMUs as peers in its reference set. In the second stage, the lambda values derived from the first stage are fed to a Multiobjective Mixed Integer Linear Programming model, which filters peers in the reference set based on weights assigned to the spatial and temporal dimension. The approach is demonstrated on a real-world example drawn from software development.

Non-stationary stochastic inventory lot-sizing with emission and service level constraints in a carbon cap-and-trade system

Firms worldwide are taking major initiatives to reduce the carbon footprint of their supply chains in response to the growing governmental and consumer pressures. In real life, these supply chains face stochastic and non-stationary demand but most of the studies on inventory lot-sizing problem with emission concerns consider deterministic demand. In this paper, we study the inventory lot-sizing problem under non-stationary stochastic demand condition with emission and cycle service level constraints considering carbon cap-and-trade regulatory mechanism. Using a mixed integer linear programming model, this paper aims to investigate the effects of emission parameters, product- and system-related features on the supply chain performance through extensive computational experiments to cover general type business settings and not a specific scenario. Results show that cycle service level and demand coefficient of variation have significant impacts on total cost and emission irrespective of level of demand variability while the impact of product's demand pattern is significant only at lower level of demand variability. Finally, results also show that increasing value of carbon price reduces total cost, total emission and total inventory and the scope of emission reduction by increasing carbon price is greater at higher levels of cycle service level and demand coefficient of variation. The analysis of results helps supply chain managers to take right decision in different demand and service level situations.