Multi-dimensional clearing functions for aggregate capacity modelling in multi-stage production systems

Nonlinear clearing functions have been proposed in the literature as metamodels to represent the behaviour of production resources that can be embedded in optimisation models for production planning. However, most clearing functions tested to date use a single-state variable to represent aggregate system workload over all products, which performs poorly when product mix affects system throughput. Clearing functions using multiple-state variables have shown promise, but require significant computational effort to fit the functions and to solve the resulting optimisation models. This paper examines the impact of aggregation in state variables on solution time and quality in multi-item multi-stage production systems with differing degrees of manufacturing flexibility. We propose multi-dimensional clearing functions using alternative aggregations of state variables, and evaluate their performance in computational experiments. We find that at low utilisation, aggregation of state variables has little effect on system performance; multi-dimensional clearing functions outperform single-dimensional ones in general; and increasing manufacturing flexibility allows the use of aggregate clearing functions with little loss of solution quality.     

An exploratory study of disaggregated clearing functions for production systems with multiple products

Clearing functions (CFs) have shown considerable promise for representing production capacity in production planning models due to their ability to capture the non-linear relationships between throughput, order releases and lead times. Most CFs developed to date use the total work in progress of all products, in units of processing time, as the state variable. In this paper, we investigate CFs for multi-product systems where the overall throughput of the system is affected by the product mix. We show that the aggregate work in process (WIP) variable used in the previous CF literature may lead to inaccurate estimates of expected throughput for individual products. To address this issue, we explore the use of multi-dimensional CFs (MDCFs) that use an extended definition of resource state based on the disaggregated WIP levels for individual products. Several new functional forms for MDCFs are postulated for single machine multi-product systems and their ability to represent system behaviour is assessed using simulation experiments. Results reveal that MDCFs are better able to predict system performance in the presence of mix-dependent capacity losses. We also discuss the extension of the MDCF approach to multi-stage production systems.     

Rheological and Microscopic Properties of Fat Blends with Similar Solid Fat Content but Different Trans Composition

In this study, two different groups of fat samples were prepared in a way that samples of each group had different trans fatty acid (TFA) composition but similar solid fat content (SFC). Samples of the first group (named group A) had TFA between 0.0 and 56.23 %, while the samples of the second group (group B) contained trans isomers ranging from 0.0 to 44.4 %. A polarized microscope was used to monitor the differences between the samples in terms of crystal size and crystal number during isothermal crystallization. In general, increasing TFA resulted in formation of larger crystals in a shorter time. Similar findings were also observed when small deformation time and frequency sweep experiments were conducted. A higher TFA content led to higher complex modulus values during isothermal crystallization. On the other hand, when the samples were stored at 4 °C for 48 h, the samples with the lower trans isomer had higher hardness values.     

Fatigue fracture of SnAgCu solder joints by microstructural modeling

The ongoing miniaturization trend in the microelectronic industry enforces component sizes to approach the micron, or even the nano scale. At these scales, the underlying microstructural sizes and the geometrical dimensions are comparable. The increasing influence of microscopic entities on the overall mechanical properties makes conventional continuum material models more and more questionable. In this study, the thermomechanical reliability of lead-free BGA solder balls is investigated by microstructural modeling. Microstructural input is provided by orientation imaging microscopy (OIM), converted into a finite element framework. Blowholes in BGA solder balls are examined by optical microscopy and a statistical analysis on their size, position and frequency is conducted. Combining the microstructural data with the appropriate material models, three dimensional local models are created. The fatigue life of the package is determined through a critical solder ball. The thermomechanical reliability of the local models are predicted using cohesive zone based fatigue damage models. The simulation results are validated by statistical analyses provided by the industry.     

The impact of lot-sizing in multiple product environments with congestion

We present a production planning model for a multiple product single machine dynamic lot-sizing problem with congestion. Using queuing models, we develop a set of functions to capture the nonlinear relationship between the output, lot sizes and available work in process inventory levels of all products in the system. We then embed these functions in a nonlinear optimization model with continuous variables, and construct an approximate solution to the original problem by rounding the resulting fractional solution. Computational experiments show that our model with congestion provides significantly better flow time and inventory performance than a benchmark model that does not consider the effects of congestion. These advantages arise from the use of multiple smaller lots in a period instead of a single large lot as suggested by conventional fixed-charge models without congestion.     

Designs for Discriminating Between Two Rival Models

The usual process inspection scheme for controlling the standard deviation (S.D.) of a normal distribution is to plot a Shewhart chart on which are recorded the ranges of small samples; a common size is 5 items. Action is taken if any sample range exceeds a previously determined amount. The rapidity with which the scheme detects a departure from the accepted value of σ can be increased by considering the results of several of the latest samples together. A fixed number of samples can be taken into account by Warning Lines on the Shewhart-type chart (4); a more sensitive scheme uses cumulative sums (cusums) of the sample ranges together with a rule for deciding what change of direction of the cusum path should require action. Both these approaches can be applied to gauged observations. In this paper we compare these four schemes and provide a short table of cusum schemes using the range.     

Anytime merging of appearance-based maps

We consider the problem of merging together multiple appearance-based maps independently built by a team of robots jointly exploring an indoor environment. Due to the lack of accepted metrics to evaluate the quality of merged appearance-based maps, we propose to use algebraic connectivity for this purpose, and we discuss why this is an appropriate measure. Next, we introduce QuickConnect, an anytime algorithm aiming to maximize the given metric and we show how it can merge couple of maps, as well as multiple maps at the same time. The proposed algorithm has been implemented and tested on a fully functioning robotic system building appearance-based maps using a bag of words approach. QuickConnect outperforms alternative methods and features a convenient tradeoff between accuracy and speed.     

Changes in Olive and Olive Oil Characteristics During Maturation

Changes in olive properties and oil quality, oxidative stability, phenolic and chemical composition of two common Turkish varieties (Memecik and Edremit) during maturation were investigated. Olive samples were collected in their own growing region for five different harvest dates and processed to oil with a laboratory scale mill. Metabolic behaviors of these two varieties along with the maturation were different in terms of some compositional parameters. Oleic acid, triolein, β-sitosterol, oleuropein, hydroxytyrosol, and tyrosol contents of olive or olive oils fluctuated with maturation. However, changes in average weight, flesh/pit ratio, water and oil contents of the olives were observed. Phenolics such as trans cinnamic acid contents of both olive fruits decreased whereas cyanidin 3-O-glucoside and cyanidin 3-O-rutinoside anthocyanins increased. Free fatty acids of virgin olive oils were found independent of maturity although some slight changes were determined in peroxide value, dien and trien conjugations. Some compositional parameters such as pigment concentration, tocopherols, stearic acid, linolenic acid, palmitodiolein and monounsaturated/polyunsaturated fatty acid ratio decreased while linoleic acid, dioleolinolein, palmitooleolinolein and Δ-5-avenasterol percentages increased with the maturation. A clear discrimination was observed with principal component analysis. The data obtained can also be considered useful for providing information to determine the ideal maturity stage.