used an MIP model and a heuristics based on beam search to solve a worker assignment problem with a ﬁxed number of workers and the production rate maximization criterion.
Corominas et al. (2008) study a problem that differs from problem P in that it distinguishes permanent and temporary workers, introduces incompatible groups of tasks and a change of stations is not possible. The objective is to minimize the number of temporary workers. A binary linear programming formulation for this problem is proposed and a commercial solver is applied. A heuristic algorithm for the assignment of workers in a lean U- shaped line is developed by Shewchuk (2008) . Nakade and Nishiwaki (2008) study a problem of allocating non-identical workers to machines in a U-shaped production line to minimize the takt time, provided that the number of workers is minimized. A constructive heuristic algorithm for a multi-period problem of the workforce assignment in a mixed-model vehicle production assembly line is proposed by Karabak et al. (2011) . A mathematical model for scheduling skilled permanent workers and unskilled temporary workers in a mixed-model ﬂow line is developed by
Keywords: rotary machine; product variety; machine engineering; production system design; integrated process planning and system conﬁguration; line design and balancing; combinatorial design; combinatorial optimisation; industrial case study
Within the today’s context of increasing demand and product diversiﬁcation, companies must be able to adapt their manu- facturing systems for high variety production in order to proﬁtably produce in small quantities different models of products. Mixed-model production is the practice of proces- sing products without changeovers in the manufacturing sys- tem (Rabbani, Ziaeifar, and Manavizadeh 2014 ). Such a production mode poses new challenges in production system design, planning and management. In order to be cost-efﬁ- cient, several decision problems have to be considered jointly (Leonesio et al. 2013 ) such as process planning, system con- ﬁguration and scheduling. In literature, each of these decision problems has attracted a large amount of research interest (Xu, Wang, and Newman 2011 ; Battaïa et al. 2012b ; Guschinskaya et al. 2009 ; Dolgui et al. 2008 ). However, conventionally, they have been performed sequentially (Lv and Qiao 2014 ). Under the modern production constraints and global competition, the strong dependence between these issues and its inﬂuence on the proﬁtability of product manufacturing, resource utilisation and product delivery time cannot be ignored anymore. The growing amount of research work in the direction of joint consideration of these problems proves the importance of such an integrated approach.
Figure 2.4 - Diagram of Cycle Time in Two Model Assembly System
2.5 Mixed-Model Sequencing Constraints
The current mixed-model sequencing constraints relate to capacity balancing, as described above. The sequencing system is constrained by how frequently a vehicle with a longer than average cycle time can be produced on the assembly line. For example, if a vehicle has a sunroof, there are some additional processes which must be carried out, compared to a vehicle without a sunroof. These additional processes could include lifting a glass panel above the vehicle into place, connecting additional electrical components to control the sunroof and function testing all of these additional components. As this vehicle with a sunroof has a longer cycle time, the vehicle before or after it on the assembly line must take less than the average cycle time in order for the line workers to ‘catch up’ the time and maintain the target production level. Similar constraints apply to a variety of other vehicle options, as well as entire vehicle models.
Recommendations should be addressed based on these findings. In any analysis evaluating risk factors on a psychometric test change over time, the standard LMM should not be used without a precise inspection of the psychometric test properties. In particular, a more adequate mixedmodel that accounts for curvilinearity and ceiling/floor effects should be estimated to evaluate the violation of the LMM assumptions and the reliability of the associations highlighted. For many psychometric tests like MMSE and BVRT, the standard LMM is most likely not reliable, and mixedmodel that accounts for curvilinearity should be systematically preferred. The threshold mixedmodel is the most reliable model as it models directly each level of the outcome but it is computationally intensive. Therefore, for psychometric tests including a relatively large number of levels, a model assuming a curvilinear continuous outcome can be used instead. For example, the Beta LMM ( 16 ) provided similar fits as the threshold LMM and more importantly gave unbiased inference in our simulations while avoiding the computational problems. In contrast, for psychometric tests with a small number of levels, the threshold LMM should be preferred. The 1 cmm user-friendly R function is available within the 1 cmm R package ( http://cran.r-project.org/web/packages/lcmm/ ) for estimating latent process LMM including threshold and Beta LMM, and SAS macros are available on
The cost aspect of efficiency can be measured by the inventory accumulation in the work-in-process (WIP) buffers. Higher efficiency implies lower WIP levels of buffers. However, buffers can play two important roles in mixed-model assembly lines. First, a buffer is important to ensure that a bottleneck station will not be starved or blocked as a result of stochastic assembly times, e.g., unexpected machine break down, materials missing, or workers absence. Secondly, between a final assembly line and subassembly lines, it may be necessary to follow a different sequence for each individual line due to operational constraints. For example, prior to entering a final assembly line, workpieces may be required to go through a painting line, where workpieces with the same color are preferred to enter the line in batches. A buffer at the end of a subassembly line will allow these workpieces to enter a final assembly line with a rearranged sequence. Such a buffer will improve line throughput by reducing setup time. On the other hand, it will increase cost due to inventory accumulation. Alternate scenarios on sequencing and buffer size should be simulated and evaluated to find a trade-off.
3.3 Analysis of transformed data
We tried several transformations of CD4 and found the fourth root led to the best results for adequacy of model (10) as it can be seen on the plot of conditional residuals (figure 2b) and the QQ-plot of Cholesky residuals (figure 1b). With this transformation the value of the Royston criteria was dramatically decreased to 2.5 (even if the Shapiro-Francia test was still significant with p=0.02). Parameter of model (10) estimated on the transformed data are displayed in table 1. Both models exhibit a treatment effect on CD4 counts change, a higher slope for the D4T+DDI group, but interpretation of parameter values is more difficult when the transformed variable is used. Futhermore, calculation of variance for the backtransformed prediction is not direct. In addition, adjustment to the normal distribution is not yet perfect and questions arise on the robustness of the model. Thus, it is interesting to investigate robustness of the linear mixedmodel to heteroscedasticity and other departures from the model to evaluate the need for such variable transformation.
Probabilistic analysis are considered nowadays an interesting solution for real-time systems as the proba- bility of appearance of worst-case values is small (10 −45 per hour of functioning) compared to the accepted probability of failure (10 −9 per hour of functioning for the highest safety level in avionics). In order to take into account this information, Burns and Edgar  have introduced the notion of probabilistic worst case execution time (pWCET). The pWCET of a program is bounding the probability that the execution time of that program exceeds a given value. A possible method to estimate the pWCET is based on measure- ments and the associated analysis is called measurement-based probabilistic timing analysis (MBPTA). Such method has been proposed by Cucu-Grosjean et al.  and the obtained estimate is sensitive to the observed execution times. To our best knowledge this dependence of MBPTA on the observations is an open problem. Within this paper we propose a first solution based on a mixedmodel using genetic algorithms.
Fig. 12 Time solution diagram
This paper has proposed a joint formulation for process planning and system configuration for design of rotary transfer machines for a mixed-model production of different parts. The objective of suggested models is to minimize the total system cost. A mathematical formulation with several variants for this combinatorial optimization problem was developed and evaluated on an industrial case study. It was shown that the developed models could be successfully applied to the production cases with 6 different types of parts to be machined simultaneously at such a transfer machine. However, since the problem size is substantially increasing when the number of different types of parts is growing, as a consequence, it makes difficult to obtain optimal solutions for larger problem sizes. To address such problems efficiently within reasonable solution time, approximate methods have to be developed. Having such methods available will also allow envisaging the extension of the optimization problem by considering the sequence of the parts to be determined at the same time as the process planning and the system configuration.
Bivariate linear mixed models are useful when analyzing longitudinal data of two associated markers. In this paper, we present a bivariate linear mixedmodel including random effects or first-order auto-regressive process and independent measurement error for both markers. Codes and tricks to fit these models using SAS Proc MIXED are provided. Limitations of this program are discussed and an example in the field of HIV infection is shown. Despite some limitations, SAS Proc MIXED is a useful tool that may be easily extendable to multivariate response in longitudinal studies.
Our objective is to propose a way of reducing the computation time of the SAEM- MCMC algorithm (Kuhn and Lavielle, 2005) for complex mixed models, together with a theoretical study of the resulting estimator. When the regression function is not analytically available (and we call it also computer model in the rest of the paper), extensions of SAEM have already been proposed. Donnet and Samson (2007) deal with the case of an ODE mixedmodel, approximating the solution with a numerical scheme and studying the influence of this scheme to the properties of the approximate maximum likelihood estimator. But this approach remains time consuming when the ODE is multi-dimensional. For a PDE mixedmodel, Grenier et al. (2014) propose to approximate the PDE with a numerical scheme on a predefined grid, and then to interpolate the solution of the PDE linearly between two points of the grid. This linear approximation allows substantially reducing the computation time from 23 days to around 30 minutes, but may lead to biased estimates depending on the non linearity of the model.
(4) Analysis of treatment effects. Treatment group covariates are introduced in the mixedmodel and selected using statistical tests. Significant differ- ences are emphasized between, on the one hand, therapeutic strategies and, on the other hand, treatment durations in radiochemotherapy. This paper is organized as follows. In Section 2, a new empirical kinetic model of tumor growth is proposed. Experimental setup of data collection and statis- tical methods are then presented in Section 3. Modeling results are analyzed in Section 4. The case of non-treated tumor growth is firstly examined. In a second subsection three loco-regional therapies for cancer treatment are com- pared. Finally the estimation results for the concomitant radiochemotherapy group to assess effects of the treatment duration are presented. The conclu- sions and perspectives of this work are drawn in Section 5.
Abstract. Mixed-effects models provide a rich theoretical framework for the analysis of longitudinal data. However, when used to analyze or predict the progression of a neurodegenerative disease such as Alzheimer’s disease, these models usually do not take into account the fact that subjects may be at different stages of disease progression and the in- terpretation of the model may depend on some implicit reference time. In this paper, we propose a generative statistical model for longitudinal data, described in a univariate Riemannian manifold setting, which esti- mates an average disease progression model, subject-specific time shifts and acceleration factors. The time shifts account for variability in age at disease-onset time. The acceleration factors account for variability in speed of disease progression. For a given individual, the estimated time shift and acceleration factor define an affine reparametrization of the average disease progression model. This statistical model has been used to analyze neuropsychological assessments scores and cortical thick- ness measurements from the Alzheimer’s Disease Neuroimaging Initiative database. The numerical results showed that we can distinguish between slow versus fast progressing and early versus late-onset individuals.
Furthermore, the breeder needs to secure a minimum income C at any time. It repre- sents the cash value needed to secure the annual family’s subsistence requirements when all male offspring have been sold. This is a fixed value, estimated for a reference fam- ily . The highest offtake rate on females does not lead the herd to extinction. This means that offtake decisions are determined by the need to meet a minimum income with- out jeopardising herd existence in the future. Therefore, the minimum income constraint reads as follows (3): , where C > 0, thus the viable offtake of females at every point in time depends on the current wealth. The minimum income constraint (3) mixed with inequality (2) provides the state constraint , which induces a minimum wealth level . To summarise the state con- straints, K denotes the constraint set defined by (4): and control con- straints are summarised by (5):
Abstract. To help designers face the complexity of mixed interaction and iden- tifying original and adapted solutions, we developed and evaluated an original approach to interaction design. This approach, called Model Assisted Creativity Sessions (MACS), aims to combine the best elements of both a model of mixed interaction, and a collaborative and creative session. The objective is twofold: to support the exploration of the design space, and to establish a common lan- guage between participants. To assess the viability of this approach, we relied on a protocol analysis of the verbal recordings of two existing design situations. Results show that the model impacts the generation of ideas and that partici- pants use the model concepts to share their thoughts during the session.
By assessing short-term and long-term effects of management practices, the model provides some insight into the pastoralists’ foresight capacity when confronted with uncertainty. A mixed herd enables breeders to take advantage of opposed species-spe- cific traits. Llamas behave as a stabilising component due to their ability to thrive dur- ing environmental perturbation, whereas sheep, which have a faster growth rate in good years, promote rapid recovery from drought. At this stage, our results are likely to contribute to the debate about maximis- ing strategies, since these need to be related to the livestock system sustainability. Pol- icies that advocate destocking, assuming that the ecological carrying capacity is being exceeded, are increasingly common espe- cially in drylands . If sustainability (related to family survival) is a common goal to pastoralists, since all of them are not wealthy, they are likely to develop differ- entiated strategies according to their wealth level . If rich breeders can afford to develop precautionary behaviour, poor breed- ers have to take risks. For the latter, rapid herd growth when forage is available is likely to remain a sound practice to avoid destitution when droughts occur. While unable to master exogenous uncertainty, breeders can anticipate and mitigate it thanks to particular breeding practices. These prac-