On varieties of combinatorial inverse semigroups II

Communicated by L. N. Shevrin     

A robust optimization model for multi-site production planning problem in an uncertain environment

This paper addresses the multi-site production planning problem for a multinational lingerie company in Hong Kong subject to production import/export quotas imposed by regulatory requirements of different nations, the use of manufacturing factories/locations with regard to customers’ preferences, as well as production capacity, workforce level, storage space and resource conditions at the factories. In this paper, a robust optimization model is developed to solve multi-site production planning problem with uncertainty data, in which the total costs consisting of production cost, labor cost, inventory cost, and workforce changing cost are minimized. By adjusting penalty parameters, production management can determine an optimal medium-term production strategy including the production loading plan and workforce level while considering different economic growth scenarios. The robustness and effectiveness of the developed model are demonstrated by numerical results. The trade-off between solution robustness and model robustness is also analyzed.     

Heuristics approach to printed circuit board insertion problem

This paper studies the operation of a surface mount technology (SMT) machine which basically consists of three main movable parts: an X–Y table containing a printed circuit board (PCB), ten rotating ‘pick-and-place’ heads and a carriage feeder of reels. The machine inserts electronic components into defined positions on a PCB and the components are supplied from a set of reels each containing a tape of identical components. In the current production setup, the assembly plan comprising both the insertion sequence of components and the placement orders of the reels in the feeder is by human experience. Our study suggests that the problem is computationally difficult for its mathematical optimum with the insertion problem alone being NP-complete. We propose a heuristic solution technique of low computational complexity to find a better assembly plan comprising of the assembly sequence of electronic components and the placement order of the reels in the feeder. The algorithm developed combines the physical constraints of the SMT machine and a ‘grouping’ concept that takes advantage of the natural structure of a PCB. Using multiple reels in the PCB insertion problem are also considered. Simulated results are reported on a set of illustrative data.     

Effects of Cyclodextrin Derivatives on the Catalytic Activity of Tyrosine Phenol-Lyase

The impact of permethylated α-, β-, γ-cyclodextrin (TMα-CD, TMβ-CD, TMγ–CD, respectively) on TPL-catalysed decomposition of L-tyrosine was investigated by means of spectrophotometric measurements. The inhibitory effects of TM-CDs on the catalytic activity of the enzyme were shown. This phenomenon is supposed to be connected with the host–guest complex formation. CDs were found to have impact on maximal velocity and on Michaelis constant of described catalysis.     

A higher-order Markov model for the Newsboy's problem

Markov models are commonly used in modelling many practical systems such as telecommunication systems, manufacturing systems and inventory systems. However, higher-order Markov models are not commonly used in practice because of their huge number of states and parameters that lead to computational difficulties. In this paper, we propose a higher-order Markov model whose number of states and parameters are linear with respect to the order of the model. We also develop efficient estimation methods for the model parameters. We then apply the model and method to solve the generalised Newsboy's problem. Numerical examples with applications to production planning are given to illustrate the power of our proposed model.     

Grouped Dirichlet distribution: A new tool for incomplete categorical data analysis

Motivated by the likelihood functions of several incomplete categorical data, this article introduces a new family of distributions, grouped Dirichlet distributions (GDD), which includes the classical Dirichlet distribution (DD) as a special case. First, we develop distribution theory for the GDD in its own right. Second, we use this expanded family as a new tool for statistical analysis of incomplete categorical data. Starting with a GDD with two partitions, we derive its stochastic representation that provides a simple procedure for simulation. Other properties such as mixed moments, mode, marginal and conditional distributions are also derived. The general GDD with more than two partitions is considered in a parallel manner. Three data sets from a case-control study, a leprosy survey, and a neurological study are used to illustrate how the GDD can be used as a new tool for analyzing incomplete categorical data. Our approach based on GDD has at least two advantages over the commonly used approach based on the DD in both frequentist and conjugate Bayesian inference: (a) in some cases, both the maximum likelihood and Bayes estimates have closed-form expressions in the new approach, but not so when they are based on the commonly-used approach; and (b) even if a closed-form solution is not available, the EM and data augmentation algorithms in the new approach converge much faster than in the commonly-used approach.