Although there is a long history of the applications of mathematics to biology, only recently has mathematical biology become an accepted branch of applied mathematics. Undergraduates are doing research projects and graduate students are writing Ph.D. dissertations in mathematical biology, and departments are trying to hire them. But what should the Ph.D. training consist of? How should departm...

I. VALUING THE COMMONS The failure of markets to allocate environmental public goods and handle externalities satisfactorily has long vexed economists. The tragedy of the commons stands in sharp rebuke to the idea that unsophisticated, privately organized markets work well enough to please Pareto. Since Paul Samuelson (1954) laid out the problem of efficient production of public goods in simple...

 This paper considers a bi-objective scheduling problem in a flexible manufacturing cell (FMC) which minimizes the maximum completion time (i.e., makespan) and maximum tardiness simultaneously. A new mathematical model is considered to reflect all aspect of the manufacturing cell. This type of scheduling problem is known to be NP-hard. To cope with the complexity of such a hard problem, a genet...

The use of probiotics, once discussed primarily in the context of alternative medicine, is now entering mainstream medicine. However, only a few of the potential health benefits attributed to probiotics have been confirmed in well-designed, well-conducted, randomized, controlled trials. This is especially true in the pediatric population. We review here the available evidence on efficacy of pro...

the aim of this paper is to study a multi-product, multi-period production systems in a hybrid flow shop so that lot-sizing and scheduling will be detemined simultaneously. a new mixed-integer programming model is proposed to formulate the studied problem. the objective function in this investigation includes the total cost of production, inventory and external supply. in the case of not satisf...