Proportionate Flow Shop Games

In a proportionate flow shop problem several jobs have to be processed through a fixed sequence of machines and the processing time of each job is equal on all machines.By identifying jobs with agents, whose costs linearly depend on the completion time of their jobs, and assuming an initial processing order on the jobs, we face an additional problem: how to allocate the cost savings obtained by ordering the jobs optimally?In this paper, PFS games are defined as cooperative games associated to proportionate flow shop problems.It is seen that PFS games have a nonempty core.Moreover, it is shown that PFS games are convex if the jobs are initially ordered in decreasing urgency.For this case an explicit expression for the Shapley value and a specific type of equal gain splitting rule which leads to core elements of the PFS game are proposed.Proportionate flow shop problems;core;convexity

Proportionate Flow Shop Games

In a proportionate flow shop problem several jobs have to be processed through a fixed sequence of machines and the processing time of each job is equal on all machines.By identifying jobs with agents, whose costs linearly depend on the completion time of their jobs, and assuming an initial processing order on the jobs, we face an additional problem: how to allocate the cost savings obtained by ordering the jobs optimally?In this paper, PFS games are defined as cooperative games associated to proportionate flow shop problems.It is seen that PFS games have a nonempty core.Moreover, it is shown that PFS games are convex if the jobs are initially ordered in decreasing urgency.For this case an explicit expression for the Shapley value and a specific type of equal gain splitting rule which leads to core elements of the PFS game are proposed

Characterizing Cautious Choice

The class of maximin actions in general decision problems is characterized.Maximin actions;Decision problems

Characterizing Cautious Choice

The class of maximin actions in general decision problems is characterized.

Organic farming in northeast of Portugal: effects of soil fertility management on DM yield and nutrients composition of pastures

The aim of this work was to evaluate the effect of six types of soil fertility management: no fertiliser (NF), lime inputs (Ca), mineral fertilisation combined with hming (CaP (lime and phosphorous), CaPB (lime, phosphorous and boron), manure (M), and manure+lime+mineral fertilisation (MCaPB), and two types of pasture (unsown and sown) on DM yield, botanical composition and nutrients content of pasture during two years of study. DM yield was significantly increased when plots were fertilised with manure (M and MCaPB), which also improved the proportion of legumes, mainly in the sown pasture

Large-scale magnetic fields from inflation due to a CPTCPT-even Chern-Simons-like term with Kalb-Ramond and scalar fields

We investigate the generation of large-scale magnetic fields due to the breaking of the conformal invariance in the electromagnetic field through the $CPT$-even dimension-six Chern-Simons-like effective interaction with a fermion current by taking account of the dynamical Kalb-Ramond and scalar fields in inflationary cosmology. It is explicitly demonstrated that the magnetic fields on 1Mpc scale with the field strength of $\sim 10^{-9}$G at the present time can be induced.Comment: 18 pages, 6 figures, version accepted for publication in Eur. Phys. J.