tendency to optimization in last decades has resulted in creating multi-product manufacturing systems. production planning in such systems is difficult, because optimal production volume that is calculated must be consistent with limitation of production system. hence, integration has been proposed to decide about these problems concurrently. main problem in integration is how we can relate pro...

Using data from the Survey of Income and Program Participation, this study analyzes the effects of AFDC benefits on living arrangements in combination with welfare participation. The study finds high rates of cohabitation and marriage among women receiving welfare. As well, results from the multivariate models indicate that the welfare system influences the decisions to cohabit and receive welf...

Tendency to optimization in last decades has resulted in creating multi-product manufacturing systems. Production planning in such systems is difficult, because optimal production volume that is calculated must be consistent with limitation of production system. Hence, integration has been proposed to decide about these problems concurrently. Main problem in integration is how we can relate pro...

The convex hulls of more-part Sperner families is defined and studied. Corollaries of the results are some well-known theorems on 2 or 3-part Sperner families. Some methods are presented giving new theorems.

Let X= X, v ,I’?, X, n X2 = 0 be a partition of an n-element set. Suppose that the family % of some subsets of X satisfy the following condition: if there is an inclusion F, G Fz (F,, Fz E 5”) in %, the difference F, F, cannot be a subset of X, or ,I’>. Kleitman (Math. Z. 90 (1965), 251-259) and Katona (Sfudia Sci. Math. Hungar. 1 (1966) 59-63) proved 20 years ago that 1% 1 is at most n choose ...