since lean concept has appeared many works have been done on decreasing or even eliminating of wastes such as extra inventory. although these studies have not taken into account expected availability seriously. so in this paper, a multiple objective decision making (modm) model has been developed by viewpoint of these subjects. they are decreasing wastes and increasing system availability. wast...

In this paper, we prove that the quadratic polynomials modulo 3 with the largest correlation with parity are unique up to permutation of variables and constant factors. As a consequence of our result, we completely characterize the smallest MAJ◦ MOD3 ◦ AND2 circuits that compute parity, where a MAJ ◦MOD3 ◦ AND2 circuit is one that has a majority gate as output, a middle layer of MOD3 gates and ...

This pa.per descril>es Mull;i-ModMMethod, a. design n le thod for bu ih l i ng gra.nnna.r-i)a.sed lnul l ; i i i iodaJ systeins. M u l t i -ModM-MeIJ iod defhies the procediire, which hlllerfa.ce desiguers i i iay l 'of low hi developing niui l ; il l iodaJ sys/,e, ii is, and provides M M I ) ( ] G , a. gl'a.ii i l l ia.ti(',a.] [i'&lll(eW()i:k for lll/i]i,i-illOd;i.l hlpul, ill tel:prel~a.tion...

Let F0 = 0, F1 = 1, and Fn = Fn−1 + Fn−2 for n ≥ 2 denote the sequence F of Fibonacci numbers. For any modulus m ≥ 2 and residue b (modm), denote by vF (m, b) the number of occurrences of b as a residue in one (shortest) period of F modulo m. Moreover, let vL(m, b) be similarly defined for the Lucas sequence L satisfying L0 = 2, L1 = 1, and Ln = Ln−1 + Ln−2 for n ≥ 2. In this paper, completing ...

A permutation of a set of N elements is decomposing this set into y cycles of lengths xs, defining a partition N = x1 + · · · + xy. The length X1, the height y and the fullness λ = N/xy of the Young diagram x1 ≥ x2 ≥ · · · ≥ xy behave for the large random permutation like x ∼ an, y ∼ b lnN , λ ∼ c/ lnN . The finite 2-torus M is the product Zm × Zm, and its Fibonacci automorphism sends (u, v) to...

We give a uniform proof of the theorems of Yao and Beigel-Tarui representing ACC predicates as constant depth circuits with MODm gates and a symmetric gate. The proof is based on a relativized, generalized form of Toda’s theorem expressed in terms of closure properties of formulas under bounded universal, existential and modular counting quantifiers. This allows the main proofs to be expressed ...