We reveal in this paper that the environmental noise will not only suppress a potential population explosion in the stochastic delay Lotka–Volterra model but will also make the solutions to be stochastically ultimately bounded. To reveal these interesting facts, we stochastically perturb the delay Lotka–Volterra model ẋ(t) = diag(x1(t), . . . , xn(t))[b + Ax(t − τ)] into the Itô form dx(t)= dia...

Optimal pricing and marketing planning plays an essential role in production decisions on deteriorating items. This paper presents a mathematical model for a three-level supply chain, which includes one producer, one distributor and one retailer. The proposed study considers the production of a deteriorating item where demand is influenced by price, marketing expenditure, quality of product and...

The stability of discrete universal integrals based on copulas is discussed and examined, both with respect to the norms L1 (Lipschitz stability) and L∞ (Chebyshev stability). Each of these integrals is shown to be 1-Lipschitz. Exactly the discrete universal integrals based on a copula which is stochastically increasing in its first coordinate turn out to be 1-Chebyshev. A new characterization ...

in this paper a single server queuing production system is considered which is subject to gradual deterioration. the system is discussed under two different deteriorating conditions. a planning horizon is considered and server which is a d/m/1 queuing system is gradually deteriorates through time periods. a maintenance policy is taken into account whereby the server is restored to its initial c...