in this study, a bi-objective model for integrated planning of production-distribution in a multi-level supply chain network with multiple product types and multi time periods is presented. the supply chain network including manufacturers, distribution centers, retailers and final customers is proposed. the proposed model minimizes the total supply chain costs and transforming time of products ...

this paper will investigate the optimum portfolio for an investor, taking into account 5 criteria. the mean variance model of portfolio optimization that was introduced by markowitz includes two objective functions; these two criteria, risk and return do not encompass all of the information about investment; information like annual dividends, s&p star ranking and return in later years which...

Motivated by a real world application, we study the multiple knapsack problem with assignment restrictions (MKAR): We are given a set of items N = f1; : : : ; ng and a set of knapsacks M = f1; : : : ;mg. Each item j 2 N has a positive real weight wj and each knapsack i 2 M has a positive real capacity ci associated with it. In addition, for each item j 2 N a set Aj M of knapsacks that can hold ...

Duality theory is important in finding solutions to optimization problems. For example, linear programming problems, the primal and dual problem pairs are closely related, i.e., if optimal solution of one known, then for other can be obtained easily. In order an solved through dual, first step formulate its analyze characteristics. this paper, we construct model uncertain multi-objective as wel...

A three stage production system is considered in this paper. There are two stages to fabricate and ready the parts and an assembly stage to assembly the parts and complete the products in this system. Suppose that a number of products of different kinds are ordered. Each product is assembled with a set of several parts. At first the parts are produced in the first stage with parallel machines a...

Knapsack public-key encryption schemes are based on the knapsack problem, which is NP-complete. Merkle-Hellman knapsack encryption scheme was the first concrete realization of a public-key encryption scheme. As its secure basis is superincreasing knapsack problem, it has been demonstrated to be insecure. Many variations have subsequently been proposed, whose knapsack vector density are less tha...

Since no competitive online algorithms exist for general knapsack problems, we consider online variants of knapsack problems with two assumptions: (i) the weight of each item is very small compared to the knapsack capacity; (ii) the value-to-weight ratio of each item is lower and upper bounded by two positive constants L and U . We design a deterministic threshold-based algorithm for the online...