We suggest a programming realization of an algorithm for a verification of a given set of algebraic relations in the form of a supercommutator multiplication table for the Verma module, which is constructed according to a generalized Cartan procedure for a quadratic superalgebra and whose elements are realized as a formal power series with respect to noncommuting elements. To this end, we propo...

The business environment is full of uncertainty. Allocating the wealth among various asset classes may lower the risk of overall portfolio and increase the potential for more benefit over the long term. In this paper, we propose a mixed singlestage R&D projects and multi-stage securities portfolio selection model. Specifically, we present a bi-objective mixed-integer stochastic programming mode...

an interactive heuristic approach can offer a practical solution to the problem of linear integer programming (lip) by combining an optimization technique with the decision maker’s (dm) judgment and technical supervision. this is made possible using the concept of bicriterion linear programming (blp) problem in an integer environment. this model proposes two bicriterion linear programs for iden...

This paper investigates the Stackelberg equilibrium for pricing and ordering decisions in a multi-channel supply chain. We study a situation where a manufacturer is going to open a direct online channel in addition to n existing traditional retail channels. It is assumed that the manufacturer is the leader and the retailers are the followers. The situation has a hierarchical nature and...

This paper presents a multi-level linear programming problem with random rough coefficients in objective functions. At the first phase of the solution approach and to avoid the complexity of this problem, we begin by converting the rough nature of this problem into equivalent crisp problem. At the second phase, we use the concept of tolerance membership function at each level to solve a Tchebch...

Nowadays, coordination between members in a supply chain has become very important and beneficial to channel members. Through cooperative advertising, manufacturers and retailers can jointly participate in promotional programs. This action not only reduces the cost of advertising, but also is important to create a link with local retailers in order to increase immediate sales at the retail leve...

H. A. Khalifa Department of Operations Research, Institute of Statistical Studies and Research, Cairo University, Cairo, Egypt. Abstract Linear programming (LP) has been widely applied to solving real world problems. The conventional LP model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This paper de...

abstract it is the purpose of this article to introduce a linear approximation technique for solving a fractional chance constrained programming (cc) problem. for this purpose, a fuzzy goal programming model of the equivalent deterministic form of the fractional chance constrained programming is provided and then the process of defuzzification and linearization of the problem is started. a samp...

This paper proposes an improved approach to our previous work [11]. [11] uses Stackelberg game to model the interactions between electricity retailer and its customers and genetic algorithms are used to obtain the Stackelberg Equilibrium (SE). In this paper, we propose a bi-level programming model by considering benefits of the electricity retailer (utility company) and its customer. In the upp...

Pricing is one of the major aspects of decision making in supply chain. In the previous works mostly a centralized environment is considered indicating the retailers cannot independently apply their decisions on the pricing strategy. Although in a two-echelon decentralized environment it may be possible that supply chain contributors have encountered with different market power situations which...