Optimization of Transmission Systems for Chain-Type Markets
We consider a market for a homogeneous good with a chain-type transmission network. Every node corresponds to a local market with a perfect competition characterized by supply and demand functions. The initial transmission capacity, the cost of the capacity expansion and the unit transmission cost are given for every transmission line. The cost of the capacity expansion includes fixed and variable components. We examine the social welfare optimization problem for such a market. The welfare corresponds to the difference between the total consumption utility and the costs of production, transportation, and expansion of the transmission lines. Due to fixed costs of lines expansion, the problem is in general NP-hard with respect to the number of the nodes. We generalize the concept of supermodularity of the welfare function on the set of expanded lines and propose an algorithm for the solution of the problem. Results of computer simulation confirm the statistical efficiency of the algorithm.
KeywordsMixed optimization problem Social welfare Transmission network
- 6.Magnus, Y.R., Katyshev, P.K., Peresetsky, A.A.: Econometrics. Beginner’s Course. Tutorial. Delo, Moscow (2004)Google Scholar