This study is part of a series of research projects on a distribution system we developed to deal with cases in a state-owned company. It concerns the design of the Public Service Obligation State-owned Company (PSO-SOC) distribution system. The intrinsic features of PSO-SOC are distributing strategic commodities and having subsidies within the cost function. Hence their distribution flow has to be secured under consideration of moving the commodities within road networks that have traffic flow dependency. This paper focuses on the solution of the proposed model which represents traffic flow dependency within a freight distribution network. The mathematical formulation takes the form of a Minimum Cost Multicommodity Flow (MCMF) problem. Traffic flow dependency is incorporated into the model by introducing a coefficient of speed, which is derived from the traffic assignment of ordinary traffic associated with the transportation of the type of freight under consideration The solution of the proposed model is formulated by Network Representation (NR), in which all of the components of the mathematical model are represented in the form of dummy links and nodes added to the original (physical) network. It is to be noted then, that the traffic flow on each road or link is represented by a link performance function (LPF), depicting traffic flow dependent travel time and consequent cost. The MCMF problem of NR is further solved by a Primal-Dual Algorithm. Finally, an illustrative example is exercised to show how the proposed step-wise solution works.
- Minimum Cost Multicommodity Flow problem
- Product differentiation
- Traffic flow dependency