Using mixed integer programming models to synchronously determine production levels and market prices in an integrated market for roundwood and forest biomass

Abstract

We study a problem of integrating the supply chain of roundwood with the supply chain of forest biomass. The developed optimization model is a multiperiod, multicommodity network planning problem with multiple sources of supply, i.e., harvest areas, and multiple types of destinations, i.e., sawmills, pulp mills, and heating plants. This paper presents an extension of previous work where the set of harvest areas was given and market prices for raw materials had linear relationship with corresponding volumes. In this paper, the assumption of predefined areas is removed, and we must make the selection of harvest areas. Instead of using a traditional sequential approach to first select areas and then determine the prices, we present a new synchronous approach that can jointly choose areas and define price levels for different assortments at those chosen supply points. We test the possible settings of discretized price and use sensitivity analysis to evaluate how the variation of fixed cost concerning log forwarding at each supply point affects the wood procurement decisions. A case study from Sweden is used to analyze the market prices in an integrated market. The computational results also highlight the advantage of the proposed synchronous approach over the sequential one in both solution quality and solution time.