Efficiency measurement with products and partially desirable co-products

Many operational processes that set out to create a specific set of products will often involve the creation of a set of associated co-products. The problem of interest is how to evaluate the efficiencies of a set of comparable such processes in the presence of both products and co-products. In particular, there has been an increasing interest in co-products that can be considered as playing a dual role as either outputs from or inputs to the process involved. Efficiency measurement in certain situations where both products and co-products are present can be addressed using data envelopment analysis (DEA). For example, reclaimed asphalt coming from the resurfacing of highways in various districts offers an opportunity to perform maintenance at a lower cost, when that reclaimed material serves as an input together with new or virgin materials. At the same time, there is an undesirable environmental impact when reclaimed asphalt (not reused) serves as an output. In the current paper, we develop a DEA-based methodology to evaluate the efficiency of maintenance activities in the presence of both products and co-products. The problem concerns how to examine co-products that can have positive value, up to a certain point, but beyond this point there are disposal/environmental costs that must be considered. We use our developed model to examine the efficiency of resurfacing operations in a set of 18 districts in a Canadian province.