Value Loss in Allocation Systems with Provider Guarantees

Centralized planning systems routinely allocate tasks to workers or service providers in order to generate the maximum possible value. These allocations can also critically influence the service providers’ well-being, and thus the planning systems are often concerned with ensuring that their allocations satisfy particular desirable attributes. In some cases, such guarantees may induce a loss in the total value created or in the system’s share of that value. We provide a broad framework that allows quantifying the magnitude of such value losses due to provider guarantees. We consider a general class of guarantees that includes many considerations of practical interest arising in the design of sustainable two-sided markets, workforce welfare and compensation, sourcing and payments in supply chains, among other application domains. We derive tight bounds on the relative value loss, and show that this loss is limited for any restriction included in our general class. Our analysis shows that when many providers are present, the largest losses are driven by fairness considerations; but when few providers are present, the main loss driver is the heterogeneity in the providers’ ability to generate value. We study additional loss drivers such as the variation in the value of jobs and the supply-demand balance, and find that these can influence the loss in a non-intuitive fashion, with less variability in value and a more balanced supply-demand ratio leading to larger losses. Lastly, we demonstrate numerically using both real-world and synthetic data that the relative loss can be very small in several cases of practical interest.