A fair task and time allocation of multiple human operators using decentralized Nash bargaining solution

Abstract

Motivated by challenging problem of human operators coordination in administrative offices specially in remote-working conditions as in Corona virus time, we consider a system in which multiple parallel and independent tasks need to be performed in a specified time by multiple human operators with a reasonable level of accuracy. In this paper, we determine the optimal task and time allocation (resource allocation) policy to “fairly” allocate the tasks and the processing time duration for each task to the human operators. We study a dynamic queue with a deadline for each task which is considered as a latency penalty. The tasks are assumed to have a discrete distribution and to arrive according to a Poisson process. The performance function of the human operator is also modeled, and a trade-off is established between the expected reward obtained by processing each task and the penalty incurred due to the delay in the processing of the waiting tasks. To find the optimal allocation policies with a focus on the fairness goal, the Nash bargaining solution NBS is utilized. We develop a decentralized algorithm to obtain the NBS of the proposed bargaining model using a stochastic dual decomposition scheme. The convergence of proposed algorithm to NBS is also proven. In addition, we provide a motivating example for task and time allocation to the employees in a commercial bank system. The numerical simulations are also given to demonstrate effectiveness of the proposed decentralized solution.