This thesis studies the problem of production and inventory planning for an organization facing uncertainty in demand. Specifically, we examine the problem of assigning workers to tasks, seeking to maximize profits, while taking in consideration learning through experience and stochasticity in demand. As quantitative descriptions of human learning are nonlinear, we employ a reformulation technique that uses binary and continuous variables and linear constraints. Similarly, as demand is not assumed to be known with certainty, we embed this mixed integer representation of how experience translates to productivity in a stochastic workforce assignment model. We further present a matheuristic solution technique and a Markov decision process formulation with a one-step lookahead that allows for the problem to be solved in stages in time as demand information becomes available.
With an extensive computational study, we demonstrate the advantages of the matheuristic approach over an off-the-shelf solver and derive managerial insights about task assignment, workforce capacity development, and inventory management. We show that cross training increases as demand uncertainty increases, worker practice increases as inventory holding costs increase, and workers with less initial experience receive more practice than workers with higher initial experience. We further observe that the proposed lookahead MDP model outperforms similar myopic models by producing both increased profit and decreased lost sales and is especially valuable when expecting high demand variation. By recognizing individual differences in learning and modeling the improvement in productivity through experience, results show that the ability to manage workforce capacity can be an effective substitute for inventory. Additionally, we observe that optimal solutions favor the use of inventory for more valuable products and rely on higher productivity for less valuable ones. Further analysis suggests that slower learners tend to specialize more and teams with slower average learning rate tend to produce more inventory.