Solving the stochastic machine assignment problem with a probability-based objective: problem formulation, solution method and practical applications

In this research, a variation of the assignment problem is formulated. Diverging from many studies which model the assignment problem in a deterministic setting, we consider a noisy and complex manufacturing process consisting of several workstations, each of which must be assigned a machine from a set of machine types which vary randomly according to processing time. The objective is to determine the optimal assignment solution which maximises the probability that a production task is completed within a prespecified completion time interval. To solve the proposed problem, we develop an efficient simulation optimisation method which incorporates a factor screening method into a nested partitions-based framework. A series of numerical experiments are conducted to test the efficiency of the proposed algorithm in comparison to competing ones. Compared to existing algorithms, the proposed solution methodology was able to find feasible machine assignment solutions which generated substantially higher probabilities of job completion. [Received: 29 September 2022; Accepted: 16 February 2023]