MANUFACTURING PLANNING AND SHOP FLOOR CONGESTION ANALYSIS IN MULTI-PRODUCT NETWORKS USING A DATA-DRIVEN APPROACH

Abstract

The clearing function (CF) models the non-linear relationship between work-in-process (WIP) and throughput and has been proposed for production planning in environments with queuing (congestion) effects. However, incorporating the CF concept in multi-product multi-stage manufacturing networks is still a challenging problem. One approach proposed in literature is to model the CF at the bottleneck machines only. However, since the bottleneck may shift as the product mix changes and the queuing network effect is difficult to capture at the bottleneck, this approach has its limitations. The dominant method in the literature to modelling congestion in multi-product multi-stage networks is the allocated clearing function (ACF) approach. In this approach, the CF is developed at the resource level using a numerical estimation method such as discrete-event simulation. Based on these estimates, the CF is fit using piecewise linear equations. The ACF linear program (LP) then partitions the CF for resource product combinations. This thesis proposes an alternative methodology to ACF, where the release and WIP levels in each period are discrete (FPR). The CF is estimated at discrete load combinations using simulation, mean-value analysis (MVA), or queuing network analysis. A mixed-integer programming (MIP) formulation is developed to determine optimal material release. The approach is data-driven and does not require the use of a curve-fitting function. The CF estimates at the discrete lattice points in this approach are network based, as opposed to resource based as in ACF. The MIP behaviour is illustrated using the MVA approximation for a well-known multi-product re-entrant semiconductor manufacturing case in the literature. The FPR-MIP formulation is extended to allow release quantities between the lattice points using a cubic approximation technique (CA). This approach allows the MIP to potentially obtain better solutions in continuous space and can be seen as a generalization of piecewise linearization for the single product case. A detailed comparison between FPR and CA is discussed using an example case. Finally, FPR and CA are compared and contrasted with the ACF approach. In summary, this thesis presents an alternative approach to the state-of-art in the modelling of congestion in manufacturing networks.