Using linear programming to analyze and optimize stochastic flow lines

Setting Inventory Levels of CONWIP Flow Lines via Linear Programming

“…DES, on the other hand, is extremely flexible, but often requires a substantial computational effort to evaluate a single configuration precisely. Neither method can be easily combined with the powerful optimization methodology of linear programming, see Helber, Schimmelpfeng, Stolletz, and Lagershausen (2011). Our objective in this paper is therefore to close this gap for the particular case of CONWIP flow lines.…”

“…Our objective in this paper is therefore to close this gap for the particular case of CONWIP flow lines. The basic idea of our approach originally introduced in Helber, Schimmelpfeng, Stolletz, and Lagershausen (2011) is to approximate the stochastic behavior of a discrete-material flow line operating in continuous time within a large discrete-time linear program (LP). An attractive feature of this approach is the possibility to combine simulation and optimization within a single linear optimization framework.…”

“…In this simulation run we assume that the work station operates in isolation so that it can neither be blocked nor starved. The realizations of the stochastic processing times are transferred via sampling to realizations of maximum production capacities c kt for each work station k and period t. If one considers a sequence of simulated processing times or durations d kw to process an ordered set of workpieces w at a work station k, one just has to count the number of finished workpieces within period t. An example is shown in Figure 2, see Helber, Schimmelpfeng, Stolletz, and Lagershausen (2011). In the upper part of Figure 2, three discrete-time periods 1 to 3 are depicted.…”

“…That means that a substantial number of periods is required within the linear program, each with a specific sampled production capacity c kt . For a detailed discussion of these aspects see Helber, Schimmelpfeng, Stolletz, and Lagershausen (2011).…”

“…To explore the accuracy of that approach for flow lines with limited buffer capacity (but without CONWIP control), Helber, Schimmelpfeng, Stolletz, and Lagershausen (2011) analyzed a large and systematically created set of flow lines both via DES and the LP approach. That earlier paper also presents a detailed discussion of the errors induced by simulating a flow line that operates in continuous time within a discrete-time linear program, see Helber, Schimmelpfeng, Stolletz, and Lagershausen (2011).…”