It should be noted that the optimal solution to the DEP has the best expected performance with respect to the scenarios included in the DEP. While including more scenarios is obviously one way to increase the accuracy of the expected performance of the configuration, this comes at significant increase in the computational burden. The selection of the scenarios to include is also a non-trivial problem. One would like to include all the possible scenarios that represent significant trends in the economic conditions. However, most often there exist too many combinations of major trends, so that including all the corresponding scenarios would make the design problem computationally unsolvable. Rather than selecting specific scenarios, the sample average approximation (SAA) method creates scenarios through random sampling of the parameter probability distributions, Kleywegt et al. (1999).While each decision variable and each constraint in itself is simple, the total number of variables and constraints creates very large problem instances.The creation and maintenance of the model formulation, data, and model solution requires significant information technology and computational resources.Typical comprehensive strategic supply chain design models may contain thousands of the binary variables and millions of the continuous variables in tens of thousands of constraints. Santoso et al. (2003) report solving a formulation with 1.25 million continuous variables for an industrial case.Papageorgiou et al. (2001) report that 3000 binary variables are present in a small illustrative example.A schematic representation of didactic example of a single-period logistics system is given in Fig. 6.2. If there are multiple periods in the planning horizon, they would have a similar structure and typically would be displayed in different windows.
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