| Summary: | Supply chain network design (SCND) identifies the production and distribution
resources essential to maximizing a network’s profit. Once implemented, a SCND
impacts a network’s performance for the long-term. This dissertation extends the
SCND literature both in terms of model scope and solution approach.
The SCND problem can be more realistically modeled to improve design decisions
by including: the location, capacity, and technology attributes of a resource;
the effect of the economies of scale on the cost structure; multiple products and
multiple levels of supply chain hierarchy; stochastic, dynamic, and correlated demand;
and the gradually unfolding uncertainty. The resulting multistage stochastic
mixed-integer program (MSMIP) has no known general purpose solution methodology.
Two decomposition approaches—end-of-horizon (EoH) decomposition and
nodal decomposition—are applied.
The developed EoH decomposition exploits the traditional treatment of the end-of-horizon effect. It rests on independently optimizing the SCND of every node of the
last level of the scenario-tree. Imposing these optimal configurations before optimizing
the design decisions of the remaining nodes produces a smaller and thus easier to
solve MSMIP. An optimal solution results when the discount rate is 0 percent. Otherwise,
this decomposition deduces a bound on the optimality-gap. This decomposition is neither SCND nor MSMIP specific; it pertains to any application sensitive to the
EoH-effect and to special cases of MSMIP. To demonstrate this versatility, additional
computational experiments for a two-stage mixed-integer stochastic program
(SMIP) are included.
This dissertation also presents the first application of nodal decomposition in
both SCND and MSMIP. The developed column generation heuristic optimizes the
nodal sub-problems using an iterative procedure that provides a restricted master
problem’s columns. The heuristic’s computational efficiency rests on solving
the sub-problems independently and on its novel handling of the master problem.
Conceptually, it reformulates the master problem to avoid the duality-gap. Technologically,
it provides the first application of Leontief substitution flow problems
in MSMIP and thereby shows that hypergraphs lend themselves to loosely coupled
MSMIPs. Computational results demonstrate superior performance of the heuristic
approach and also show how this heuristic still applies when the SCND problem is
modeled as a SMIP where the restricted master problem is a shortest-path problem.
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