Mathematics for Management Science Notes 05

Transshipment problems:
Transshipment problems have the same basic goals as transportation problems (in
particular, there is a need to ship goods from origins to destinations at minimum cost),
but
• Goods may travel from a source through an intermediate location (known as a
transshipment node) to a destination,
• Some destinations may also serve as transshipment points to other destinations,
• etcetera.
The locations (sources, destinations, and transshipment points) are visualized as nodes in
a network, and are numbered consecutively. If nodes i and j are connected by a direct
route in the network (a link), then the decision variable x ij is used to represent the number
of items shipped from node i to node j. For example, if a company has
1. two plants (sources),
2. a warehouse (serving as a pure transshipment point), and
3. two retail outlets (destinations),
a transportation network could look like the following:
1: Plant 1 4: Outlet 1
2: Plant 2 5: Outlet 2
3: Warehouse
The links correspond to (i, j) equal to (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,5).
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