Proposed by Ian Miguel, Armagan Tarim

A basic distribution problem is described as follows. Given:

• A supply chain structure of stocking points divided into L levels, such as:
              |                   Level
V
+---+
| F |                   3
+---+
/     _
/         \
V           V
+---+       +---+
| D |       | E |             2
+---+       +---+
/     _          _
/         \           \
V           V           V
+---+       +---+       +---+
| A |       | B |       | C |       1
+---+       +---+       +---+
|           |           |
V           V           V

• A holding cost (c) per unit of inventory at each stocking point, where it is assumed that a parent has lower holding cost than any of its children.
• A procurement cost (c0) per stocking point (per order, not per unit of inventory received).
• A number of periods, T.
• A demand for each leaf (A - C) at each period.

Find an optimal ordering policy: i.e. a decision as to how much to order at each stocking point at each time period that minimises cost.

The Wagner-Whitin form of the problem assumes that the holding costs and procurement costs are constant, and that the demands are known for the entire planning horizon. Furthermore, the stocking points have no maximum capacity and the starting inventory is 0.