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Supply Network Planning: two stages

In this module a two-stage supply network is considered.

The main trade-off considered exists between

  • inventory costs
  • overtime costs and
  • purchasing costs

In this module two factories and optionally external supplies are modeled. Factory 1 produces up 3 end products. Factory 2 produces up to 3 components, that are delivered to factory 1 and used for the production of the end products. Both factories may purchase products from an external source. This source is represented by a single supply node. The maximum planning horizon includes 24 periods. The user interface of the module looks as follows.

The products a numbered from 1 to n (end products) and (n+1) to (n+m) (components). Then material flow (BOM structure) is described via the table shown and depicted in the graph. The external source (which in fact may be several suppliers) is able to deliver end products to factory 1 and components to factory 2. Product-specific external demands may be assigned to each factory.

Transportation between factories is neglected.

In both factories maximum total inventory capacities and product-dependent minimum inventory levels may be considered.

In what follows two situations supported by this module are described.

Application 1: Two factories, no supplier

The LP model looks as follows:



k index of products
t index of periods
K set of indices of all products
K(s) set of indices of products produced in factory s
q(jk) number of units of component j required to produce of unit of end product k
a(k) personal capacity requirements per unit produced
b(k) technicall capacity requirements per unit produced
l(k) inventory holding cost
u(t) overtime cost
C(t)max available technical capacity
U(t)max maximum overtime
N(t)max available personal capacity
L(kt) inventory of product k at the end of period t
U(t) overtime (hours)
X(kt) Produktionsmengen

Application 2: Two factories, supplier

The second application adds the external supplier to the model.


  • linear objective function and constraints
  • multi-stage supply chain
  • maximum 3 end products and 3 components
  • maximum 24 periods
  • maximum two factories


- Silver/Pyke/Peterson (1998)

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