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# Stochastic Programming Method for Procuring Components for Assemblies the Demands for which are Uncertain

IP.com Disclosure Number: IPCOM000117274D
Original Publication Date: 1996-Jan-01
Included in the Prior Art Database: 2005-Mar-31
Document File: 2 page(s) / 63K

IBM

## Related People

Donohue, C: AUTHOR [+3]

## Abstract

Disclosed is a new method for computing minimum procurement quantities for components required to achieve target customer service levels for product assemblies whose demands are probabilistically known. The technique employed here can be used in manufacturing, design of reliable systems, multi-stage portfolio optimization and other areas where service levels or chance constraints are used.

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Stochastic Programming Method for Procuring Components for Assemblies
the Demands for which are Uncertain

Disclosed is a new method for computing minimum procurement
quantities for components required to achieve target customer service
levels for product assemblies whose demands are probabilistically
known.  The technique employed here can be used in manufacturing,
design of reliable systems, multi-stage portfolio optimization and
other areas where service levels or chance constraints are used.

The disclosed method to compute minimum procurement quantities for
components is made up of the following basic steps:
Step 1: A demand scenario tree that represents possible future
demands is constructed.
Step 2: A stochastic optimization model is formulated with
procurement quantities as decision variables, cost
minimization as objective and service level as a
constraint.
Step 3: An equivalent (0,1) mixed integer stochastic
optimization model is derived from Step 2.
Step 4: The model in Step 3 is solved using a standard package
for mathematical optimization to determine the procurement
quantities.

A new method for creating a demand scenario tree (Step 1) is
disclosed.  The demand scenario tree has a root node and many
scenarios branching from the root node.  Each scenario is a distinct,
possible realization of future demands for all the future products
and periods under consideration.  Each scenario is generated by Monte
Carlo  sampling from specified probability distributions of demands
and is added to the tree if the s...