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Description
This example emphasizes on a multi-period inventory control problem with uncertain demand.
The volume of production is decided before the actual demand is known at the beginning of each period. The objective of this example is to minimize overall costs to obtain maximum profit. This type of problem can be categorized as a multi-stage stochastic optimization model.
The scenario of this inventory control example takes place within a beer company that serves 2 different kinds of beer (i.e. light and regular). The company will need to decide on how much beer to bottle during a particular week for each type. There is a limit on the overall bottling capacity. The cost to bottle and store each kind of beer is proportional to the amount of beer that is either bottled or stored. Moreover, there is a minimum amount of storage required at the end of the last period.
The figure below will show the various events and probabilities needed to solve this example. A node in the tree refers to a state of the system. The label associated with each arc is the event description. The fraction associated with each arc is the corresponding event probability.
Keywords
Multi-Stage, Control-State Variables, Mathematical Derivation
Industries
Model Types
Linear Programming, Stochastic Programming
References
Chapter 17 - An Inventory Control Problem in the Optimization Modeling Guide
Download AIMMS Example
You can download an AIMMS example dealing with this problem via the link below, and run it after installing the AIMMS software. If you don't have an AIMMS license yet, you can download a free license of AIMMS.
ftp://ftp.aimms.com/pub/Download/Examples/Inventory Control.aimmspack
Please make sure to save this file including the .aimmspack extension so that it can be opened by AIMMS.
This example application is a simplification of reality. Please do not hesitate to contact us to discuss how AIMMS enables you to build a complete optimization application that captures the full complexity of your problem.
Screenshot AIMMS Example
