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Master-Slave Constraints

Using zero/one variables, we can control the range of values that other variables take. Suppose that $x_{AB}$ (the amount shipped from $A$ to $B$) is either 0 (we don't ship from $A$ to $B$) or between 20 and 100 (we ship from $A$ to $B$ with limits specified by the transportation company). We introduce a new binary (0-1) variable $z_{AB}$ that is 1 if there is a shipment from $A$ to $B$ and 0 otherwise. Then we can use master-slave constraints to let $z_{AB}$ control $x_{AB}$

\begin{align*} x_{AB} &\geq 20 z_{AB} \\ x_{AB} &\leq 100 z_{AB} \end{align*}

Master-Slave Constraint Topics

To see master-slave constraints in action, check out some case studies that use them:

Results from OpsRes web retrieved at 16:51 (GMT)

CokeSupplyChain
r20 - 2018-11-23 - 01:32  TWikiAdminUser

\usepackage{amsmath} Case Study: Submitted: Operations Research Topics: Application Areas: Contents Problem Description Problem Description Return...
CosmicComputersProblem
r26 - 2018-11-23 - 01:32  TWikiAdminUser

\usepackage{amsmath} Case Study: Submitted: Operations Research Topics: Application Areas: Contents Problem Description Problem Description Return...
Number of topics: 2

-- TWikiAdminGroup - 22 Apr 2008

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Topic revision: r6 - 2018-11-23 - TWikiAdminUser
 
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