# Constraint set with max function

**URL:** <https://discourse.julialang.org/t/constraint-set-with-max-function/91997>\
**Category:** Optimization (Mathematical)\
**Tags:** jump\
**Created:** [December 22, 2022, 11:29am UTC](https://discourse.julialang.org/t/constraint-set-with-max-function/91997 "2022-12-22T11:29:47Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![baprata](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/baprata/32/204269_2.png) [@baprata](https://discourse.julialang.org/u/baprata)\
**Post date:** [December 22, 2022, 11:29am UTC](https://discourse.julialang.org/t/constraint-set-with-max-function/91997/1 "2022-12-22T11:29:47Z")

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Concerning the constraint set  
 ![Screenshot from 2022-12-22 08-19-35](https://global.discourse-cdn.com/julialang/original/3X/c/d/cdc8c493782f89c2357b8794903722b25a4c2347.png)

I am having problem with the last term of the constraint **(?)**:  
@constraint(model, [m in 1:machines, j in 1:jobs], PT[m,j] == SET[m] \* Z[m,j] + VT[m]\*(sum(v[i] \* X[m,j,i] for i in 1:parts) + HT[m] \* **(?)**))

How can I determine  
 ![Screenshot from 2022-12-22 08-26-43](https://global.discourse-cdn.com/julialang/original/3X/7/e/7ec30569db099df7ed765740480ccd978d94dc46.png)  
Note: X and Z are a binary decision variables; PT is a continuous decision variable; SET, VT, and HT are parameters (input data).

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<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [December 22, 2022, 4:50pm UTC](https://discourse.julialang.org/t/constraint-set-with-max-function/91997/2 "2022-12-22T16:50:17Z")

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One reformulation is [Tips and tricks · JuMP](https://jump.dev/JuMP.jl/dev/tutorials/linear/tips_and_tricks/#Max)

```julia
@variable(model, t[1:parts])
@constraint(model, [i=1:parts], t >= h[i] * X[m,j,i])

```

but this will only work if `t` wants to minimize. That is, you might get a case where t \> \max\limits\_{i \in I} \left\{h\_i \cdot X\_{mji}\right\}.

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<div class="post-metadata">

**Author:** ![baprata](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/baprata/32/204269_2.png) [@baprata](https://discourse.julialang.org/u/baprata)\
**Post date:** [December 23, 2022, 9:59am UTC](https://discourse.julialang.org/t/constraint-set-with-max-function/91997/3 "2022-12-23T09:59:13Z")

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Dear Oscar, thank you very much!  
Bruno