# Writing a simple production scheduling (optimal control) problem in JuMP
**URL:** https://discourse.julialang.org/t/writing-a-simple-production-scheduling-optimal-control-problem-in-jump/17748
**Category:** Optimization (Mathematical)
**Created:** [November 19, 2018, 7:40pm UTC](https://discourse.julialang.org/t/writing-a-simple-production-scheduling-optimal-control-problem-in-jump/17748 "2018-11-19T19:40:44Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@rotsoc](https://discourse.julialang.org/u/rotsoc)
#### Post date: [November 19, 2018, 7:40pm UTC](https://discourse.julialang.org/t/writing-a-simple-production-scheduling-optimal-control-problem-in-jump/17748/1 "2018-11-19T19:40:44Z")
Hi! I am working through the introductory exercises of “Linear Programming & Network Flows” by Bazaraa et.al by writing and solving them as JuMP programs. Actually, my question is about an example from the Introduction.
The problem is basically this:
```julia
# A company wishes to determine the production rate over the planning
# horizon of the next T weeks such that the known demand is satisfied
# and the total production and inventory cost is minimized.
```
and the mathematical formulation is:
which we can discretize as:
and this is the linear program I am trying to write.
To be honest, I haven’t tried a lot to do this, but I got this far:
```julia
using JuMP
using Clp
m=Model(with_optimizer(Clp.Optimizer))
T = 4 # 4 weeks horizon
@expression(m, g[t=0:T], -t+5)
@variable(m, 0 <= x[0:T] <= 0.8)
@variable(m, 0 <= y[0:T] <= 0.9, start=0.0)
@objective(m, Min, 2*sum(x) + 3*sum(y))
@constraint(m, [t in 0:(T-1)], y[t+1] == y[t] + (x[t+1] - g[t+1]))
JuMP.optimize!(m)
println("Objective value: ", JuMP.objective_value(m))
```
where I didn’t really discretize time (or discretized it in 1-year intervals…) but I still got an error:
```julia
ERROR: LoadError: KeyError: key MathOptInterface.VariableIndex(1) not found
```
Is this something that can be easily corrected? Am I missing something essential about JuMP? This is the first time I am using it.
---
### Author:  [@miles.lubin](https://discourse.julialang.org/u/miles.lubin)
#### Post date: [November 19, 2018, 9:34pm UTC](https://discourse.julialang.org/t/writing-a-simple-production-scheduling-optimal-control-problem-in-jump/17748/2 "2018-11-19T21:34:18Z")
> [@rotsoc](#):
>
> Am I missing something essential about JuMP? This is the first time I am using it.
Welcome to JuMP 🙂
It looks like you’re using `0.19-alpha` which is not recommended if you’re a first-time JuMP user. Please use the latest release (0.18.4) instead. This is the version you’ll get by default from `] add JuMP`. The error you’re seeing is a know issue with the alpha release.
---
### Author:  [@rotsoc](https://discourse.julialang.org/u/rotsoc)
#### Post date: [November 20, 2018, 12:32pm UTC](https://discourse.julialang.org/t/writing-a-simple-production-scheduling-optimal-control-problem-in-jump/17748/3 "2018-11-20T12:32:34Z")
> [@miles.lubin](#):
>
> Welcome to JuMP 🙂
Thank you 🙂
I downgraded to v.0.18.4 but it seems that the examples I’ve seen in the documentation use 0.19 syntax…
I guess I’m asking if someone could point me to some examples that I could use… thanks!
For instance when I write
```julia
using JuMP
using Clp
solver = Clp.Optimizer
m=Model(with_optimizer(solver))
```
I get `ERROR: LoadError: UndefVarError: with_optimizer not defined` error.
---
### Author:  [@miles.lubin](https://discourse.julialang.org/u/miles.lubin)
#### Post date: [November 20, 2018, 1:53pm UTC](https://discourse.julialang.org/t/writing-a-simple-production-scheduling-optimal-control-problem-in-jump/17748/4 "2018-11-20T13:53:36Z")
The JuMP README has links to the [documentation](http://www.juliaopt.org/JuMP.jl/0.18/) and [examples](https://github.com/JuliaOpt/JuMP.jl/tree/release-0.18/examples) for the latest release.
---
### Author:  [@rotsoc](https://discourse.julialang.org/u/rotsoc)
#### Post date: [November 20, 2018, 2:31pm UTC](https://discourse.julialang.org/t/writing-a-simple-production-scheduling-optimal-control-problem-in-jump/17748/5 "2018-11-20T14:31:18Z")
Ok! Thank you