The Batch Flow problem generally is one of scheduling. For any given job there is a sequence of tasks that must be performed in a certain order. Each task requires a specific machine to complete its task. The crux of the problem is that the same machine is often required by different tasks; jobs will require many of the same machines and thus each job must be prioritzed. The goal is to minimize the makespan - the length of time all the jobs, processed one after another, will take. In the realm of a bakery, batch flow shop methods are an applicable model for job scheduling. Some machines will run in parallel, others will not.
Building on the Model Stub, I worked at a bakery this past summer. It was a great experience, but it struck me as inefficient in how batches of cookies were scheduled. What model could aid in scheduling batches of cookies? Different scheduling problems have unique solution approaches. Fixed infrastructure implies a flow production type, but flexible employees imlply batch production.
Several simplifying assumptions have been made. These assumptions not only change what the model truly represents, but also may make the model more generally applicable than it was previously.
- No intermediate storage
- Varying batch sizes (Linearly scaling, 1x, 2x or 3x)
- Job processing will flow through a factory in workstation order
- Not all machines will be utilized by a given job
- All jobs end on the same workstation
- All machines in a given workstation are the same type
- No intermediate storage
The mathematical framework necessary to create a Model Simulation: relate each of the assumptions to a part of the math
- Though a job doesn't execute out of order, it may leave some wokrstations untouched. Cookie 1 is a good example.
- Yeilds are computed based on experience at a bakery
- Yeilds are for a 1x batch size Future work to come in this section
- M1: Mixer - Raw dough (D)
- M2: Balling - Condensed or Ready-to-bake Trays (Tc or Tr) 35 or 12 cookies
- M3: Decondensing - Ready-to-bake Trays (Tr) 12 cookies
- M4: Oven - Baked trays of cookies (Tb) 12 cookies
| Machines | Cookie 1 | Cookie 2 | Cookie 3 |
|---|---|---|---|
| Mixer (M1) | 20 min | 20 min | 20 min |
| Balling (M2) | 6 min | 17 min | 17 min |
| Decondensing (M3) | - | 5 min | 5 min |
| Oven (M4) | 14 min | 14 min | 16 min |
| Machine | Cookie 1 | Cookie 2 | Cookie 3 |
|---|---|---|---|
| Mixer (M1) | 320 oz D | 320 oz D | 320 oz D |
| Balling (M2) | 1 Tready | 1 Tcondensed | 1 Tcondensed |
| Decondensing (M3) | - | 1 Tready | 1 Tready |
| Oven (M4) | 8 Tbaked | 8 Tbaked | 8 Tbaked |
Model approximation for batch flow shop scheduling with fixed batch sizes
Future work
Future work