Production Scheduling

Parts of this page were generated by AI.

Resources

• Script Part 7: Lot Sizing and Scheduling
• Exercise Questions 1, Exercise Questions 2

Note on this Note

I did not take lecture notes on Production Management. Below is an AI-generated summary of this chapter, and you’ll want to check out the resources above.

Sequencing and Scheduling

Job Shop Scheduling

Detailed scheduling in job shops involves determining the order of processing for various jobs on machines.

Goals of Detailed Scheduling

• Minimize:
  • Job lateness (adherence to due dates)
  • Idle times of machines
  • Throughput times of orders
  • Sequence-dependent setup times

Popular Dispatching Rules

Used to dispatch orders from queues in front of machines:

• Shortest Processing Time (SPT): Minimizes average throughput time and waiting time.
• Longest Processing Time (LPT)
• Most Work Remaining (MWR)
• Least Work Remaining (LWR)
• Nearest Due Date (NDD): Often used for prioritizing urgent orders.
• First-Come-First-Served (FCFS): Serves as a benchmark.

Scheduling Dilemma

Scheduling often involves a trade-off between conflicting objectives, such as minimizing idle times (capacity utilization) vs. minimizing job lateness (due date adherence).

Flow Shop Scheduling

Commonly applies to mixed-model assembly lines, where variants of a product type are manufactured on the same production line.

• No setup times.
• Similar task sequences with varying task times.
• Cycle time is usually considered as a flexible target.
• Key planning problem: Determination of the product sequence considering the flexible cycle time.

Bottleneck Station Scheduling

The goal is the smoothing of capacity load at the bottleneck station to avoid:

• Starvation: Processing at the predecessor station takes too long based on the chosen product sequence, causing idle times.
• Blocking: Processing at the successor station takes too long based on the chosen product sequence, causing buffer storages to overflow and blocking the station.

Simplifying assumption: Only one single bottleneck station is considered for which the product sequence is systematically determined. The bottleneck station shows the heaviest average workload based on the given production volume of the product variants.

Priority Rule for Product Sequencing

Determines the product sequence by minimizing the deviation between the actual and projected workload at the bottleneck station.

$\min {\delta }_j=|b_j+B_{p-1}-p\cdot c|$

Where:

• $b_j$: Per unit production time of product $j$ in the bottleneck station.
• $p\cdot c$: Projected average workload at the bottleneck station after $p$ product units ($c$ = cycle time; $p$ = counter for products in the sequence).
• $B_{p-1}$: Workload of the bottleneck station caused by the preceding $p-1$ product units.

$B_{p-1}={\sum }_{k=1}^{p-1}{b}_k\text{with}{B}_0=0$

Cellular Manufacturing

Production Scheduling for Cellular Manufacturing was not covered in the lecture.

Cellular manufacturing frequently involves key production centers, such as automated machine tools.

• Manufacture of various products on the same equipment.
• Changeover times between products often depend on the production sequence (e.g., setup tasks, exchange of tools in the magazine of the machine).
• Key planning problem: Determination of the product sequence with the objective of minimizing total (sequence-dependent) setup effort.

Travelling Salesman Problem (TSP)

The problem of finding the sequence that minimizes setup times can be modeled as a Travelling Salesman Problem (TSP).

• Analogy: A salesperson starts from a home base, visits customers at different locations, and returns. The distances between locations are given. The goal is to determine the shortest tour which includes each customer just once.
• Simple solution technique: Nearest neighbour heuristic. At each step, choose the product that has the minimum changeover time from the current product.