Operations Management S4

Capacity Definition: the most a place can make, hold, or handle in a set amount of time.
Capacity Utilization Formula: shows how much you are actually using:
$\text{Utilization} = \frac{\text{Output}}{\text{Capacity}}$
Excess Capacity ( $\text{Demand} < \text{Capacity}$ ):
- What happens: Machines and people sit around with nothing to do, and utilization is low.
- What managers can do: Cut staff, close weak plants, lower prices, make products for other companies, or try to sell more.
Insufficient Capacity ( $\text{Demand} > \text{Capacity}$ ):
- What happens: You can’t fill all orders, customers wait, and you’re running at 100% all the time.
- What managers can do: Add work shifts, hire people, buy more machines, raise prices, or speed up the process (for example, shorter setup times).
Types of System Constraints:
- Internal Constraints: Machine limits, not enough skilled workers, or rules such as “no overtime.”
- External Constraints: Late or scarce raw materials, or not enough customers.

Process Time: The duration required to process a single unit at a specific workstation. If a station takes 2 minutes per unit, it can do ½ unit per minute.
Bottleneck: The slowest station. It sets the speed limit for the whole process.
Bottleneck time: The process time of that slowest station.
System Capacity: Determined strictly by the bottleneck workstation capacity ( $\text{Capacity} = \frac{1}{\text{Bottleneck Time}}$ ).
Throughput Time: The total time required for a unit to pass through an entire process from start to finish without waiting in queue: $\text{Throughput Time} = \sum_{i=1}^{n} \text{Process Time}_i$
Bottleneck Improvement Rule: Strengthening non-bottleneck resources doesn’t help. It just piles up extra inventory. Always fix the bottleneck first..

Foundational Premise: Every system has a few weak points (constraints) that limit how much it can produce.
How to run it: Keep the bottleneck busy at all times. Other stations shouldn’t make more than the bottleneck can handle.
The Five Focusing Steps of TOC:
1. Identify the system's constraint: Locate the operational bottleneck.
2. Use it fully: Get as much output as possible from the bottleneck, with no downtime..
3. Make everything else follow it: Set the pace of all other stations to match the bottleneck.
4. Upgrade it: Spend money or resources to make the bottleneck bigger or faster.
5. Repeat: Once it’s fixed, a new bottleneck will appear. Find it and start over.

Step 1: Identify the Bottleneck:
- Calculate the total workload required on each machine ( $M_j$ ) across all products: $\sum (\text{Demand}_i \times \text{Processing Time}_{ij})$ .
- Identify the machine where required time exceeds available production capacity. The machine that needs more time than it has available is the bottleneck.
Step 2: Calculate Marginal Profit per Bottleneck Minute:
- Determine the unit contribution margin: $\text{Margin} = \text{Selling Price} - \text{Unit Cost}$ .
- Determine the priority ratio: $\text{Priority Metric} = \frac{\text{Unit Margin}}{\text{Processing Time on Bottleneck}}$
- Rank products from highest to lowest.
Step 3: Allocate Bottleneck Capacity (Determine what to make):
- Make all the demand for the top-ranked product first.
- Use the bottleneck time that’s left for the next product, and so on, until the time runs out.
Step 4: Calculate Total Profit:
- For each product, multiply the quantity you’ll make by its profit per unit, then add them all up.: $\text{Total Profit} = \sum (\text{Units Produced}_i \times \text{Margin}_i)$

Parameters: Total available weekly production time = $2400\,\text{min}$ .
- Product A: Selling Price = $60$ , Cost = $40$ , Margin = $20$ , $\text{Pt}(M_1) = 20\,\text{min}$ , $\text{Pt}(M_2) = 12\,\text{min}$ , Demand = $100\,\text{units}$ .
- Product B: Selling Price = $40$ , Cost = $10$ , Margin = $30$ , $\text{Pt}(M_1) = 10\,\text{min}$ , $\text{Pt}(M_2) = 60\,\text{min}$ , Demand = $30\,\text{units}$ .
Step 1 (Workload vs. Capacity):
- Machine 1 Time: $(100 \times 20) + (30 \times 10) = 2300\,\text{min} \le 2400\,\text{min}$
- Machine 2 Time: $(100 \times 12) + (30 \times 60) = 3000\,\text{min} > 2400\,\text{min}$
- Machine 2 ( $M_2$ ) is the constraint.
Step 2 (Priority Ratio on $M_2$ ):
- Product A: $\frac{20}{12} \approx 1.67\,\text{EUR/min}$
- Product B: $\frac{30}{60} = 0.50\,\text{EUR/min}$
- Priority order: Product A, followed by Product B.
Step 3 (Capacity Allocation):
- Produce $100\,\text{units}$ of Product A: $100 \times 12 = 1200\,\text{min}$ .
- Remaining capacity on $M_2$ : $2400 - 1200 = 1200\,\text{min}$ .
- Units of Product B produced: $\frac{1200}{60} = 20\,\text{units}$ .
Step 4 (Profit Calculation): $\text{Total Profit} = (100 \times 20) + (20 \times 30) = 2000 + 600 = 2600\,\text{EUR}$