Operations Management: Key Concepts & Case Studies
Little’s Law
Little’s Law states that the average inventory in a system is equal to the product of the average flow rate and the average flow time.
Inventory
Inventory refers to the number of flow units currently within a process, including those in buffers.
Capacity of a Resource
Resource capacity is the rate at which a resource can process flow units.
Capacity of a Single Resource
The capacity of a single resource is calculated as the reciprocal of its activity time (1 / activity time).
Capacity of Resources in Parallel
For resources operating in parallel, the capacity is determined by dividing the number of resources by the activity time (# of resources in parallel / activity time).
Process Capacity (Bottleneck)
The process capacity, also known as the bottleneck, is the minimum capacity among all resources. In cases of a tie, there can be multiple bottlenecks.
Flow Rate
Flow rate is the rate at which a process delivers output at a specific point in time, measured in flow units per unit of time.
- Flow units can represent physical goods or people.
- Flow rate depends on both demand rate and process capacity.
- Flow rate = minimum of demand and process capacity.
Demand-Constrained vs. Supply-Constrained Processes
- Demand-constrained process: Demand is less than process capacity.
- Supply-constrained process: Demand exceeds process capacity.
- Demand and supply-constrained process: Demand equals process capacity.
Flow Time
Flow time is the time it takes for a flow unit to complete a process, including time spent waiting in buffers.
Rush Order Flow Time
Rush order flow time is the time it takes for a rush order to go through the process, assuming it is processed as quickly as possible. This typically involves adding the processing times of each activity, considering only the longest set of simultaneous activities.
Cycle Time
Cycle time is the average time between the production of two consecutive flow units.
- Cycle time = 1 / flow rate
- Time to process N units = Rush Order Flow Time + (N-1) * Cycle Time
Utilization
Utilization measures the percentage of time a resource is actively processing flow units.
Process Utilization
Process utilization = Flow Rate / Process Capacity
Utilization of Resource(s)
Utilization of (set of) resource(s) = Flow rate / capacity of (set of) resources
Labor Utilization
Labor utilization = Labor Content / (Cycle Time) * Number of employees
Labor Content
Labor content is the total amount of work required to serve one flow unit, typically calculated by summing the product of laborers per activity and the number of activities.
Batching
A batch process involves a fixed time per batch (F) and a variable time per unit (v). For a batch size of Q:
- Total time required = F + vQ
- Capacity (# of batches per unit time) = Q / (F + vQ)
- Time between batches = Q * Flow Rate
- Average Batch Inventory = [Q * Activity Time + (Q/2 * Activity Time * Q)] / Q * Flow Rate
- Average Buffer Inventory = Q/2
- Average Inventory = Average Buffer + Batch Inventory
- % Idle Time: Time between batches – (F + vQ) / Time between batches
- Choosing a batch size to match flow: Demand = Q / (F + vQ) → Solve for Q
Cost Structure
Breakeven Volume
Breakeven volume is the point where revenue equals total costs (fixed + variable).
- Revenue per unit * number of units = Fixed cost + Variable cost per unit * number of units
Profit
- Profit = Revenue per unit * number of units – (Fixed cost + Variable cost per unit * number of units)
- % change in profit = Increase or Decrease in Profit / Old Profit
Project Management – Activity on Node and Critical Path Analysis
Network Diagram and Critical Path
A network diagram visually represents the sequence of activities in a project. The critical path is the longest path through the network, with no slack, and determines the minimum project duration.
Slack
Slack is the amount of time an activity can be delayed without affecting the project duration. Activities on the critical path have zero slack.
Critical Path Analysis (Forward and Backward Pass)
Critical path analysis involves calculating the earliest start time (EST), earliest completion time (ECT), latest start time (LST), and latest completion time (LCT) for each activity.
- Forward Pass (Top to Bottom):
- EST = Max EF of all immediate predecessors
- ECT = EST + Activity Time
- Backward Pass (Bottom to Top):
- LST = LCT – Activity Time
- LCT = Min LST of all immediate successors
- Slack (of an activity) = LCT – ECT or LST – EST
Crashing
Crashing involves shortening the project duration by expediting activities at an additional cost.
Crash Cost per Period
Crash cost per period = (Crash Cost – Normal Cost) / (Normal Time – Crash Time)
Crashing Process
Crashing is an iterative process of reducing activity durations one period at a time, aiming to minimize the project duration at the lowest cost.
Optimal Project Duration
The optimal project duration balances the cost of crashing activities with the benefits of a shorter project timeline, considering factors such as overhead costs and potential fines for exceeding deadlines.
Case Studies
Toyota Production System (TPS)
The Toyota Production System emphasizes worker empowerment, just-in-time inventory, and continuous improvement (Kaizen) to achieve high efficiency and quality.
Benihana
Benihana’s business model focuses on high volume and productivity, with a unique dining experience and a cost structure that favors high customer turnover.
Formulas
- VC = Variable cost per unit
- FC = Fixed cost
- Q = Unit volume
- P = Price
- Breakeven volume = FC / (P – VC)
- Profit = Revenue – VC – FC
- Marginal Profit = (Capacity – Throughput) * (P – VC)