Cycle time: Time a job spends in a process (time).
Departure time: Service time + max (arrival time, Departure time of prev. cust)
Cycle time = Service time – Arrival Time.
Inventory: Jobs that accumulate in a process (jobs)
Throughput: Rate at which jobs “come and go” through the process (jobs/time)
Capacity: Maximum achievable average throughput (jobs/time)
Utilization = Throughput/Capacity
Average Throughput (Lambda) = No. of Jobs/Time
Average CT = Sum (CTi/N)
Average Inv = Area/T
Little’s law: Inv = Throughput * CT. Relates to averages of three metrics. Holds for a broad range of processes. Holds in transient and steady states.
Inventory turns = Lamda/INV = 1/CT
Inv (in) – Inv (out) = Change in Inv.
Bottleneck: A resource or resource pool that limits the minimum average sustainable throughput. It determines capacity. Activity with the highest cycle time is the bottleneck. Capacity when there is a bottleneck is 1/CT of bottleneck.
In an OR System CT = Sum of CT of each activity and capacity = sum of individual capacity.
In an AND system CT = Max (CT of each activity) and capacity = Min (flow rate/time at each activity)
If the processing time of a non-bottleneck resource has decreased, the cycle time will decrease.
Linear Program: Continuous Decision variables. Linear Objective function. Linear constraints and no uncertainty.
Shadow Price: Marginal value of a resource at the current level of production. (value of a resource). SP>0 only when the constraint is tight. Bottleneck: When the shadow price is >0.
Problem: Consider max x, x+y <=1 and x, y>=0
Optimal Solution for the linear program is x =1 and y =0. The Objective is 1
How does the solution change if we add the constraint x+y <=2; Doesn’t change because the new constraint is redundant. If x+y <=1 then definitely x+y <=2
How does the solution change if we drop the constraint x, y >=0. If we allow negative values of x then we can allow arbitrarily values for y = 1-x. So, the solution is unbounded (the solution is infinity)
Key Take Away from CRU
Three Key Operational measures: Flow time, inventory ad throughput
The business flow paradigm links operational measures to financial flows
CRU’s inter functional macro process view of the organization incorporates both the revenue and cost side of the business
Highlights key operational measures of the business (profitability, no. of units on rent, depreciation cost, throughput cost)
Use the business flow paradigm to identify, value and prioritize improvement areas. For performance measures: need more than only utilization. For targeted improvement of customer segments + internal ops.
On the analysis side: distinguish throughput rate from flow time. Costs (throughput driven). Revenues (flow time driven)
Analyze different routes and product segments: Pricing.
IBM Case: Workers were able to be multi-trained. Batching was eliminated. Effects of processing time variances and imbalances mitigated. Eliminate “Blocking” and “Starving” workers always working when there is a queue. Able to segment the demand into “hard” and ‘Easy’ Cases. Broke assumptions that kept their process slow – division of labor according to function not always good and focus on performing well on the average case (with generalists) rather than the worst case (with specialists)
Critical path: Whereas capacity is defined by a bottleneck, cycle time is determined by a critical path. It is the longest path through a process which all jobs must pass including the wait time.
In a split system (AND) the stage with the longest processing time (excluding waiting time) is the bottleneck and dictates capacity
Causes of Waiting
Demand rate > Service Rate. Change in inventory is negative (INV In > Inv Out)
Deal with the uncertainty, variability – Arrival variability, Order Variability (batches) and Service time variability.
Utilization = Demand/Capacity
When there is a queue