Intermediate Process Analysis Capacity and Inventory Buildup Why is capacity important? What determines capacity and thruput? Inventory buildup to match capacity to demand & supply Effects of change-over times and batch sizes

The Big Picture m In the Beer Game, as in real life, there is lots of variability in demand and supply. m Compensating for this through capacity alone is very expensive. m Inventory provides a cheaper alternative, but we need to understand how to use it efficiently.

Why is Capacity Mgt. Critical to Operational Success? Capacitys Big Trade-off (under variable demand) Too little capacity means delays in supplying customers and ultimately lost market share. Too much capacity leads to poor utilization of resources and operational inefficiency (ie throughput/capacity ratio is low). AVG DEMAND PEAK DEMAND DEMAND TIME UNITS/MONTH

Factors Affecting Capacity and Thruput? Recall: Thruput = Capacity * Utilization * Yield Utilization is, in part, a function of uptime Design aspects (long-term, capacity aspects) Product design Process design Incentives Control aspects (short-term, thruput issues) Product Mix Lot sizing decisions Sequencing decisions Yield Maintenance

How can inventory help us? Recall the Iron Law of Inefficiency Complexity * Variability = Inefficiency Variability - Supply of raw materials and demand for finished goods often vary with time, making the capacity trade-off very difficult to manage. Inventory Raw Material Inventory allows us to smooth the supply of Raw Materials to Capacity, allowing a smaller capacity to achieve the same throughput. Finished Goods Inventory allows us to use a smoother throughput to satisfy varying demand, again allowing us to use a smaller capacity.

How can inventory help us? Consider the following diagram Inventory allows us to store up capacity for use at a later time. This allows us to reduce our capacity from peak down towards average demand. but only at a price! AVG DEMAND PEAK DEMAND DEMAND TIME UNITS/MONTH

Inventory Calculations 1 Consider the diagram below: Case 1: No Starvation or Blockage From the beer game what happens if: Can we generalize for no blockage/starvation? Inflow = Outflow = Chg. in Inventory = Ending Inventory = Capacity = SCapacity = D

Inventory Calculations 2 Case 2: You have no inventory and demand exceeds supply, i.e. starvation. (Assume no backlogs). What happens if: Can we generalize for starvation? Inflow = Outflow = Chg. in Inventory = Ending Inventory =

Inventory Calculations 3 Case 3: You have the maximum inventory possible and supply exceeds demand, i.e. blockage. What happens below if max inventory storage = 10 cases? Can we generalize for blockage? Inflow = Outflow = Chg. in Inventory = Ending Inventory =

To summarize, the 3 cases are: 1) No blockage or starvation In = S; Out = D; I = (S-D)*(T end -T beg ) I Tend = I Tbeg + I; I avg = (I Tbeg + I Tend )/2 2) Starvation, i.e. No inventory and S<D In = S; Out = In; I = 0; I Tend = I Tbeg =0 3) Blockage i.e Max inventory and S>D (Sometimes there is no max) In = Out; Out = D; I = 0; I Tend = I Tbeg =I max Trick is to figure out when you switch from one case to another. Inventory Calculations 4 T beg TIME INVENTORY T end I svg

Process Flow Exercises: Fishing Fleet & Cannery Input rate(tons/month) Capacity (tons/month) (a) Inventory (tons) time(month) time(month)

Fishing Fleet Calculations A What 3 time periods do we have to worry about? Can be blocked or starved? Find inventory at times 0.0 : : 12.0 : Note to simplify things we use continuous time (0.1, 1.321, 3.0 months) as opposed to discrete time in our calculations (0, 1, 2, 3...).

(a) Avg. inventory = TimeMonthsAI year Process flow exercises: Fishing fleet & cannery

Avg. waiting time Total Waiting Time Total Production Avg. Inventory Avg. Outflow Rate Or Avg. Inv. Avg. Waiting Time * Avg. Outflow This last equation is known as Littles Law. Process flow exercises: Fishing fleet & cannery

Process Flow Exercises: Fishing Fleet & Cannery Supply rate(tons/month) max. inventory = 2400 (b) Inventory (tons) time(month) time(month) Capacity (tons/month)

Fishing Fleet Calculations B What 3 time periods do we have to worry about? Can we be blocked or starved? Find inventory at times 0.0 : : 12.0 :

(b) Avg. inventory = TimeMonthsAI year Process flow exercises: Fishing fleet & cannery

Avg. production = Avg. waiting time Avg. Inventory Avg. Outflow Rate Process flow exercises: Fishing fleet & cannery Limited inventories limit the ability to match demand to capacity

Take-Aways m Usually demand is piecewise constant, but in general: m When do we have to worry about this (i.e. when wont our piecewise constant approximations for demand and supply work)?

The Message Inventory isnt sexy, but it is your one great weapon for coping with variability. Understanding its behavior is essential to business success.