Lecture 1 Process Capacity Little s Law I RT Days of supply T I R Inventory Turns 1 T R I R Flow Rate or COGS Annual inventory holding cost as a percentage of COGs Annual inventory holding cost percentage yearly turns Inventory Turns 1 T or R I COGS Inventory Capacity unit time Bottleneck minimum capacity or maximum utilization Annual holding costs as of COGS per unit holding costs annual inventory costs annual inventory turns Flow rate min available input demand supply Time to fulfill X units X Flow Rate Utilization Flow Rate Capacity Lecture 2 Capacity Management Demand minutes per unit minutes of work demanded of resources 60 minutes minutes of work supplied Implied Utilization Demand Capacity Utilization Flow Rate Capacity Note USE SAME UNITS Process capacity Bottleneck Flow rate minimum Demand process capacity Time through an empty process Sum of processing times Time through a full process T I R Time to finish X units starting with an empty system sum of processing times X 1 Flow Rate Time to finish X units with a full system X Flow Rate Cycle Time 1 Flow Rate time between produced units Lecture 3 Process interruptions setup times batching Capacity Number of units produced Time to produce units Capacity Batch Size Setup Time Batch Size Processing Time units time Time to produce batch setup time batch size x Proc Time Maximum Capacity 1 Processing Time Batch Size Capacity Setup Time 1 Capacity Processing Time Batch time Batch Size x Processing Time Utilization Flow Rate x Processing Time Utilization Time Producing Time Producing setup time Idle Time Utilization Time producing Total time demanded Inventory at End of Production Amount Produced Amount Demanded Avg Inventory Max Inventory 2 Production Time x Rate of increase x B x 1 R x P Total Inventory Number of types avg inventory Inventory builds at rate of Supply Demand Sample Problems How many units should be produced with each setup to minimize inventory without decreasing the current flow rate Batch size with Campbell soup example Historical Examples The printing process replaced a high processing time process with a process with a setup time but low processing time Henry Ford Customers can have any color they want as long as it is black Single Minute Exchange of Die reduces setup times Retailers can sell fast turning items at slow margin but slow selling items require a large margin to be profitable Capacity of process is the minimum capacity of the sub processes Don t forget to use the right units If they ask for inventory costs don t forget to account for the time The slower an item turns the greater the gross margin needed to be profitable Costco has lower margins than Wal Mart and therefore needs higher inventory turns Greatest profit high gross margin high inventory turns Same inventory turns same days of supply Highest implied utilization is the bottleneck Demand capacity supply constrained Supply contrained bottleneck has 100 utilization Demand flow rate capacity demand constrained Demand constrained Process is capable of producing more than what is demanded Utilization implied utilization if demand constrained Implied utilization w different flow units USE Minutes per hour normalize units can use 60 min hr as capacity Line balancing Reallocating tasks from bottleneck to another resource improves capacity w o adding resources Integrating work improves line balancing best with short scope and homogenous tasks i e each person can do all tasks Add up all processing times multiply by of resources o Utilization of time not spent idle Balance Tasks Processing Can increase capacity without hiring more workers by reassigning work Add demands together to find target capacity of batch process Processing time how long it takes to make one of the items in a batch Minimum batch size increases a lot if target capacity demand increases and everythign is constant variety vs inventory Can reduce setup times to reduce batch size so more variety Capacity increases as batch size increases Inventory increases as batch size increases Utilization may increase if batch size gets larger only to a point Tradeoff between capacity and inventory Flow rate minimum available input demand process capacity If a batch producing step does not incur a setup time its capacity is unaffected by the batch size Setup time down time Idle Time Long setup times are bad for product variety Graph of capacity and batch size capacity goes up with batch size and then levels off logarithmic function More product variety more inventory Produce in proportion to demand Campbell Soup example Results of more product variety lowered capacity increased batch sizes increased inventory Utilization with just right batch neither process has idle time Assembly often just flow rate capacity no set up time o If demand contrained batch size can be reduced Find the batch sizes that will give the steps up till last the demand capacity and pick the larger of the two Use batch size equation Add setup times and add demands to find target capacity production time rates for different soups should be the same Determine total batch size produce in proportion to demand Q quantity in each order or EOQ R flow rate of demand Q R time between shipments Q 2 Average inventory h inventory holding costs per unit time h cost of item x discount if applicable x holding x time change if applicable K setup cost K Q R setup cost per unit time Setup Cost Holding Cost at Q Starved lack of inventory to work on Blocked have no place to put inventory Variaability can reduce capicity considerably without buffers Concepts Costco must be hyper efficient with restocking shelves because it has a much smaller margin less variety higher SKU Don t convert setup times to setup costs When setup costs holding costs it s at the minimum of C Q o EOQ doesn t work when setup costs are sunk When setup costs are sunk object should be to minimize inventory Blocking and starving at bottlneck reduces flow rate very costly orange juice example with extraction airport screening with X ray Avoid sending re work through the bottleneck Use probabilities to solve for average processing time i e 0 9 x 20 0 1 x 40 22 sec Check quality at the source Tq waiting time increases exponentially as utilization approaches 100 Shortest Processing Time minimizes average wait time FCFS has longer wait time but appears more fair Pooling reduces time in queue withs ame amount of labor Pooling multiple queues reduces of customers in waiting not