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Based on Anupindi1

Chapter 5Flow Rate and Capacity Analysis1Flow Rate and CapacityQUAN 6610Based on Anupindi2

Tp = unit load = total time resource works to process flow unit.Example 5.15.1 ResourcesSee Table 5.1 for data.Based on Anupindi3Theoretical capacity of a process = theoretical capacity of bottleneckCapacity = 1/unit load = 1 / TpResource Pool Capacity = cp / Tp

Example 5.2Based on Anupindi4Scheduled availability = the amount of time that a resource is schedule for operation.Theoretical Capacity of a Resource Unit in a Pool = Rp = (cp / Tp) x Load batch x Scheduled availabilityExample 5.3

Based on Anupindi5Capacity utilization of a resource pool (rp) measures the degree to which resources are effectively utilized by a process.Capacity utilization of a resource pool (rp) = Throughput / theoretical capacity of resource pool p = R / RpExample 5.4Given: R = 480 / day

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Example 5.5See Table 5.6 for Work Content and ResourcesDemonstration of concepts thus far.Based on Anupindi7

Given: R = 5.5 patients per hourBased on Anupindi85.3 Effect of Product Mix on Theoretical CapacityExample 5.7Theoretical capacity for Hospital Claims:

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Theoretical capacity for 60%/40% Mix

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Example 5.8See Table 5.12 for Activities, Work Content and Resource Pools for a Standard ShedBased on Anupindi11

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Based on Anupindi155.4 Other Factors Affecting Process CapacityNet availability = actual time during which the resource is available for processing flow unitsAvailable Loss Factor = 1 (Net Availability / Scheduled Availability)

Based on Anupindi16Improving Theoretical CapacityDecrease the unit load on the bottleneck resource pool (work faster, work smarter.Increase the load batch of resources in the bottleneck resource pool (increase scale of resource).Increase the number of units in the bottleneck resource pool (increase scale of process).Increase the scheduled availability of the bottleneck resource pool (work longer).Based on Anupindi17

Based on Anupindi18How increase capacity? Summary of Typical ActionsKey action = optimize only bottleneck management

Decrease the work content of bottleneck activitiesNever unnecessarily idle (starve) bottlenecks = eliminate bottleneck waits:Reduce variability if it leads to bottleneck waitingSynchronize flows to and from the bottleneck: sync when resources start an activitywork smarter:Reduce & externalize setups/changeover times, streamline + eliminate non-value added workdo it right the first time: eliminate rework/correctionswork faster

Move work content from bottlenecks to non-bottleneckscreate flexibility to offload tasks originally assigned to bottleneck to non-critical resource or to third partyCan we offload tasks to cross-trained staff members?

Increase Net Availability of Processwork longer: increase scheduled availabilityincrease scale of process: invest in more human and capital resourceseliminate unscheduled downtimes/breakdownsPreventive maintenance, backups, etc.Based on Anupindi19

Based on Anupindi, et al, MBPF (2e)20Assume three activities with times of 13 min/unit, 11 min/unit and 8 min/unit, each staffed by one worker.

Assume an hourly rate of $12/hour and a demand of 125 scooters per week. Assume the process operates 35 hours per week.

Activity 1Activity 2Activity 3ComponentsFinished Product(Problem Scenario from Cachon and Terwiesch)Additional Concepts4.2 Time to Process a Quantity X Starting with an Empty ProcessWorker-paced system: each worker is free to work at his or her own pace; if the first worker finishes before the first worker is ready to accept the parts, then the first worker puts the completed work in the inventory between them.Time through an empty worker-paced process = Sum of the activity times= 13 + 11 + 8 = 32 minutesMachine-paced system: all the steps must work at the same rate.Time through an empty machine-paced process = Number of resources in sequence x Activity time of the bottleneck step= 3 x 13 = 36 minutesTime to make X units = Time through empty system +

Cachon and Terwiesch, Matching Supply with Demand.QUAN 6610Process Labor Costs214.3 Labor Content and Idle TimeLabor content = sum of activity times with labor = 13 min/unit + 11 + 8 = 32 min/unitCost of direct labor =

To correctly compute the cost of direct labor, we need to look at two measures: The number of scooters produced per unit of time (the flow rate). The amount of wages we pay for the same time period.Cachon and Terwiesch, Matching Supply with Demand.QUAN 6610Process Labor Costs22ComponentsFinished XootrsActivity 1Activity 2Activity 3Conveyor BeltFigure 4.4. : A machine paced process lay-out (Note: conveyor belt is only shown for illustration)TIME TO PROCESS A QUANITY X STARTING WITH AN EMPTY PROCESSFind the time it takes the flow unit to go through the empty system: In worker-paced line, this is the sum of the activity times In machine-paced line, this is the cycle time x the number of stationsCompute the capacity of the process (see previous methods). Since we are producing X units as fast as we can, we are capacity constrained; thus,Flow rate = Process capacityTime to finish X units

Exhibit 4.1Time to make X units = Time through empty system +

Q 4.1 a.Cachon and Terwiesch, Matching Supply with Demand.QUAN 6610Process Labor Costs23SUMMARY OF LABOR COST CALCULATIONSCompute the capacity of all resources; the resource with the lowest capacity is the bottleneck (see previous methods) and determines the process capacity.Compute Flow rate = Min {Available input, Demand, Process Capacity};compute Cycle time =

Compute the total wages (across all workers) that are paid per unit of time:Cost of direct labor =

Compute the idle time of each worker for each unit:Idle time for worker at resource i = Cycle time x (Number of workers at resource i) Activity time at resource iCompute the labor content of the flow unit: this is the sum of all activity times involving direct laborAdd up the idle times across all resources (total idle time); then compute

Exhibit 4.2

Cachon and Terwiesch, Matching Supply with Demand.QUAN 6610Process Labor Costs24Table 4.1 Basic Calculations Related to Idle TimeWorker 1Worker 2Worker 3Activity time13 min/unit11 min/unit8 min/unitCapacity

1/13 unit/minutes= 4.61 units/hr1/11 units/minutes= 5.45 units/hr1/8 unit/minutes= 7.5 units/hrProcess capacityMinimum {4.61 units/h, 5.45 units/h, 7.5 units/h} = 4.61 units/hFlow rateDemand = 125 units/week = 3.57 units/hrFlow rate = Minimum {demand, process capacity} = 3.57 units/hrCycle time1/3.57 hours/unit = 16.8 minutes/unitIdle time

{Total = 18.4 min/unit}16.8 minutes/unit- 13 minutes/unit= 3.8 minutes/unit16.8 minutes/unit- 11 minutes/unit= 5.8 minutes/unit

16.8 minutes/unit- 8 minutes/unit= 8.8 minutes/unit

Utilization

3.57 / 4.61 = 77%3.57 / 5.45 = 65.5%

3.57 / 7.5 = 47.6%Average Labor Utilization= 1/3 x (77.4% + 65.5% + 47.6%) = 63.5% Or = 32 / (32 + 18.4) = 63.5%Cachon and Terwiesch, Matching Supply with Demand.QUAN 6610Process Labor Costs254.4 Increasing Capacity by Line BalancingComparing the utilization levels in table 4.1 reveals a strong imbalance between workers. Imbalances within a process provide micro-level mis-matches between what could be supplied by one step and what is demanded by the following steps. Line balancing is the act of reducing such imbalances. It provides the opportunity to: Increase the efficiency of the process by better utilizing the various resources Increase the capacity of the process by reallocating either workers from underutilized resources to the bottleneck or work from the bottleneck to the underutilized resources.

Utilization3.57 / 4.61 = 77%3.57 / 5.45 = 65.5%3.57 / 7.5 = 47.6%Worker 1Worker 2Worker 3Utilization3.57 / 4.61 = 77%3.57 / 5.45 = 65.5%3.57 / 7.5 = 47.6%Cachon and Terwiesch, Matching Supply with Demand.QUAN 6610Process Labor Costs26Observations on Table 3.4 Unlike utilization, implied utilization can exceed 100 percent. The fact that a resource has an implied utilization over 100 percent does not make it the bottleneck. There is only one bottleneck in the process -- the resource where the implied utilization is the highest. In the case of capacity expansion of a process, it might be worthwhile to add capacity to these other resources as well, not just to the bottleneck. Depending on the margins we make and the cost of installing capacity, we could make a case to install additional capacity for all resources with an implied utilization above 100 percent. Capacity requested by demandImplied Utilization = -------------------------------- Available capacityCachon and Terwiesch, Matching Supply with Demand.QUAN 6610Process Capacity27