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**Flow Rate and Capacity Analysis**

QUAN 6610 Chapter 5 Flow Rate and Capacity Analysis Based on Anupindi Flow Rate and Capacity

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5.1 Resources Tp = unit load = total time resource works to process flow unit. Example 5.1 See Table 5.1 for data. Based on Anupindi

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**Theoretical capacity of a process = theoretical capacity of bottleneck**

Capacity = 1/unit load = 1 / Tp Resource Pool Capacity = cp / Tp Example 5.2 Based on Anupindi

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**Theoretical Capacity of a Resource Unit in a Pool **

Scheduled 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 availability Example 5.3 Based on Anupindi

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**Capacity utilization of a resource pool (rp) = **

Capacity 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 / Rp Example 5.4 Given: R = 480 / day Based on Anupindi

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**Demonstration of concepts thus far.**

Example 5.5 See Table 5.6 for Work Content and Resources Based on Anupindi

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**Given: R = 5.5 patients per hour**

Based on Anupindi

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**5.3 Effect of Product Mix on Theoretical Capacity**

Example 5.7 Theoretical capacity for Hospital Claims: Based on Anupindi

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**Theoretical capacity for 60%/40% Mix**

Based on Anupindi

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Example 5.8 See Table 5.12 for Activities, Work Content and Resource Pools for a Standard Shed Based on Anupindi

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Based on Anupindi

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Based on Anupindi

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Based on Anupindi

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Based on Anupindi

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**5.4 Other Factors Affecting Process Capacity**

Net availability = actual time during which the resource is available for processing flow units Available Loss Factor = 1 – (Net Availability / Scheduled Availability) Based on Anupindi

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**Improving Theoretical Capacity**

Decrease 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 Anupindi

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Based on Anupindi

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**How increase capacity? Summary of Typical Actions**

Key action = optimize only bottleneck management Decrease the work content of bottleneck activities Never unnecessarily idle (“starve”) bottlenecks = eliminate bottleneck waits: Reduce variability if it leads to bottleneck waiting Synchronize flows to and from the bottleneck: sync when resources start an activity work smarter: Reduce & externalize setups/changeover times, streamline + eliminate non-value added work do it right the first time: eliminate rework/corrections work faster Move work content from bottlenecks to non-bottlenecks create flexibility to offload tasks originally assigned to bottleneck to non-critical resource or to third party Can we offload tasks to cross-trained staff members? Increase Net Availability of Process work longer: increase scheduled availability increase scale of process: invest in more human and capital resources eliminate unscheduled downtimes/breakdowns Preventive maintenance, backups, etc. Based on Anupindi

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Based on Anupindi

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Additional Concepts (Problem Scenario from Cachon and Terwiesch) Assume 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 1 Activity 2 Activity 3 Components Finished Product Based on Anupindi, et al, MBPF (2e)

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**4.2 Time to Process a Quantity X Starting with an Empty Process**

Worker-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 = = 32 minutes Machine-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 minutes Time to make X units = Time through empty system + Cachon and Terwiesch, Matching Supply with Demand. Process Labor Costs

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**4.3 Labor Content and Idle Time**

QUAN 6610 4.3 Labor Content and Idle Time Labor content = sum of activity times with labor = 13 min/unit = 32 min/unit Cost 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. Process Labor Costs

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QUAN 6610 Exhibit 4.1 TIME TO PROCESS A QUANITY X STARTING WITH AN EMPTY PROCESS Find 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 stations Compute 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 capacity Time to finish X units Time to make X units = Time through empty system + Components Finished Xootrs Activity 1 Activity 2 Activity 3 Conveyor Belt Figure 4.4. : A machine paced process lay-out (Note: conveyor belt is only shown for illustration) Q 4.1 a. Cachon and Terwiesch, Matching Supply with Demand. Process Labor Costs

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**Exhibit 4.2 SUMMARY OF LABOR COST CALCULATIONS**

QUAN 6610 Exhibit 4.2 SUMMARY OF LABOR COST CALCULATIONS Compute 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 i Compute the labor content of the flow unit: this is the sum of all activity times involving direct labor Add up the idle times across all resources (total idle time); then compute Cachon and Terwiesch, Matching Supply with Demand. Process Labor Costs

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**Table 4.1 Basic Calculations Related to Idle Time**

QUAN 6610 Table 4.1 Basic Calculations Related to Idle Time Worker 1 Worker 2 Worker 3 Activity time 13 min/unit 11 min/unit 8 min/unit Capacity 1/13 unit/minutes = 4.61 units/hr 1/11 units/minutes = 5.45 units/hr 1/8 unit/minutes = 7.5 units/hr Process capacity Minimum {4.61 units/h, 5.45 units/h, 7.5 units/h} = 4.61 units/h Flow rate Demand = 125 units/week = 3.57 units/hr Flow rate = Minimum {demand, process capacity} = 3.57 units/hr Cycle time 1/3.57 hours/unit = 16.8 minutes/unit Idle time {Total = 18.4 min/unit} 16.8 minutes/unit - 13 minutes/unit = 3.8 minutes/unit - 11 minutes/unit = 5.8 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% % %) = 63.5% Or = 32 / ( ) = 63.5% Cachon and Terwiesch, Matching Supply with Demand. Process Labor Costs

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**4.4 Increasing Capacity by Line Balancing**

QUAN 6610 4.4 Increasing Capacity by Line Balancing Comparing 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. Worker 1 Worker 2 Worker 3 Utilization 3.57 / 4.61 = 77% 3.57 / 5.45 = 65.5% 3.57 / 7.5 = 47.6% Utilization 3.57 / 4.61 = 77% 3.57 / 5.45 = 65.5% 3.57 / 7.5 = 47.6% Cachon and Terwiesch, Matching Supply with Demand. Process Labor Costs

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QUAN 6610 Observations 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 demand Implied Utilization = Available capacity Cachon and Terwiesch, Matching Supply with Demand. Process Capacity

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