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Based on Anupindi 1 Chapter 5 Flow Rate and Capacity Analysis

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Based on Anupindi 2 T p = unit load = total time resource works to process flow unit. Example Resources See Table 5.1 for data.

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Based on Anupindi 3 Theoretical capacity of a process = theoretical capacity of bottleneck Capacity = 1/unit load = 1 / T p Resource Pool Capacity = c p / T p Example 5.2

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Based on Anupindi 4 Scheduled availability = the amount of time that a resource is schedule for operation. Theoretical Capacity of a Resource Unit in a Pool = R p = (c p / T p) x Load batch x Scheduled availability Example 5.3

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Based on Anupindi 5 Capacity utilization of a resource pool ( p ) measures the degree to which resources are effectively utilized by a process. Capacity utilization of a resource pool ( p ) = Throughput / theoretical capacity of resource pool p = R / R p Example 5.4Given: R = 480 / day

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Based on Anupindi 6 Example 5.5 See Table 5.6 for Work Content and Resources Demonstration of concepts thus far.

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Based on Anupindi 7 Given: R = 5.5 patients per hour

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Based on Anupindi Effect of Product Mix on Theoretical Capacity Example 5.7 Theoretical capacity for Hospital Claims:

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Based on Anupindi 9 Theoretical capacity for 60%/40% Mix

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Based on Anupindi 10 Example 5.8 See Table 5.12 for Activities, Work Content and Resource Pools for a Standard Shed

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Based on Anupindi 11

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Based on Anupindi 12

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Based on Anupindi 13

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Based on Anupindi 14

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Based on Anupindi 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)

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Based on Anupindi 16 Improving Theoretical Capacity 1.Decrease the unit load on the bottleneck resource pool (work faster, work smarter. 2.Increase the load batch of resources in the bottleneck resource pool (increase scale of resource). 3.Increase the number of units in the bottleneck resource pool (increase scale of process). 4.Increase the scheduled availability of the bottleneck resource pool (work longer).

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Based on Anupindi 17

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Based on Anupindi 18 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.

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Based on Anupindi 19

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Based on Anupindi, et al, MBPF (2e) 20 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 1Activity 2Activity 3 Components Finished Product (Problem Scenario from Cachon and Terwiesch) Additional Concepts

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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.

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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.

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ComponentsFinished Xootrs Activity 1Activity 2Activity 3 Conveyor Belt Figure 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 PROCESS 1.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 2.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 3.Time to finish X units Exhibit 4.1 Time to make X units = Time through empty system + Q 4.1 a. Cachon and Terwiesch, Matching Supply with Demand.

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SUMMARY OF LABOR COST CALCULATIONS 1.Compute the capacity of all resources; the resource with the lowest capacity is the bottleneck (see previous methods) and determines the process capacity. 2.Compute Flow rate = Min {Available input, Demand, Process Capacity}; compute Cycle time = 3.Compute the total wages (across all workers) that are paid per unit of time: Cost of direct labor = 4.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 5.Compute the labor content of the flow unit: this is the sum of all activity times involving direct labor 6.Add up the idle times across all resources (total idle time); then compute Exhibit 4.2 Cachon and Terwiesch, Matching Supply with Demand.

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Table 4.1 Basic Calculations Related to Idle Time Worker 1Worker 2Worker 3 Activity time13 min/unit11 min/unit8 min/unit Capacity1/13 unit/minutes = 4.61 units/hr 1/11 units/minutes = 5.45 units/hr 1/8 unit/minutes = 7.5 units/hr Process capacityMinimum {4.61 units/h, 5.45 units/h, 7.5 units/h} = 4.61 units/h Flow rateDemand = 125 units/week = 3.57 units/hr Flow rate = Minimum {demand, process capacity} = 3.57 units/hr Cycle time1/3.57 hours/unit = 16.8 minutes/unit Idle time {Total = 18.4 min/unit} 16.8 minutes/unit - 13 minutes/unit = 3.8 minutes/unit 16.8 minutes/unit - 11 minutes/unit = 5.8 minutes/unit 16.8 minutes/unit - 8 minutes/unit = 8.8 minutes/unit Utilization3.57 / 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.

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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. Utilization3.57 / 4.61 = 77%3.57 / 5.45 = 65.5%3.57 / 7.5 = 47.6% Worker 1Worker 2Worker 3 Utilization3.57 / 4.61 = 77%3.57 / 5.45 = 65.5%3.57 / 7.5 = 47.6% Cachon and Terwiesch, Matching Supply with Demand.

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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.

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