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Optimizing Knee Surgery Product Shipping
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Table of Contents • Background and Problem Statement • Assumptions • Our Approach • Our Results • Recommendations
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Background and Problem Statement
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There are 600,000 knee surgeries in the United States every year
There are 600,000 knee surgeries in the United States every year
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In spite of growing demand for knee replacements, the entire industry has a problem. Hospitals are negotiating the cost of these surgeries down, and topline revenue is decreasing for companies that develop implants.
Profit margins are decreasing
While costs are increasing
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So what actually goes into a total knee implant? Each of these parts is shipped individually, at every size distribution, for every surgery.
Main Takeaway: Shipping costs are going through the roof.
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In spite of only using 4 parts, this much inventory is shipped for EACH knee surgery.
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Our Assignment: Create rules to closely match each implants shipment to the individual patient sizing needs.
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Our Approach: How we solved this problem
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Assumptions • The probability of patient sizing follows a normal distribution
• For each of the 9 sizes of femoral implant, a particular femoral size would encompass + .25 of the stated size of the implant. For example, femoral size 2.5 would encompass a size range between 2.25 and 2.75. Similarly, femoral size 4 would encompass a size between 3.75 and 4.25.
• Size 4N represents size “4 narrow”. Per DePuy’s engineering specifications, size 4N occurs with the same probability as size 4 and represents a range extending from 3.25 to 3.75. In practice, if Size 4 falls within the predictive range, size 4N must be included in the send.
• We assumed $50 for standard courier cost, regardless of distance
• Each FedEx shipment was $11.71 for any package shipment including up to 10 items.
• Shipments less than 10 items have the same price as a shipment of 10 items.
• Penalty shipment cost was assumed to be $100 for expedited courier
• Penalty also adds 5% to total costs to cover other expedited costs that may occur
• Inventory will only stay at the hospital for one day, so holding costs with extra inventory is incurred for one day.
• Daily holding cost can be based on monthly holding costs and are assumed to be linear.
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Our ABC’s Model Adjustables: § Probability cutoffs for sending different size implants. Best (Objective function): Minimize the chance of an inventory “miss” at the time of surgery. Constraints: § Inventory holding costs. § Item limitations per FedEx package.
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1. Is there correlation between a person’s attributes (gender, age, height and weight) and the size of the knee part they need?
Regression for Men: Regression for Women:
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2. Find the regression mean and standard deviation of the error distribution on 905 real patients and turn that into a risk normal model
3. Use an @Risk based simulation to find the range of size values by adding the predicted femur size and distribution of the error (1000 simulations)
Std Dev Mean 0.688532367 0.0954
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4. Connecting @Risk distribution to the real world: Use of the Heat Map (We used Normdist function to generate this in Excel). Assumption of + 0.25 size range.
Size ProbabilitySize 1 Size 1.5 Size 2 Size 2.5 Size 3 Size 4N Size 4 Size 5 Size 60.412417 0.280336 0.197649 0.084228 0.021674 0.003678 0.003678 5.93877E-‐07 1.21184E-‐080.154684 0.231284 0.282927 0.208806 0.092939 0.028947 0.028947 2.26619E-‐05 8.04891E-‐070.232428 0.265701 0.266568 0.161449 0.058996 0.014714 0.014714 6.54227E-‐06 1.90117E-‐077.26E-‐05 0.000988 0.008426 0.043188 0.133293 0.526412 0.526412 0.077027126 0.0220281452.44E-‐07 8.15E-‐06 0.000166 0.002014 0.014701 0.234946 0.234946 0.260618031 0.2161500390.002104 0.014244 0.062994 0.167888 0.269938 0.415454 0.415454 0.011547299 0.0015983580.174623 0.242446 0.280443 0.195722 0.082379 0.024078 0.024078 1.60463E-‐05 5.38009E-‐070.000517 0.004788 0.028357 0.101192 0.217873 0.505763 0.505763 0.030199695 0.0057832810.000546 0.004943 0.028792 0.101557 0.217199 0.503981 0.503981 0.030783006 0.0060165080.056272 0.138578 0.252064 0.276575 0.183083 0.090653 0.090653 0.000220737 1.18549E-‐05
Main Takeaway: The green boxes indicate the parts to definitely send, yellow boxes are potential sends while the red indicates too small of a probability to warrant the cost of sending the part.
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5. How much to send? @Risk Optimizer determines costs and probability thresholds for different service levels. Minimize the total failures by adjusting the probabilities between 0 and 0.8 (80%).
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6. How well does our model compare with reality? Comparing the predictive model against the actual observations.
Main Takeaway: The blue cells are correctly predicted and the red cells indicated where our model “missed.”
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7. Different error rates for different service levels. For cost comparisons, we've decided that our max cost will not exceed $65, which will give us a 0.57% “miss” rate (error).
Main Takeaway: Given the severity of the topic (surgery), we were conservative and chose a high cost threshold with a very low failure rate.
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Chance of a “miss” vs Cost per Surgery
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Our Results
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8. Cost difference between the current system....
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8. …and our model.
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Recommendations
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Total savings Current Model Expenditures
Our Proposed Model Expenditures
Weekly Sends $2,388.31 $1,443.95
Monthly Sends $9,553.24 $5,775.80
Yearly Sends $124,192.12 $70,085.40
Main Takeaway: In our estimated model, the company will save $54,106.72 per year on average. Equally important, the inventory requirement per procedure is 50% of the current level. Average cost savings as a percentage is approximately 40%
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This is the tip of the iceberg There are almost 200 accounts in the state of Illinois. We only modeled it for one account.
Main Takeaway: $54,106.72 * 200 = $10.8 Million Dollars
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Appendix
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Mandatory probabilities that must be hit in order to send size parts