Optimizing Knee Surgery Product Shipping

Table of Contents •  Background and Problem Statement •  Assumptions •  Our Approach •  Our Results •  Recommendations

Background and Problem Statement

There are 600,000 knee surgeries in the United States every year

There are 600,000 knee surgeries in the United States every year

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

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.

In spite of only using 4 parts, this much inventory is shipped for EACH knee surgery.

Our Assignment: Create rules to closely match each implants shipment to the individual patient sizing needs.

Our Approach: How we solved this problem

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.

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.

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:

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

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.

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.”

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.

Chance of a “miss” vs Cost per Surgery

Our Results

8. Cost difference between the current system....

8. …and our model.

Recommendations

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%

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

Appendix

Mandatory probabilities that must be hit in order to send size parts