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Define:
Quantity of the single-use item purchased: n,
Original unit price of the single-use item: X,
The sale price of the reprocessed item at a discounted rate S of the original item price,
The sale price of the reprocessed item: S*X.
Items may be reprocessed several times. Average item return rates for the first, second and third reprocessing procedures: P, Q and R, respectively.
After reprocessing, the average unit cost is the Final Average Unit Cost, which is:
Final Average Unit Cost = Total Cost/Total Quantity
= {1+ [P + PQ + ...}
Where, two times reprocessing procedures with return item rates are P and Q, respectively.
For example, Company A sells its single-use electrophysiology catheter at the price of X = $100. A reprocessing company takes the used single-use catheter to reprocess, and sells it back to the hospital at half price (Resale rate S = 1/2) of the original cost, X. The reprocessed catheter sale price is SX = 0.5X = (0.5)*($100) = $50 each.
If processed only once, Q = 0, R = 0, then:
The Final Average Unit Cost = [1 + (P)(0.5)]X / [1+ P].
Let s assume the first processing return rate P = 80%, S =0.5, then:
Final Average Unit Cost = (1 + 0.8*0.5)X / (1 + 0.8) = 1.4X/1.8 = 0.78X.
That is a 22% saving.
If first processing return rate is P = 60%, then:
Final Average Unit Cost = (1 + 0.6*0.5)X / (1 + 0.6) = 1.3X/1.6 = 0.81X.
This is a 19% saving.
In day-to-day practice, a single-use item may be reprocessed many times. By simplifying the assessment of the program, we may assume every reprocess has the same item return rate J, item may be reprocessed k times. So, P = Q = R = ... = J, and the above formula becomes:
The Final Average Unit Cost =
{1 + [J + J2 + J3 + J4 + J5 + ... +Jk]S}X / {1 + J + J2 + J3 + J4 + J5 + ... + Jk}
= {1 + S* SJm}X / [1+ SJm]
Where, m = 1, 2, 3, 4, ... , k.
For example, if: J = 80% = 0.8, S = 1/2, X = $100, reprocessing k = 8 times:
The Final Average Unit Cost of the item =
{1 + 0.5$100/{1+0.800 + 0.640 + 0.512 + 0.410 + 0.328 + 0.262 + 0.210 + 0.168} = 2.665 x$100 / 4.33 = $61.50
In this example, after eight reprocessings, final savings is about 40%.
Facilitating a reprocessing program, the Final Average Unit Cost will be less than the original item cost X, and more than the single reprocessed discount price SX. The biggest portion of the savings comes from the first and second reprocessing procedures. After two times, the returned volumes get smaller, as do the further savings. Therefore, calculate one or two times, then you may evaluate the reprocessing program.
Using the assessment result as a negotiation token in the marketplace, you may find a similar product at a discount close to the saving from the reprocessing program or a reasonable reprocessing program. In the reprocessing program, some hidden costs should be added, such as manpower cost in handling, primary cleaning, etc. Each individual institution can decide if the reprocessing program is economically workable for them or not worth the efforts.

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