Abstract
We study the problem of optimizing the sampling and procurement decisions in a remanufacturing system under stochastic yield of returns in a single-period setting. Returned products are characterized by uncertainty regarding their ability to be successfully remanufactured. This uncertainty is formulated as a variable probability of each returned unit in a batch to be remanufacturable (returns yield). We study the impact of returns yield on the optimal procurement policy and the benefits of sampling inspection of returns prior to the procurement decision. It is shown that sampling inspection improves the procurement decisions since it allows the Bayesian updating of the prior information regarding the returns yield. We derive analytical expressions for the determination of the economically optimal procurement quantity and structural properties that facilitate the optimization procedure and provide useful insights. The determination of the economically optimal sample size is also discussed and the benefits of sampling are illustrated through numerical examples.
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Abbreviations
- D :
-
Demand for remanufactured products
- Q :
-
Procurement quantity
- Q v :
-
Remanufacturable units in Q
- v :
-
Sales revenue per unit
- c p :
-
Procurement cost per unit
- c in :
-
Inspection cost per unit in the batch after procurement
- c r :
-
Remanufacturing cost per unit
- c n :
-
Inspection cost per unit in the sample before procurement
- n :
-
Sample size
- r :
-
Number of remanufacturable units in the sample
- p :
-
Probability of a returned unit to be remanufacturable (yield)
- \({\bar{p}}\) :
-
Expected yield of returns
- p cr :
-
Critical ratio of p
- P(r|n):
-
Probability to find r remanufacturable units in the sample n
- P(p):
-
Probability that the yield is p
- P(p|n,r):
-
Probability that the batch yield is p given the number of remanufacturable units r in the sample n
- P(r|p,n):
-
Probability to find r remanufacturable units in the sample given that the batch yield is p
- f(p):
-
Probability density function of the yield
- f(p|n,r):
-
Probability density function of the yield given the number of remanufacturable units r in the sample n
- \({Q_{p}^\ast }\) :
-
Optimal procurement quantity when the batch yield is p
- \({Q_{r/n}^\ast }\) :
-
Optimal procurement quantity when the number of remanufacturables in the sample n is r
- TP(Q|p):
-
Expected total profit for procurement quantity Q given p
- TP (Q):
-
Expected total profit for procurement quantity Q, taking into account all possible values of p
- TP(Q |n, r):
-
Expected total profit for procurement quantity Q, given the number of remanufacturable units r in the sample n
- TP(n ):
-
Expected total profit for sample size n, taking into account all possible values of r and their respective optimal procurement quantities (\({Q_{r/n}^\ast }\))
- TP(n )− :
-
Expected total profit for sample size n excluding sampling cost
- TP * :
-
Maximum expected total profit if the exact yield is known a priori
- MP(Q |p):
-
Marginal profit of procuring Q + 1 units instead of Q given p
- MP(Q ):
-
Marginal profit of procuring Q + 1 units instead of Q, taking into account all possible values of p
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Panagiotidou, S., Nenes, G. & Zikopoulos, C. Optimal procurement and sampling decisions under stochastic yield of returns in reverse supply chains. OR Spectrum 35, 1–32 (2013). https://doi.org/10.1007/s00291-010-0234-z
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DOI: https://doi.org/10.1007/s00291-010-0234-z