Lot Sizing with Randomly Graded Yields

Steven Nahmias and Kamran Moinzadeh
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Steven Nahmias: Santa Clara University, Santa Clara, California
Kamran Moinzadeh: University of Washington, Seattle, Washington

Operations Research, 1997, vol. 45, issue 6, 974-989

Abstract: We consider a single inventory item that is graded into one of two quality levels after production. The proportion of grade one units produced in a lot is a random variable assumed to follow the lognormal distribution. Demands for grade 2 may be filled with grade 1 product, but not vice versa. Assuming that demands for the two grades are known and constant, we develop a continuous review model in which cycles are defined as times when total inventory equals zero. Since grade 1 inventory may be depleted before total stock and shortages are not permitted, cycles may consist of multiple set-ups. We show that the optimal order-to-point, S , has a form similar to the EOQ. Tables of the CDF of an appropriately defined unit normal multivariate distribution are incorporated into a spreadsheet to facilitate calculations for any parameter setting.

Keywords: inventory/production; stochastic; one-way substitutions; production/scheduling; random grading after production (search for similar items in EconPapers)
Date: 1997
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