Joint product durability and lot sizing models

Diwakar Gupta, Yigal Gerchak

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


This paper concerns the simultaneous selection of product durability and order quantity for items that deteriorate over time. Choices of product durability are modelled as the values of a single design parameter that affects the distribution of the time-to-onset of deterioration (TOD). Once deterioration has begun, individual items are assumed to have exponential remaining lifetimes. We analyze two scenarios. In the first case items are guaranteed to be good if used prior to an expiry date. Therefore, TOD is a constant and the store manager may choose an appropriate value (at cost). In the second case, TOD is a random variable. Then, the design parameter can affect TOD distribution in either mean-preserving or variance-preserving or mixed manner. We report insightful numerical examples for each case and derive highly plausible conditions, which when true, imply that the corresponding expected cost per unit time is strictly quasi-convex.

Original languageEnglish (US)
Pages (from-to)371-384
Number of pages14
JournalEuropean Journal of Operational Research
Issue number2
StatePublished - Jul 20 1995

Bibliographical note

Funding Information:
Items which require special climate conditions for safe storage often experience an onset of deterioration due to the combined effects of age, durability and random shocks that can be caused either by sudden changes in weather conditions or by failures of the climate control equipment. Common examples of such items include pharmaceutical drugs, photographic films, electronic components and perishable foodstuffs like frozen fruit juices. The precise duration of the time to onset of deterioration (TOD) is typically unknown. The resulting uncertainty in product durability has a direct effect on optimal order quantities, and models that permit investigation of the nature of this interaction are likely to be of interest to a store manager. In many such situations, the store manager has the option to exercise some control over the distribution of TOD through (i) addition of special preserving chemicals; for example, fresh produce is routinely sprayed with preservatives to affect onset of decay, (ii) choice of degree of * This research has been supported in part by the Natural Sciences and Engineering Research Council of Canada through research grants to the authors. * * Corresponding author.


  • Deterministic demand
  • Durability-lotsizing
  • Exponential decay
  • Inventory-production
  • Perishable-aging items


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