An integrated vendor-buyer model with quadratic demand under inspection policy and preservation technology

Pervin M., Roy S. K., Weber G.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.49, no.3, pp.1168-1189, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.15672/hujms.476056
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1168-1189
  • Keywords: integrated inventory model, quadratic demand, inspection policy, preservation technology, optimization, VARIABLE HOLDING COST, INVENTORY MODEL, IMPERFECT PRODUCTION, INVESTMENT, QUALITY
  • Middle East Technical University Affiliated: Yes


An integrated vendor-buyer model for deteriorating items is formulated in this study. To control deterioration rate, the vendor adopts preservation technology. Shortages are allowed for both vendor and buyer. During shortage period, the vendor simply doubles the production rate to meet the demand of buyer. The vendor's demand during non-shortage period follows a constant rate but, the demand is a quadratic decreasing function of time in shortage period. The buyer's demand is a quadratic increasing function of time when shortage does not occur but at shortages period, the demand is constant. The buyer accepts an inspection policy for imperfect product. Total cost is calculated for both the model and integrated system. Thereafter, the model is solved by minimizing the total cost. Numerical examples are given to show the applicability of the model. A sensitivity analysis is done to display the realistic applicability of our model and method.