Inventory Model and Pricing in the Supply Chain Approach VMI Considering Incremental Discount

Document Type : Original Article


Industrial Engineering Group، Abhar Branch، Islamic Azad University، Abhar، Iran


Given the globalization of competition and the existence of many rivals, the optimization supply chain has been highly regarded. One of the key issues in optimizing supply chain is to increase profitability and cost reduction. Since inventories have a large part of the cost of supply chain, the determination of the optimal level of inventory can have an effective role in cost reductions. In addition to costs reduction, attracting a larger share of the demand market can increase profitability. One of the effective factors in attracting customers is market price. On the other hand, discounts on the supply chain will encourage more buy and, of course, buy will further increase the costs. Therefore, this article addresses the issues of simultaneous pricing and inventory control in a supply chain bi-level, and optimal buy policy the mode of existence of incremental discounts and optimal pricing policies has been determined. In this regard, the mathematical model and numerical examples have been solved.


  • Kamkar Yazdannezhad, L. (2006) " The ratio of Arts and mental health improvement of children." Master of Arts thesis. Tehran: Faculty of Art and Architecture; Islamic Azad University; Central Tehran Branch.
  • Dadsetan P;. (2011). "Evaluation of children's character based graphical tests." Sixth edition. Tehran: Roshd Publications.
  • Oliverio Ferraris, A; (1996). "Children's painting and its concepts." Translated by Sarafan A. (2009). Tenth Edition. Tehran: Dastan publications
  • Thomas, J, and Silk, A. M. J. (1990). " An Introduction to the Psychology of Children's Drawings." New York: Harvester Wheatsheaf Translated by Faramarzi (2010). Fifth Edition. Tehran: Nashr-e –Donyae No.
  • A .(2006). Neuropsychology & Art. USA: Psychology press.
  • Case, C, Dalley, T. (2008). »Art Therapy with children from Infancy to Adolescence« .USA & UK: Newyork & London : Routledge.
  • Oliverio Ferraris, Anna; Significa to deL disegno infantile; 1996
  • Case, C, Dalley, T. (2006). Working with children in Art Therapy. 2end Ed. London: Rutledge.
  • Case, C, Dalley, T. (2006). The Handbook of Art Therapy. 2nd ed. London: Routledge.
  • Rajabi Behjat, b. (2011). Design and testing an art therapy program to improve social interaction of 6 – 12- year autistic students; Master's thesis in psychology. Tehran: Faculty of Psychology and Educational Sciences, Al-Zahra University.
  • Silvers J. (2008). "Art therapy for Autistic Children and adolescents." Translated by Tavakoli Toroghi. A. Shafieefar, A. (2013). Tehran: Fararavan.
  • Martin, N. (2009). Art Therapy & Autism: overview & Recommendations. Art Therapy : journal of the American Art Therapy Association, 26 (4) , 187-190.
  • Landgartn, H. B. (2003). "The Art of clinical treatment." Translated by K. Hashemian,. Abu Hamza. (2008). second edition. Tehran: Danzheh Publication
  • Ganji, M. (2013). "Psychopathology according to DSMV». Volume II. Third edition. Tehran: Publication of Savalan.
  • Wall, k. (2004) "Education and care of adolescents and adults with autism- guide for parents and professionals." Translated by A. Jahanian najafabadi; H. Aflakian. (2009). Tehran: Danzheh
  • Wall, K. (2004). Autism & Early years practice. London: paul, chapman.
  • Ahmadi, S J; Safari, T; Hemmatian, M; Khalili, Z. (2011). Evaluation of psychometric indicators OF diagnostic test for autism (Gars). Majaleh Pajooheshhaeh Olom Shenakhti va Raftari (Journal of Cognitive and Behavioral Sciences' Studies) (in Persian). fall and winter 2011; (1) pp 87-104.
  • American Art Therapy Association. (2009). »About Art Therapy.« Retrieved February. 17, 2009. From art.html.