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An optimal inventory model for perishable items under successive price discounts with permissible delay in payments

  • Bhaskar Bhaula
  • Jayanta Kumar Dash
  • M. Rajendra Kumar
Application Article


This article derives an optimal ordering policy for non-instantaneously deteriorating items under successive price discounts with delay in payments. Here successive price discounts is a strategy to sell almost all the items before decomposition. The cause of implementing this concept in the model is the fact that about 25% of vegetables and fruits of India gets decayed before selling, due to lack of facilities and awareness of business strategies, although poverty is its vital factor. Thus we propose to offer successive price discounts of 20% and 40% after selling the stock up to 50% and 90% respectively to raise the customer’s inflow and so also rotate the cycle early to avoid more deterioration. This type of business not only reduces the factory of decomposability but also saves the holding cost partially. In addition to, the delay in payment is another business strategy of the wholesaler by which he keeps the retailers in track and so also reduces the holding cost. In this case the wholesaler offers an interest-free credit period to the retailers till the settlement of the accounts. The retailers earn interest on selling the revenue during this opportunity. Supplier charges interest on the outstanding balance after exceeding the period. Besides the above, again the inventory cost does not remaining constant due to various factors like inflation, salary, house rent etc. so a time varying holding cost has been well thought out instead of constant holding cost. Once more customers’ flow not only depends upon the price instigating but also on timings, hence we assume an exponential demand function which depends on these variables. The main idea of the task is to determine optimal selling price, optimal refill schedule and optimal ordering quantity such that the total profit is maximized under exponential constraints. The literal idea of the work is (a) to avoid the deterioration through successive price discounts, (b) to attract the customers through successive price discounts, (c) to sell all the items through successive price discounts, (d) to rotate the cycle early through successive price discounts, (e) to keep the retailers in track through delay in payment, (f) to keep variable holding cost instead of constant holding cost due to market inflation, (g) to get the optimum results under exponential constraints.


Inventory Price and time dependent exponential demand Successive price discounts Time varying holding cost 



The authors would like to thank all the anonymous reviewers and the associate editor for their valuable and constructive suggestions to improve the quality of the manuscript. We would also like to thank our management for their kind cooperation and encouragement.


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Copyright information

© Operational Research Society of India 2019

Authors and Affiliations

  • Bhaskar Bhaula
    • 1
  • Jayanta Kumar Dash
    • 2
  • M. Rajendra Kumar
    • 2
  1. 1.Department of MathematicsNational Institute of Science & Technology (Autonomous)BerhampurIndia
  2. 2.Department of MathematicsSiksha ‘O’ Anusandhan University (Deemed to be University)BhubaneswarIndia

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