A Discount Technique-Based Inventory Management on Electronics Products Supply Chain
1. Introduction and Literature Review
- It critically evaluates when one needs to impose a discount and when to not, especially when a bulk purchase has been made by a retailer with a huge investment in a limited storage shop in a highly expensive location.
- A synergy between stock, price, and time-dependent demand and implications of discount policy has been meticulously explained.
- A sensitivity analysis with some theoretical findings has been suggesting to achieve the maximum profit in the chain for the managers of the industry and shown a threshold point of discount offered time.
1.1. Literature Review
1.1.1. Influence of Stock Dependent Demand on Traditional Inventory Model
1.1.2. Influence of Price Sensitive Demand on Tradition Inventory Model
1.1.3. Influence of Sensitiveness of Time on Traditional Inventory Mode
1.1.4. Impacts of Discount Policy on Electronic Products
2. Assumption and Notations
- The replenishment rate is infinite and Lead-time is negligible.
- This model is for a single type of item.
- The planning horizon is considered infinite.
- In this paper, the demand function comprises price, time, and stock-dependence in the form ofis the initial rate of demandis the rate decrease demand on pricesis the product priceis the discount rate on price of productis the rate with which the demand rate increases on timeis the rate of changes of rate on time in the demand rate itselfis the rate depending on stock,
- There are no shortages considered in this model.
3. Mathematical Formulation for Proposed Electronics Product Inventory Model
3.1. Solution of Differential Equations from (1) and (2)
3.2. The Total Cost per Unit Time per Cycle
- Ordering cost per cycle =
- Holding cost (HC) =i.e.,
- Purchase cost (PC) =
- Transportation cost (TC) =
- Sales revenue (SR) =
4. Theoretical Derivations
4.1.1. Algorithm for Single Decision Variable
- Step 1.
- Input all the parameters value ().
- Step 2.
- Evaluate the value of from Equation (13).
- Step 3.
- Evaluate the value of ω from Equation (12) using all the parameters and the value of p*.
- Step 4.
- Output the value of p* and ω.
- Step 5.
4.1.2. Algorithm for Double Decision Variable
- Step 1.
- Declare and from Equations (18) and (19).
- Step 2.
- Input all the parameters value ().
- Step 3.
- Take where and iterative variable .
- Step 4.
- Step 5.
- IF and , Go to Setp 3. And IF and Go to Step 10.
- Step 6.
- Find and
- Step 7.
- Set and .
- Step 8.
- If and , Go to Step 10 ( is small value).
- Step 9.
- Update and . Go to Step 4.
- Step 10.
- Evaluate from Equation (12).
- Step 11.
- Output the value of and .
- Step 12.
4.2. Case Study
4.3. Numerical Illustration:
4.4. Sensitivity Analysis
- When the ordering cost (C) of the system increased, the selling price (p) and as well as the cycle length (T) of the chain were raised. This happens because a higher ordering cost brings a more considerable lot and intensifies the total cost of the business. As a result, the retailer will need to sell his products at a comparatively higher selling price, and as the lot is massive so it is challenging to sell the products quickly. However, the profits without discount and with discount were increased.
- With the intensification of purchase costs, the profit was decreasing. However, the selling price and total cycle length also increased. If a retailer purchased any item at a high price to maintain the profit margin, he needs to sell it at a high price. Moreover, an increase in stock provides fluctuations in the profit and selling price of the system.
- The profit becomes lower with the upsurge of the per-unit holding cost of the item. Moreover, it increases the selling price (p) and cycle length (T) of the system. Furthermore, the increase in initial demand parameter (a) provides a more significant profit than usual. In contrast, an increase in another parameter (b) will give a decrease in profit.
- The increase of the rate of change of demand rate () provides a lower profit for the system while it is vice versa for the increasing rate of demand parameter (). The profit of the chain decreased with the increase of the period (). However, the rate depending on stock (s) when increased the system’s profit has been reduced. A significant change in profit has been noticed with variable transportation () and fixed transportation (). However, for both costs, the retailer’s profit margin slightly drops due to the excessive expenses in the transportation system.
Data Availability Statement
Conflicts of Interest
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|$/Cycle||Ordering cost per cycle|
|$/Unit||Purchasing cost per unit|
|$/Unit||Holding cost per unit per unit time|
|Units/Cycle||Ordering quantity per cycle|
|$/Cycle||Fixed transportation cost|
|$/unit||Variable transportation cost|
|Months||Discount time from the beginning of cycle|
|Units||inventory level at any time t where when i = 1, when i = 2|
|Constant||Discount rate on price of product|
|$/Month||Total profit per unit time|
|$/Unit||Selling price per unit of product|
|N.B. (…) means infeasible solution|
|Parameter||% Change||With Discount||Without Discount|
|N.B. (…) means infeasible solution|
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Miah, M.S.; Islam, M.M.; Hasan, M.; Mashud, A.H.M.; Roy, D.; Sana, S.S. A Discount Technique-Based Inventory Management on Electronics Products Supply Chain. J. Risk Financial Manag. 2021, 14, 398. https://doi.org/10.3390/jrfm14090398
Miah MS, Islam MM, Hasan M, Mashud AHM, Roy D, Sana SS. A Discount Technique-Based Inventory Management on Electronics Products Supply Chain. Journal of Risk and Financial Management. 2021; 14(9):398. https://doi.org/10.3390/jrfm14090398Chicago/Turabian Style
Miah, Md. Sujan, Md. Mominul Islam, Mahmudul Hasan, Abu Hashan Md. Mashud, Dipa Roy, and Shib Sankar Sana. 2021. "A Discount Technique-Based Inventory Management on Electronics Products Supply Chain" Journal of Risk and Financial Management 14, no. 9: 398. https://doi.org/10.3390/jrfm14090398