An Order Quantity Model for Delayed Deteriorating Items with Time-varying Demand Rate and Holding Cost, Complete Backlogging Rate and Two-level Pricing Strategies under Trade Credit Policy

Authors

  • Aisha Ahmed Madugu Department of Mathematics and Statistics, Umaru Musa Yar’adua University, Katsina, Nigeria.
  • Babangida Bature Department of Mathematics and Statistics, Umaru Musa Yar’adua University, Katsina, Nigeria. https://orcid.org/0000-0003-0533-0001
  • Ibrahim M. Idris Department of Mathematics and Statistics, Umaru Musa Yar’adua University, Katsina, Nigeria.
  • Mustapha Malumfashi Lawal Department of Mathematics and Statistics, Umaru Musa Yar’adua University, Katsina, Nigeria.

DOI:

https://doi.org/10.56919/usci.2323.022

Keywords:

Economic Order Quantity, Non- instantaneous deteriorating item, two-phase demand rates, Linear Holding, two-level pricing strategies, complete backlogging rate, Trade Credit Policy

Abstract

In some classical inventory models for non-instantaneous deteriorating items, it is tacitly assumed that the selling price before and after deterioration sets in is the same.  However, in real practice, when deterioration sets in, the retailer may decide to reduce the selling price to encourage more sales, reduce the cost of holding stock, attract new customers and reduce losses due to deterioration.  This research developed an economic order quantity model for non-instantaneous deteriorating items with two-phase demand rates, linear holding cost, complete backlogging rate and two-level pricing strategies under trade credit policy.  It is assumed that the holding cost is linear time-dependent, the unit selling price before deterioration sets in is greater than that after deterioration sets and the demand rate before deterioration sets in is considered as continuous time-dependent quadratic, after which it is considered as constant up to when the inventory is completely exhausted.  Shortages are allowed and completely backlogged.  The proposed model determines the optimal time with positive inventory, cycle length and order quantity such that the total profit of the inventory system has a maximum value.  The necessary and sufficient conditions for the existence and uniqueness of optimal solutions have been established.  Numerical experiments have been conducted to illustrate the theoretical result of the model.  Sensitivity analysis of some model parameters on the decision variables has been carried out, and suggestions towards maximising the total profit were also given.

References

Ahmed, Y. and Musa, A. (2016). Economic order quantity model for delayed deteriorating items with time dependent exponential declining demand and shortages. ABACUS: Journal of the Mathematical Association of Nigeria, 43(2), 14–24.

Babangida, B. and Baraya, Y. M. (2018). An inventory model for non-instantaneous deteriorating item with time dependent quadratic demand under trade credit policy. Journal of the Nigerian Association of Mathematical Physics, 47(4), 93–110.

Babangida, B. and Baraya, Y. M. (2019a). An inventory model for non-instantaneous deteriorating item with time dependent quadratic demand and linear holding cost under trade credit policy. ABACUS: Journal of the Mathematical Association of Nigeria, 46(1), 191–217.

Babangida, B. and Baraya, Y.M. (2019b). An inventory model for non-instantaneous deteriorating item with time dependent quadratic demand and complete backlogging under trade credit policy. ABACUS: Journal of the Mathematical Association of Nigeria, 46(1), 488–505.

Babangida B. and Baraya Y. M. (2020). An inventory model for non-instantaneous deteriorating items with time dependent quadratic demand, two storage facilities and shortages under trade credit policy. International Journal of Modelling in Operations Management, 8(1), 1-44. DOI: 10.1504/IJMOM.2020.10029879. https://doi.org/10.1504/IJMOM.2020.108893

Babangida B. and Baraya Y. M. (2021a). An EOQ model for non-instantaneous deteriorating items with two-phase demand rates and two level pricing strategies under trade credit policy. Transaction of the Nigerian Association of Mathematical Physics, 17(4), 117-130.

Babangida B. and Baraya Y. M. (2021b). An EOQ model for non-instantaneous deteriorating items with time dependent quadratic rate, linear holding cost and partial backlogging rate under trade credit policy. Transaction of the Nigerian Association of Mathematical Physics, 17(4), 131-144.

Babangida B. and Baraya Y. M. (2022). An EOQ model for non-instantaneous deteriorating items with two-phase demand rates, linear holding cost and time dependent partial backlogging rate under trade credit policy. ABACUS: Journal of the Mathematical Association of Nigeria, 49(2), 91-125.

Baraya, Y. M. and Sani, B. (2016). A deteriorating inventory model for items with constant demand rate under warehouse capacity constraint. ABACUS: Journal of the Mathematical Association of Nigeria, 43(2), 180–192.

Bello, Y. and Baraya, Y. M. (2018). An inventory model for non-instantaneous deteriorating item with two-phase demand rate and partial backlogging. Journal of the Nigerian Association of Mathematical Physics, 47(4), 77–86.

Bello, Y. and Baraya, Y. M. (2019). An inventory model for non-instantaneous deteriorating item with two-phase demand rates and exponential backlogging. ABACUS: Journal of the Mathematical Association of Nigeria, 46(1), 377–390.

Choudhury, K. D., Karmakar, B., Das, M. and Datta, T. K. (2013). An inventory model for deteriorating items with stock dependent demand, time-varying holding cost and shortages. Journal of the Operational Research Society, 23(1), 137–142. https://doi.org/10.1007/s12597-013-0166-x.

Covert, R. B. and Philip, G. C. (1974). An EOQ model with Weibull distribution deterioration. IIE Transactions, 5(4), 323–326.. https://doi.org/10.1080/05695557308974918

Deo, D. A., Yogendra, K. R., Neha, G., Yashpal, S. R., Rakesh, R., Rahul, B. and Ajay, K. (2022). Selling price, time dependent demand and variable holding cost inventory model with two storage facilities. Material today: Proceedings, 56(1), 245-251. https://doi.org/10.1016/j.matpr.2022.01.111

Geetha, K. V. and Uthayakumar, R. (2010). Economic design of an inventory policy for non-instantaneous deteriorating items under permissible delay in payments. Journal of Computational and Applied Mathematics, 233(10), 2492–2505.. https://doi.org/10.1007/s40819-015-0053-7

Geetha, K. V. and Udayakumar, R. (2016). Optimal lot sizing policy for non-instantaneous deteriorating items with price and advertisement dependent demand under partial backlogging. International Journal of Applied and Computational Mathematics, 2(1), 171–193. https://doi.org/10.1007/s40819-015-0053-x

Ghare, P. M. and Schrader, G. F. (1963). A model for an exponentially decaying inventory. Journal of Industrial Engineering, 14(5), 238–243.

Giri, B. C., Chakraborty, T. and Chaudhuri, K. S. (2000). A note on lot-sizing heuristic for deteriorating items with time-varying demands and shortages. Computers and Operations Research, 27(6), 495–505. https://doi.org/10.1016/S0305-0548(99)00013-1

Harris, F. (1913). How many parts to make at once, factory. The Magazine of Management, 10(2), 135–136.

Haley, C. W. and Higgins, R. C. (1973). Inventory policy and trade credit financing. Management Science, 20(4), 464–471. https://doi.org/10.1287/mnsc.20.4.464

Jaggi, C. K., Gupta, M. and Tiwari, S. (2019). Credit financing in economic ordering policies for deteriorating items with stochastic demand and promotional efforts in two-warehouse environment. International Journal of Operational Research, 35(4), 529–550. https://doi.org/10.1504/IJOR.2019.101459

Jaggi, C. K., Sharma, A. and Tiwari, S. (2015). Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand under permissible delay in payments: A new approach. International Journal of Industrial Engineering Computations, 6(4), 481–502. https://doi.org/10.5267/ijiec.2015.5.003

Kar, S., Bhunia, A. K. and Maiti, M. (2001). Deterministic inventory model with two-levels of storage, a linear trend in demand and a fixed time horizon. Computers and Operations Research, 28(13), 1315–1331. https://doi.org/10.1016/S0305-0548(00)00042-3

Khanra, S. and Chaudhuri, K. S. (2003). A note on an order level inventory model for a deteriorating item with time dependent quadratic demand. Computers and Operations Research, 30(12), 1901–1916. https://doi.org/10.1016/S0305-0548(02)00113-2

Malumfashi, M. L., Ismail, M. T., Bature, B., Sani, D. and Ali, M. K. M (2021). An EPQ model for delayed deteriorating items with two-phase production period, variable demand rate and linear holding cost. Modelling, Simulation and Applications of Complex Systems, Springer Proceedings in Mathematics and Statistics, 359, 351-380, https://doi.org/10.1007/978-981-16-2629-6_19

Mandal, D. and Venkataraman, S. V. (2019). A dynamic programming model for perishable inventory management. International Journal of Operational Research, 35(2), 147–177. https://doi.org/10.1504/IJOR.2019.10022433

Mustapha, L. M, and Majid, K. M. (2023). A Production inventory model for non-instantaneous deteriorating items with two phase production period stock-dependent demand and shortages, International Journal of Mathematics in Operational Research, 24(2), 173-193. https://doi.org/10.1504/IJMOR.2023.129432

Malumfashi, M. L., Ismail, M. T., & Ali, M. K. M. (2022). An EPQ Model for Delayed Deteriorating Items with Two-Phase Production Period, Exponential Demand Rate and Linear Holding Cost. Bulletin of the Malaysian Mathematical Sciences Society, 45(Suppl 1), 395-424. https://doi.org/10.1007/s40840-022-01316-x

Pang, C. L., Chao, K. H., Meng, Y. K. and Indriani (2022). An inventory model for perishable item with two-stage pricing. Journal of Information and Optimization Sciences, 43(8), 2021-2030. https://doi.org/10.1080/02522667.2022.2083825

Philip, G. C. (1974). A generalized EOQ model for items with Weibull distribution. AIIE Transactions, 6(2), 159–162. https://doi.org/10.1080/05695557408974948

Priya, R. K. and Senbagam, K. (2018). An EOQ inventory model for two parameter Weibull deterioration with quadratic time dependent demand and shortages. International Journal of Pure and Applied Mathematics, 119(7), 467–478.

Rahman, M. A. and Uddin, M. F. (2021). Analysis of inventory model with time dependent quadratic demand function including time variable deterioration rate without shortage. Asian Research Journal of Mathematics, 16(12), 97-109.. https://doi.org/10.9734/arjom/2020/v16i1230258

Roy, A. (2008). An inventory model for deteriorating items with price dependent demand and time-varying holding cost. Advance Modelling and Optimization, 10(1), 25–37.

Selvaraju, P. and Ghuru, S. K. (2018). EOQ models for deteriorative items with constant, linear and quadratic holding cost and shortages - a comparative study. International Journal of Operational Research, 33(4), 462–480. https://doi.org/10.1504/IJOR.2018.096487

Shaikh, A. A., Tiwari, S. and Cárdenas-Barrón, L. E. (2018). Closed-form solutions for the EPQ-based inventory model for exponentially deteriorating items under retailer partial trade credit policy in supply chain. International Journal of Applied and Computational Mathematics, 4(2), 1–9. https://doi.org/10.1007/s40819-018-0504-z

Tripathy, M., Sharma, G. and Sharma, A. K. (2022). An inventory model for non-instantaneous deteriorating item with constant demand under progressive financial trade credit facility. OPSEARCH, 59, 1215-1243. https://doi.org/10.1007/s12597-022-00573-5

Uthayakumar, R. and Karuppasamy, S. K. (2017). An inventory model for variable deteriorating pharmaceutical items with time dependent demand and time dependent holding cost under trade credit in healthcare industries. Communications in Applied Analysis, 21(4), 533–549. https://doi.org/10.1007/978-981-10-4555-4_13

Udayakumar. R. (2022).An EOQ model for non-instantaneous deteriorating items with time-dependent demand under partial backlogging. Journal of Management Analytics, 9(4), 514-531. https://doi.org/10.1080/23270012.2022.2073571

Whitin, T. M. (1957). Theory of inventory management. Princeton University Press, Princeton.

Wu, K. S., Ouyang, L. Y. and Yang, C. T. (2006). An optimal replenishment policy for non-instantaneous deterioration items with stock dependent demand and partial backlogging. International Journal of production Economics, 101(2), 369–384. https://doi.org/10.1016/j.ijpe.2005.01.010

Downloads

Published

2023-09-30

How to Cite

Madugu, A. A., Bature, B., Idris, I. M., & Lawal, M. M. (2023). An Order Quantity Model for Delayed Deteriorating Items with Time-varying Demand Rate and Holding Cost, Complete Backlogging Rate and Two-level Pricing Strategies under Trade Credit Policy. UMYU Scientifica, 2(3), 165–180. https://doi.org/10.56919/usci.2323.022