Inventory Models for Non-Instantaneous Deteriorating Items with Expiration Dates and Imperfect Quality under Hybrid Payment Policy in the Three-Level Supply Chain

Abstract

This article considers an inventory model for non-instantaneous deteriorating items with expiration dates, such as seasonal items, first-hand vegetables, and fruits. Interestingly, an inspection will be performed to manage the quality of the items during the state of no deterioration because it is difficult to purchase items with 100% perfection. Additionally, we assume that the upstream member has the power of controlling or influencing downstream members’ decisions. That is, the supplier asks the retailer for a partial advance payment to avoid cancellation of orders and offers them a credit payment to stimulate sales; in turn, the customer must pay some cash when placing an order and pay the remainder in credit for the retailer. The goal of this article is to determine an optimal replenishment cycle and the total annual cost function, so we explore the functional properties of the total annual cost function and show that the total annual cost function is convex. Theoretical analysis of the optimal properties shows the existence and uniqueness of the optimal solution. Then, we obtain simple and easy solution procedures for the inventory system. Moreover, numerical analysis of the inventory model is conducted, and the corresponding examples are considered with a view to illustrating the application of the supply chain model that we have investigated in this article. Finally, in the concluding section, we have not only provided the motivation and the need for our usages of mathematical analytic solution procedures based upon the convexity, monotonicity (increasing and decreasing) and differentiability properties of the object function (that is, the total annual cost function), which involve some symmetry aspects of the object function, but we have also indicated the limitations and shortcomings in our investigation, which will naturally lead to some potential directions for further research on the supply chain model, which we have considered and mathematically analyzed in this article.

Optimal replenishment policy for non‐instantaneous deteriorating items with stochastic demand under advance sales discount and available capacity

“…For further research, this paper can be extended to consider other realistic situations such as a finite rate of replenishment, quantity discounts, and the trade credit in a two-warehouse environment. In order to further motivate the interested readers, we choose to cite a number of other related recent works on the subject matter of this article such as those by AlArjani et al, 32 Chung et al, [33][34][35][36] Hou et al, 37 Liao et al, [38][39][40][41] Srivastava et al, [42][43][44] and many other authors (see, e.g., Wu et al 45 ).…”

Special Issue Editorial “Symmetric Distributions, Moments and Applications”

“…The goal of the paper "Inventory Models for Non-Instantaneous Deteriorating Items with Expiration Dates and Imperfect Quality under Hybrid Payment Policy in the Three-Level Supply Chain" [5] is to determine an optimal replenishment cycle and the total annual cost function by exploring the functional properties of the total annual cost function and showing that the total annual cost function is convex. Theoretical analysis of the optimal properties shows the existence and uniqueness of the optimal solution.…”

Two Level Trade Credit Policy Approach in Inventory Model with Expiration Rate and Stock Dependent Demand under Nonzero Inventory and Partial Backlogged Shortages

“…Aliabadi et al [43] solved a non-instantaneous deteriorating inventory problem with credit period and carbon emissions dependent demand by using a geometric programming approach. Liao et al [44] addressed an EOQ inventory model with a delay in payment policy for non-instantaneous deteriorating items with the aim of finding an optimal ordering policy. Shaikh et al [45] considered price-sensitive demand, inflation, and reliability in a production inventory model for deteriorating items under trade credit policy.…”