scholarly journals An inventory model for deteriorating items with exponential declining demand and partial backlogging

2005 ◽  
Vol 15 (2) ◽  
pp. 277-288 ◽  
Author(s):  
Liang-Yuh Ouyang ◽  
Kun-Shan Wu ◽  
Mei-Chuan Cheng
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Cost Function ◽  
Waiting Time ◽  
Optimal Solution ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Partial Backlogging ◽  
Numerical Example ◽  
Declining Demand

This study proposes an EOQ inventory mathematical model for deteriorating items with exponentially decreasing demand. In the model, the shortages are allowed and partially backordered. The backlogging rate is variable and dependent on the waiting time for the next replenishment. Further, we show that the minimized objective cost function is jointly convex and derive the optimal solution. A numerical example is presented to illustrate the model and the sensitivity analysis is also studied.

scholarly journals An Inventory Model under Trapezoidal Type Demand, Weibull-Distributed Deterioration, and Partial Backlogging

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Lianxia Zhao
Keyword(s):  
Sensitivity Analysis ◽  
Waiting Time ◽  
Optimal Solution ◽  
Inventory Model ◽  
Partial Backlogging ◽  
Inventory Models ◽  
Numerical Examples ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Theoretical Results

This paper studies an inventory model for Weibull-distributed deterioration items with trapezoidal type demand rate, in which shortages are allowed and partially backlogging depends on the waiting time for the next replenishment. The inventory models starting with no shortage is are to be discussed, and an optimal inventory replenishment policy of the model is proposed. Finally, numerical examples are provided to illustrate the theoretical results, and a sensitivity analysis of the major parameters with respect to the optimal solution is also carried out.

scholarly journals An Inventory Model for Deteriorating Items with Stock Dependent Demand and Partial Backlogging

2021 ◽  
Vol 9 (12) ◽  
pp. 296-302
Author(s):  
Vikas Kumar
Keyword(s):  
Waiting Time ◽  
Simple Algorithm ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Partial Backlogging ◽  
Numerical Examples ◽  
Proposed Model ◽  
Stock Dependent Demand ◽  
Total Profit ◽  
Dependent Demand

Abstract: In this paper, we formulate a deteriorating inventory model with stock-dependent demand Moreover, it is assumed that the shortages are allowed and partially backlogged, depending on the length of the waiting time for the next replenishment. The objective is to find the optimal replenishment to maximizing the total profit per unit time. We then provide a simple algorithm to find the optimal replenishment schedule for the proposed model. Finally, we use some numerical examples to illustrate the model. Keywords- Inventory, Deteriorating items, Stock dependent demand, Partial backlogging

scholarly journals An Inventory Model for Deteriorating Items with Quantity Dependent Permissible Delay in Payment and Partial Backlogging of Shortage

2007 ◽  
Vol 59 (3-4) ◽  
pp. 239-252
Author(s):  
Manisha Pal ◽  
Sanjoy Kumar Ghosh
Keyword(s):  
Waiting Time ◽  
Fixed Time ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Partial Backlogging ◽  
Single Item ◽  
Credit Period ◽  
Numerical Examples ◽  
Time Period ◽  
Permissible Delay In Payment

Abstract: In many inventory situations, instead of making immediate payment on receiving the consigument, the purchaser is allowed a certain fixed time period to pay for the goods bought. During this time the supplier charges no interest, but beyond this period interest is charged under the terms and condition agreed upon. As for the purchaser, he can earn interest on the revenue coolected during the credit period. This paper studies a single item inventory model for deteriorating items, when the permissible delay in payment depends on the ordered quantity and shortages are partially backlogged, assuming the backlogging rate to be inversely proportional to the waiting time for the next replenishment. An algorithm has been developed to find the optimal inventory policy. Numerical examples have been cited to illustrate the model. AMS (2000) Subject Classification: 90B05.

scholarly journals A partial backlogging inventory model for non-instantaneous deteriorating items with stock-dependent consumption rate under inflation

2010 ◽  
Vol 20 (1) ◽  
pp. 35-54 ◽  
Author(s):  
Jinh Chang ◽  
Feng Lin
Keyword(s):  
Solution Process ◽  
Optimal Solution ◽  
Planning Horizon ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Optimal Order ◽  
Partial Backlogging ◽  
Demand Rate ◽  
Dependent Demand Rate ◽  
Dependent Demand

In this paper, we derive a partial backlogging inventory model for noninstantaneous deteriorating items with stock-dependent demand rate under inflation over a finite planning horizon. We propose a mathematical model and theorem to find minimum total relevant cost and optimal order quantity. Numerical examples are used to illustrate the developed model and the solution process. Finally, a sensitivity analysis of the optimal solution with respect to system parameters is carried out.

scholarly journals An Inventory Model for Deteriorating Items With Exponential Declining Demand and Return

2020 ◽  
Vol 20 (1) ◽  
pp. 31
Author(s):  
Fadli Fadli ◽  
Sudarajat Sudrajat ◽  
E. Lesmana
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Demand Function ◽  
Return Time ◽  
Optimal Number ◽  
Deteriorating Items ◽  
Total Cost ◽  
Deterioration Rate ◽  
Declining Demand ◽  
Constant Deterioration

In this paper propose an EOQ mathematical model for deteriorating items. The model is developed with a demand function that decreases exponentially, a constant deterioration rate, a shortage is permitted, and a return occurs. The purpose of this model is to determine the minimum total cost by determining the optimal return time and the optimal number of orders. A numerical example is given to describe the working model. Furthermore, a sensitivity analysis was conducted to see the effect of changing parameters on the optimal solution.Keywords: Deteriorating item, inventory, return, shortageModel Persediaan Deteriorasi Item Dengan Exponential Declining Demand dan ReturnABSTRAKDalam makalah ini mengusulkan model matematika EOQ untuk item yang mengalami deteriorasi. Model ini dikembangkan dengan fungsi permintaan yang menurun secara eksponensial, laju deteriorasi konstan, kekurangan diizinkan, dan terjadi pengembalian. Tujuan dari model ini adalah untuk menentukan biaya total minimum dengan menentukan waktu pengembalian optimal dan jumlah pesanan optimal. Contoh numerik diberikan untuk menggambarkan model bekerja. Selanjutnya, analisis sensitivitas dilakukan untuk melihat efek perubahan parameter pada solusi optimal.Kata kunci: Deteriorasi item, persediaan, pengembalian, kekurangan

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

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1695
Author(s):  
Jui-Jung Liao ◽  
Hari Srivastava ◽  
Kun-Jen Chung ◽  
Shih-Fang Lee ◽  
Kuo-Nan Huang ◽  
...  
Keyword(s):  
Supply Chain ◽  
Cost Function ◽  
Annual Cost ◽  
Optimal Solution ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Total Annual Cost ◽  
Chain Model ◽  
Object Function ◽  
Supply Chain Model

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.

Sustainable optimal ordering quantity for non-instantaneous deteriorating items under joint replenishment with substitution and carbon emission

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ranu Singh ◽  
Vinod Kumar Mishra
Keyword(s):  
Cost Function ◽  
Carbon Emission ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Joint Replenishment ◽  
Content Type ◽  
Total Cost ◽  
Optimal Ordering ◽  
Ordering Quantity ◽  
Total Cost Function

Purpose Carbon emission is a significant issue for the current business market and global warming. Nowadays, most countries have focused to reduce the environmental impact of business with durable financial benefits. The purpose of this study is to optimize the entire cost functions with carbon emission and to find the sustainable optimal ordering quantity for retailers. Design/methodology/approach This paper illustrates a sustainable inventory model having a set of two non-instantaneous substitutable deteriorating items under joint replenishment with carbon emission. In this model demand and deterioration rate are considered as deterministic, constant and triangular fuzzy numbers. The objective is to find the optimal ordering quantity for retailers and to minimize the total cost function per unit time with carbon emission. The model is then solved with the help of Maple software. Findings This paper presents a solution method and also develop an algorithm to determine the order quantities which optimize the total cost function. A numerical experiment illustrates the improvement in optimal total cost of the inventory model with substitution over without substitution. The graphical results show the convexity of the cost function. Finally, sensitivity analysis is given to get the impact of parameters and validity of the model. Originality/value This study considers a set of two non-instantaneous substitutable deteriorating items under joint replenishment with carbon emission. From the literature review, in the authors’ knowledge no researcher has undergone this kind of study.

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