scholarly journals Impact of cost of substitution and joint replenishment on inventory decisions for joint substitutable and complementary items under asymmetrical substitution

2020 ◽  
Vol 11 (2) ◽  
pp. 1
Author(s):  
Rajesh Kumar Mishra ◽  
Vinod Kumar Mishra
Keyword(s):  
Sensitivity Analysis ◽  
Solution Procedure ◽  
Substantial Improvement ◽  
Inventory Model ◽  
Inventory Cost ◽  
Joint Replenishment ◽  
Total Inventory ◽  
Inventory Decisions ◽  
Optimal Ordering ◽  
Cost Of Substitution

<p>In this paper, impact of cost of substitution and joint replenishment on inventory decisions for joint substitutable and complementary items under asymmetrical substitution has been studied. The phenomenon of substitution is considered in a stock-out situation and when items become out of stock due to demand then unfulfilled demand is asymmetrically substituted by another item. We formulate the inventory model mathematically and derived optimal ordering quantities, optimal total costs and extreme value of substitution rate for all possible cases. Moreover, pseudo-convexity of the total inventory cost function is obtained and the solution procedure is provided. Numerical example and sensitivity analysis have been presented to validate the effectiveness of the inventory model and substantial improvement in total optimal inventory cost with substitution with respect to optimal total inventory cost without substitution is seen.</p><p><em><br /></em></p>

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.

scholarly journals Inventory model for deteriorating items with negative exponential demand, probabilistic deterioration and fuzzy lead time under partial back logging

2020 ◽  
Vol 30 (3) ◽  
Author(s):  
Nabendu Sen ◽  
Sumit Saha
Keyword(s):  
Inventory Management ◽  
Lead Time ◽  
Probability Distributions ◽  
Optimal Strategies ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Optimal Time ◽  
Inventory Cost ◽  
Total Inventory ◽  
Negative Exponential

The effect of lead time plays an important role in inventory management. It is also important to study the optimal strategies when the lead time is not precisely known to the decision makers. The aim of this paper is to examine the inventory model for deteriorating items with fuzzy lead time, negative exponential demand, and partially backlogged shortages. This model is unique in its nature due to probabilistic deterioration along with fuzzy lead time. The fuzzy lead time is assumed to be triangular, parabolic, trapezoidal numbers and the graded mean integration representation method is used for the defuzzification purpose. Moreover, three different types of probability distributions, namely uniform, triangular and Beta are used for rate of deterioration to find optimal time and associated total inventory cost. The developed model is validated numerically and values of optimal time and total inventory cost are given in tabular form, corresponding to different probability distribution and fuzzy lead-time. The sensitivity analysis is performed on variation of key parameters to observe its effect on the developed model. Graphical representations are also given in support of derived optimal inventory cost vs. time.

scholarly journals Inventory Model with Partial Backordering When Backordered Customers Delay Purchase after Stockout-Restoration

2016 ◽  
Vol 2016 ◽  
pp. 1-16
Author(s):  
Ren-Qian Zhang ◽  
Yan-Liang Wu ◽  
Wei-Guo Fang ◽  
Wen-Hui Zhou
Keyword(s):  
Layer Structure ◽  
Inventory Model ◽  
Inventory Cost ◽  
Cost Component ◽  
Lipschitz Optimization ◽  
Partial Backordering ◽  
Demand Rate ◽  
Holding Cost ◽  
Total Inventory ◽  
Inventory Holding

Many inventory models with partial backordering assume that the backordered demand must be filled instantly after stockout restoration. In practice, however, the backordered customers may successively revisit the store because of the purchase delay behavior, producing a limited backorder demand rate and resulting in an extra inventory holding cost. Hence, in this paper we formulate the inventory model with partial backordering considering the purchase delay of the backordered customers and assuming that the backorder demand rate is proportional to the remaining backordered demand. Particularly, we model the problem by introducing a new inventory cost component of holding the backordered items, which has not been considered in the existing models. We propose an algorithm with a two-layer structure based on Lipschitz Optimization (LO) to minimize the total inventory cost. Numerical experiments show that the proposed algorithm outperforms two benchmarks in both optimality and efficiency. We also observe that the earlier the backordered customer revisits the store, the smaller the inventory cost and the fill rate are, but the longer the order cycle is. In addition, if the backordered customers revisit the store without too much delay, the basic EOQ with partial backordering approximates our model very well.

scholarly journals Two warehouse inventory model for deteriorating item with exponential demand rate and permissible delay in payment

2017 ◽  
Vol 27 (1) ◽  
pp. 109-124 ◽  
Author(s):  
Naresh Kaliraman ◽  
Ritu Raj ◽  
Shalini Chandra ◽  
Harish Chaudhary
Keyword(s):  
Sensitivity Analysis ◽  
Inventory Model ◽  
Deteriorating Items ◽  
The Other ◽  
Inventory Cost ◽  
Numerical Illustration ◽  
Deterioration Rate ◽  
Permissible Delay In Payment ◽  
Demand Rate

A two warehouse inventory model for deteriorating items is considered with exponential demand rate and permissible delay in payment. Shortage is not allowed and deterioration rate is constant. In the model, one warehouse is rented and the other is owned. The rented warehouse is provided with better facility for the stock than the owned warehouse, but is charged more. The objective of this model is to find the best replenishment policies for minimizing the total appropriate inventory cost. A numerical illustration and sensitivity analysis is provided.

scholarly journals Determining the Efficiency of Fuzzy Logic EOQ Inventory Model with Varying Demand in Comparison with Lagrangian and Kuhn-Tucker Method Through Sensitivity Analysis

2020 ◽  
Vol 1 (3) ◽  
pp. 1-12
Author(s):  
K. Kalaiarasi ◽  
M. Sumathi ◽  
H. Mary Henrietta ◽  
A. Stanley Raj
Keyword(s):  
Sensitivity Analysis ◽  
Fuzzy Logic ◽  
Fuzzy Numbers ◽  
Solution Procedure ◽  
Inventory Model ◽  
Variable Demand ◽  
Holding Costs ◽  
Purchase Cost ◽  
Fuzzy Logic Analysis ◽  
Varying Demand

This paper considers an EOQ inventory model with varying demand and holding costs. It suggests minimizing the total cost in a fuzzy related environment. The optimal policy for the nonlinear problem is determined by both Lagrangian and Kuhn-tucker methods and compared with varying price-dependent coefficient. All the input parameters related to inventory are fuzzified by using trapezoidal numbers. In the end, a numerical example discussed with sensitivity analysis is done to justify the solution procedure. This paper primarily focuses on the aspect of Economic Order Quantity (EOQ) for variable demand using Lagrangian, Kuhn-Tucker and fuzzy logic analysis. Comparative analysis of there methods are evaluated in this paper and the results showed the efficiency of fuzzy logic over the conventional methods. Here in this research trapezoidal fuzzy numbers are incorporated to study the price dependent coefficients with variable demand and unit purchase cost over variable demand. The results are very close to the crisp output. Sensitivity analysis also done to validate the model.

scholarly journals Controllable deterioration rate for time-dependent demand and time-varying holding cost

2014 ◽  
Vol 24 (1) ◽  
pp. 87-98 ◽  
Author(s):  
Vinod Mishra
Keyword(s):  
Linear Function ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Inventory Cost ◽  
Deterioration Rate ◽  
Preservation Technology ◽  
Demand Rate ◽  
Holding Cost ◽  
Total Inventory ◽  
Dependent Demand

In this paper, we develop an inventory model for non-instantaneous deteriorating items under the consideration of the facts: deterioration rate can be controlled by using the preservation technology (PT) during deteriorating period, and holding cost and demand rate both are linear function of time, which was treated as constant in most of the deteriorating inventory models. So in this paper, we developed a deterministic inventory model for non-instantaneous deteriorating items in which both demand rate and holding cost are a linear function of time, deterioration rate is constant, backlogging rate is variable and depend on the length of the next replenishment, shortages are allowed and partially backlogged. The model is solved analytically by minimizing the total cost of the inventory system. The model can be applied to optimizing the total inventory cost of non-instantaneous deteriorating items inventory for the business enterprises, where the preservation technology is used to control the deterioration rate, and demand & holding cost both are a linear function of time.

Penurunan Biaya Persediaan dengan Metode Joint Replenishment Multi Item Single Supplier

2018 ◽  
Vol 11 (2) ◽  
Author(s):  
Donny Montreano
Keyword(s):  
Stock Exchange ◽  
Complete Information ◽  
Simple Calculation ◽  
Raw Material ◽  
Sufficient Information ◽  
Inventory Cost ◽  
Joint Replenishment ◽  
Tissue Printing ◽  
Total Inventory ◽  
Printing Paper

The purpose of this research is to describe multi-item ordering method (Goyal, 1974) by providing a complete information of algorithm on each step. The journal itself doesn’t contain sufficient information on its example, and there is an error on a simple calculation. We observed a pulp manufacturer as raw material for making paper, tissue, printing paper and non-printing paper. There were 3 materials that purchased from a supplier and had been overstock in 2016. The materials will be examined by this method in order to reduce overstock. The results are shows that there is about 91% of the total inventory cost discrepancy between that period of total inventory cost and these methods of total inventory cost. This cost saving can be used for other investigation, for example, Indonesian Ritel Obligation or stock exchange.

Two-Echelon Inventory Stochastic Model of Supply Chain Based on Service Level Constraints

2014 ◽  
Vol 971-973 ◽  
pp. 2448-2451
Author(s):  
Da Li Jiang ◽  
Guang Fu Zhu ◽  
De Li
Keyword(s):  
Supply Chain ◽  
Stochastic Model ◽  
Service Level ◽  
Inventory Model ◽  
Inventory Level ◽  
Effective Algorithm ◽  
Inventory Cost ◽  
Total Inventory

The study on multi-echelon inventory of supply chain is becoming more and more important in E-business era. This paper proposes a two-echelon inventory model with one supplier and several retailers, in which a certain service level has to be satisfied and the goal is to minimize the total inventory cost. In addtion it puts forward an effective algorithm for this model to obtain the optimal replenishment period and inventory level of each supply chain node.

Inventory Planning with Method Q and Method P for Probabilistic Demand on Chrysanthemum Seeds at PT Transplants Indonesia

2019 ◽  
Vol 3 (01) ◽  
pp. 57
Author(s):  
Akhmad Sutoni ◽  
Dani Hamdan Taufik
Keyword(s):  
Inventory Model ◽  
Inventory Systems ◽  
Uncertain Demand ◽  
Q Method ◽  
Inventory Cost ◽  
Agricultural Cooperative ◽  
Total Inventory ◽  
The Right ◽  
Cooperative Association ◽  
A Company

Fluctuating and uncertain demand is a problem faced by manufacturing firms. The problem can be mitigated by the availability of inventory systems. This inventory serves to ensure the availability of appropriate resources in the right quantity and at the right time, so as to minimize the costs incurred. PT. Transplants Indonesia is a company engaged in the business of chrysanthemum flower in Indonesia. PT. Transplants Indonesia is a subsidiary of Okinawa Flower Agricultural Cooperative Association (OKF) in Okinawa, Japan. The purpose of this company establishment is to meet the demand of farmers who are members of the OKF. In the case of backorder, on Q method with probabilistic request the size of the lottery (Q) is always fixed for every time the order is made and the order is made if the amount of inventory has reached a certain level (r) called the reorder point. In method P with probabilistic order requests made according to a fixed interval of time (T) and the ordering does not exceed the maximum inventory limit (R). Total Inventory cost incurred by the company using the method used by the company amounted to Rp.74.995.360,84. The inventory model using the Q method generates a total inventory cost of Rp.70.253.291,46. Meanwhile, inventory model using P method resulted in total inventory cost of Rp.71.529.327,17. So economically, the selected inventory model is the inventory model with the Q method which has a lower total inventory cost value than using the P method.

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