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 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.

scholarly journals A Procedure for Scheduling Inventory of an Industry by Merging Forecasting and Linear Programming

2020 ◽  
Vol 68 (1) ◽  
pp. 65-70
Author(s):  
AKM Selim Reza ◽  
Sayma Suraiya ◽  
M Babul Hasan
Keyword(s):  
Linear Programming ◽  
Raw Materials ◽  
Minimum Cost ◽  
Inventory Cost ◽  
Model Combining ◽  
Forecasting Method ◽  
Holding Cost ◽  
Optimum Order ◽  
Total Inventory ◽  
Inventory Holding

In this paper, we develop a mathematical model combining forecasting and linear programming for a business organization of Bangladesh to calculate optimum order quantity and inventory cost. We test the model using raw data of the demand for the raw materials and spare inventory for the industry and find out minimum total inventory cost along with ordering cost and inventory holding cost. The developed model make a match between the forecasted demand of raw materials and spare inventory and the minimum total cost of inventory. Finally comparing minimum cost, we observe that our estimated appropriate forecasting method gives optimal inventory cost. Dhaka Univ. J. Sci. 68(1): 65-70, 2020 (January)

scholarly journals Inventory Model for Three–parameter Weibull Deterioration and Partial Backlogging

2019 ◽  
pp. 1-9
Author(s):  
Naresh Kumar Kaliraman
Keyword(s):  
Inventory Model ◽  
Time Dependent ◽  
Order Quantity ◽  
Inventory Cost ◽  
Numerical Illustration ◽  
Decision Variables ◽  
Demand Rate ◽  
Optimum Order ◽  
Total Inventory ◽  
Total Average Cost

This paper develops an economic order quantity inventory model for time dependent three parameters Weibull deterioration. Partially backlogged shortages are considered. The demand rate is deterministic and time dependent. The rate of deterioration is time dependent. We have derived the most favorable order quantity model by minimizing the entire inventory cost. A numerical illustration has been carried out to evaluate the result of parameters on decision variables and the total average cost of the model. The research focus of this paper is to derive the optimum order quantity by minimizing the total inventory cost.

scholarly journals Managing Spare Parts Inventory by Incorporating Holding Costs and Storage Constraints

2021 ◽  
Vol 11 (2) ◽  
pp. 139-144
Author(s):  
Babatunde Omoniyi Odedairo
Keyword(s):  
Raw Materials ◽  
Spare Parts ◽  
Inventory Model ◽  
Inventory Cost ◽  
Holding Costs ◽  
Spare Parts Inventory ◽  
Holding Cost ◽  
Total Inventory ◽  
Abc Analysis ◽  
Cost Components

AbstractA key factor for motivating intending buyers of raw materials is vendor responsiveness. Therefore, to meet demand, a pre-approved level of stocks is often maintained. In contrast, the decision to keep an uncontrolled amount of stock could be counter-productive with cost components associated with holding often ignored unintentionally. In this study, the objective is to develop a spare parts inventory model that incorporates ignored holding costs with a storage constraint for a motorcycle assembly plant (MAP). The inventory policy, structure of holding costs, and spare parts sales reports were consulted for relevant data. The spare parts were categorized and selected using ABC analysis. A spare parts inventory model, which considers ignored holding cost, was formulated. The model was executed using Lingo optimisation software release 18.0.56 to determine the pair of the order quantity (Ɋ) and reorder point (Ɍ). 177 spare part items were identified using ABC analysis. The parts categorisation revealed that 21, 31, 125 part items belong to categories A, B, and C with 81, 15 and 4% of annual sales value, respectively. From category A, nine items contributed significantly to overall sales. The demand pattern for these items was probabilistic based on their coefficient of variation. The pair (Ɋ, Ɍ) for items N, Z, AY, K, AM, J, P, AL and AZ are (174,688), (71,147), (78,150), (86,163), (18,15), (88,170), (128,118), (33,43) and (87,152), respectively. These pairs yielded a total inventory cost of ₦2,177,363 when compared to the current total inventory investment of ₦6,800,000 resulting in a 67.9% cost reduction. A model to manage spare parts inventory with relevant holding cost components was developed for MAP to ensure the availability of items, maximize usage of storage space, and minimize total inventory cost.

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.

Some Studies in Multi-Storage Inventory System

2016 ◽  
pp. 176-200
Author(s):  
Shyamal Kumar Mondal
Keyword(s):  
Planning Horizon ◽  
Inventory System ◽  
Mixed Integer ◽  
Lot Size ◽  
Continuous Release ◽  
Demand Rate ◽  
Cycle Lengths ◽  
Holding Cost ◽  
Inventory Holding ◽  
And Storage

In this chapter, a multi-storage inventory system has been considered to develop a deterministic inventory model in finite planning horizon. Realistically, it is shown that due to large stock and insufficient space of existing own warehouse (OW); excess items are stored in single rented warehouse (RW). Due to different preserving facilities and storage environment, inventory holding cost is considered to be different in different warehouses. Here, the replenishment cycle lengths are of equal length, the demand rate is a continuous linear increasing function of time and partially backlogged shortages are allowed in all cycles. In each cycle, the replenishment cost is assumed to be dependent linearly on lot size and the stocks of RW are also transported to OW in continuous release pattern. The model is formulated as a constrained non-linear mixed integer cost objective function under single management. Finally, results with a sensitivity analysis have been shown with the help of a real coded GA.

Contracts based on Inventory Cost Share for Supply Chain Coordination

2011 ◽  
pp. 126-138 ◽  
Author(s):  
Alejandra Gomez-Padilla
Keyword(s):  
Supply Chain ◽  
Supply Chain Coordination ◽  
The Other ◽  
Inventory Cost ◽  
Cost Share ◽  
Pricing Scheme ◽  
Holding Cost ◽  
Inventory Holding Cost ◽  
Inventory Holding

In this document it is analyzed the importance of contracts for coordination between two companies in a supply chain. In the studied situation, one company, or supplier, supplies one product to the other company, who is a retailer. The companies are going to coordinate by two types of decisions: economic (concerning prices fixed on a contract), and physical exchange (concerning the inventory to be held). Two types of contracts will be presented: one contract with a simple pricing scheme and two contracts with inventory holding cost shared among the companies of the supply chain. The objective is to show that contracts with inventory holding cost share allow the two companies to efficiently coordinate the chain they form.

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.

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