scholarly journals Functions of several variables analysis applied in inventory management

2013 ◽  
Vol 61 (7) ◽  
pp. 2221-2227 ◽  
Author(s):  
Martina Janková ◽  
Veronika Novotná ◽  
Tereza Varyšová
Keyword(s):  
Inventory Management ◽  
Differential Calculus ◽  
Maximum Term ◽  
Optimal Price ◽  
Several Variables ◽  
Analysis And Synthesis ◽  
Delay In Payments ◽  
Definite Period ◽  
Theoretical Results ◽  
Dependent Demand

In many cases a retailer is not capable of settling an invoice immediately upon receiving it and is given an option by the supplier to settle the invoice within a definite period. The retailer can sell the goods before the deadline, accumulate revenue and earn interest. If the retailer is not able to meet his obligations within the deadline, he is charged an interest. This paper introduces a newly constructed model which enables a retailer to set an optimal price of goods under permissible delay in payments, and to determine the maximum term of payment. The model is based on the assumption of time-dependent demand and has been developed for non-deteriorating goods. The paper further analyzes a situation in which the retailer sell all the goods in time, and a situation in which the deadline was not met. Theoretical results are demonstrated by an illustrative example. The authors of the paper used methods of analysis and synthesis, and the method of mathematical analysis (differential calculus of multivariable functions, solution of ordinary differential equations).The model suggested in the paper can be expanded in the future. One option is generalization of the model, allowing for the lack of goods, bulk discounts, etc.

SIMULATION OF INVENTORY POLICY FOR PRODUCT WITH PRICE AND TIME-DEPENDENT DEMAND FOR DETERIORATING ITEM

2012 ◽  
Vol 03 (01) ◽  
pp. 1150001 ◽  
Author(s):  
D. SHUKLA ◽  
U. K. KHEDLEKAR ◽  
R. P. S. CHANDEL ◽  
S. BHAGWAT
Keyword(s):  
Inventory Management ◽  
Dynamic Pricing ◽  
Optimal Number ◽  
Pricing Policy ◽  
Data Set ◽  
Maximum Profit ◽  
Net Profit ◽  
Recurrence Method ◽  
Theoretical Results ◽  
Dependent Demand

In a declining market for goods, we optimize the net profit in business when inventory management allows change in the selling prices n times over time horizon. We are computing optimal number of changes in prices, respective optimal prices, and optimal profit in each of the cycle for a deteriorating product. This paper theoretically proves that for any business setup there exists an optimal number of price settings for obtaining maximum profit. Theoretical results are supported by numerical examples for different setups (data set) and it is found that for every setup the dynamic pricing policy outperforms the static pricing policy. In our model, the deterioration factor has been taken into consideration. The deteriorated units are determined by the recurrence method. Also we studied the effect of different parameters on optimal policy with simulation. For managerial purposes, we have provided some "suggested intervals" for choosing parameters depending upon initial demand, which help to predict the best prices and arrival of customers (demand).

AN EOQ MODEL WITH LIMITED STORAGE CAPACITY UNDER TRADE CREDITS

2007 ◽  
Vol 24 (04) ◽  
pp. 575-592 ◽  
Author(s):  
LIANG-YUH OUYANG ◽  
KUN-SHAN WU ◽  
CHIH-TE YANG
Keyword(s):  
Storage Capacity ◽  
Optimal Solution ◽  
Inventory Systems ◽  
Simple Method ◽  
Eoq Model ◽  
Trade Credits ◽  
Cash Discount ◽  
Delay In Payments ◽  
Classical Economic ◽  
Theoretical Results

In the classical economic order quantity (EOQ) inventory model, it was assumed that the retailer must pay for the received items immediately. However, in practice, the supplier not only allows retailer to settle the account after a certain fixed period but also may offer a cash discount to encourage the retailer to pay for his purchases as soon as possible. On the other hand, it is common practice in most inventory systems to hold excess stocks in a rented warehouse whenever the storage capacity of the owned warehouse is insufficient. Therefore, the purpose of this paper is to establish an EOQ model with limited storage capacity, in which the supplier provides cash discount and permissible delay in payments for the retailer. In the model, we develop some useful theorems to characterize the optimal solution and provide a simple method to find the optimal replenishment cycle time and payment time. Finally, several numerical examples are given to illustrate the theoretical results and some managerial insights are also obtained.

Time and Price Dependent Demand with Varying Holding Cost Inventory Model for Deteriorating Items

2013 ◽  
Vol 4 (4) ◽  
pp. 75-95 ◽  
Author(s):  
Diwakar Shukla ◽  
Uttam Kumar Khedlekar ◽  
Raghovendra Pratap Singh Chandel
Keyword(s):  
Simulation Study ◽  
Demand Function ◽  
Inventory Model ◽  
Time Parameter ◽  
Suggested Model ◽  
Open Problems ◽  
Holding Cost ◽  
Theoretical Results ◽  
Dependent Demand ◽  
Better Than

This paper presents an inventory model considering the demand as a parametric dependent linear function of time and price both. The coefficient of time-parameter and coefficient of price-parameter are examined simultaneously and proved that time is dominating variable over price in terms of earning more profit. It is also proved that deterioration of item in the inventory is one of the most sensitive parameter to look into besides many others. The robustness of the suggested model is examined using variations in the input parameters and ranges are specified on which the model is robust on most of occasions and profit is optimal. Two kinds of doubly-demand function strategies are examined and mutually compared in view of the two different cases. Second strategy found better than first. Holding cost is treated as a variable. Theoretical results are supported by numerical based simulation study with robustness. Some recommendations are given at the end for the inventory managers and also open problems are discussed for researchers. This model is more realistic than considered by earlier author.

Coordination and Decision of Supply Chain Under

2019 ◽  
Vol 12 (3) ◽  
pp. 21-46 ◽  
Author(s):  
Guangdong Liu ◽  
Tianjian Yang ◽  
Yao Wei ◽  
Xuemei Zhang
Keyword(s):  
Supply Chain ◽  
Numerical Analysis ◽  
Cost Sharing ◽  
Supply Chain Coordination ◽  
Pareto Improvement ◽  
Optimal Price ◽  
Decentralized System ◽  
Risk Neutral ◽  
Future Work ◽  
Dependent Demand

In order to investigate supply chain coordination and decision under customer balking and stochastic demand, the article considers a two-echelon supply chain consisting of one manufacturer with risk-neutral and one retailer with risk-neutral and develops two models in a centralized and a decentralized system and the three contracts are designed to coordinate supply chain and the optimal price and customer balking strategies are obtained. The results show that the revenue and cost-sharing contract can coordinate supply chain under customer balking and price-dependent demand and achieve the Pareto-improvement; the expected sales quantity and expected reduced sales quantity are influenced conversely by the threshold of inventory and probability of a sale under customer balking. In addition, numerical analysis is given to verify the effectiveness of revenue and cost-sharing contract and the paper gives some managerial insights and puts forward to the future work at last.

scholarly journals Strategic Conditions for Opening an Internet Store and Pricing Policies in a Retailer-Dominant Supply Chain

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Yonghong Cheng ◽  
Zhongkai Xiong
Keyword(s):  
Supply Chain ◽  
Bargaining Power ◽  
The Internet ◽  
Optimal Price ◽  
Numerical Examples ◽  
Pricing Policies ◽  
Equilibrium Prices ◽  
Multichannel Retailing ◽  
Dominant Retailer ◽  
Theoretical Results

To examine when the manufacturer and dominant retailer open their own Internet stores and how setting prices to ensure opening Internet stores are profitable. We consider a two-echelon supply chain with one manufacturer and one dominant retailer. The retailer has a physical store in a monopolist market. Depending on whether the Internet stores are opened successfully by them, we firstly obtain equilibrium prices and profits under four possible supply chain structures. Secondly, we identify several strategic conditions when it is optimal to open an Internet store for the manufacturer and dominant retailer and discuss its implications. It is interesting to note that multichannel retailing is not necessarily the best strategy for the dominant retailer. In addition, we investigate the impacts of problem parameters (the dominant retailer’s bargaining power and consumers’ disutility of purchasing a product from Internet store) on the manufacturer and dominant retailer’s pricing policies. We find that the manufacturer’s optimal price at her Internet store is not always being lower than the dominant retailer’s. Finally, we conduct numerical examples to illustrate the theoretical results.

Inventory management in food companies with statistically dependent demand

2016 ◽  
Vol 29 (4) ◽  
pp. 450-485 ◽  
Author(s):  
Fernando Rojas ◽  
Victor Leiva
Keyword(s):  
Inventory Management ◽  
Raw Materials ◽  
Moving Average ◽  
Differential Evolution Algorithm ◽  
Statistical Dependence ◽  
Food Services ◽  
Inventory Models ◽  
Content Type ◽  
Dependent Demand ◽  
Dependence Structures

Purpose The objective of this paper is to propose a methodology based on random demand inventory models and dependence structures for a set of raw materials, referred to as “components”, used by food services that produce food rations referred to as “menus”. Design/methodology/approach The contribution margins of food services that produce menus are optimised using random dependent demand inventory models. The statistical dependence between the demand for components and/or menus is incorporated into the model through the multivariate Gaussian (or normal) distribution. The contribution margins are optimised by using probabilistic inventory models for each component and stochastic programming with a differential evolution algorithm. Findings When compared to the non-optimised system previously used by the company, the (average) expected contribution margin increases by 18.32 per cent when using a continuous review inventory model for groceries and uniperiodic models for perishable components (optimised system). Research limitations/implications The multivariate modeling can be improved by using (a) other non-Gaussian (marginal) univariate probability distributions, by means of the copula method that considers more complex statistical dependence structures; (b) time-dependence, through autoregressive time-series structures and moving average; (c) random modelling of lead-time; and (d) demands for components with values equal to zero using zero-inflated or adjusted probability distribution. Practical implications Professional management of the supply chain allows the users to register data concerning component identification, demand, and stock levels to subsequently be used with the proposed methodology, which must be implemented computationally. Originality/value The proposed multivariate methodology allows it to describe demand dependence structures through inventory models applicable to components used to produce menus in food services.

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