Imprecise Inventory Model for Items With Imperfect Quality Subject to Learning Effects Having Shortages

2018 ◽  
pp. 284-304
Author(s):  
Sumana Saha ◽  
Tripti Chakrabarti
Keyword(s):  
Optimal Solution ◽  
Inventory Model ◽  
Extension Principle ◽  
Market Demand ◽  
Screening Process ◽  
Defective Items ◽  
Inventory Costs ◽  
Eoq Model ◽  
Proposed Model ◽  
Holding Cost

The fundamental assumption of an economic order quantity (EOQ) model is that 100% of items in an ordered lot are perfect. This assumption is not always pertinent for production processes because of process deterioration or other factors. This paper develops an EOQ model for that each ordered lot contains some defective items and shortages backordered. Here, an inventory model is developed to deal the impreciseness present in market demand. It is assumed that the received items are not of perfect quality and after screening, imperfect items are withdrawn from inventory and sold at discounted price. However, in practice, errors occur in screening test. So, the screening process fails to be perfect. Due to acquaintance with handling methodology and system, holding cost and ordering cost are gradually decreases from one shipment to another. So, learning effect is incorporated on holding cost, ordering cost and number of defective items present in each lot. Due to impreciseness in market demand and in different inventory costs, profit expression is fuzzy in nature. To fuzzify the profit expression, Extension Principle is used and for defuzzification Signed distance method is applied. Finally, the feasibility of proposed model and the effect of learning on optimal solution are shown through numerical example.

scholarly journals Integrated inventory model involving quality improvement investment and advance-cash-credit payments

2021 ◽  
Author(s):  
Chih-Te Yang ◽  
Chien-Hsiu Huang ◽  
Liang-Yuh Ouyang
Keyword(s):  
Optimal Solution ◽  
Inventory Model ◽  
Decision Makers ◽  
Optimal Solutions ◽  
Order Quantity ◽  
Defective Items ◽  
Numerical Examples ◽  
Proposed Model ◽  
Production Inventory ◽  
Total Profit

This paper investigates the effects of investment and inspection policies on an integrated production–inventory model involving defective items and upstream advance-cash-credit payment provided by the supplier. In this model, retailers offer customers a downstream credit period. Furthermore, the defective rate of the item can be improved through capital co-investment by the supplier and retailer. The objective of this study was to determine the optimal shipping quantity, order quantity, and investment alternatives for maximizing the supply chain's joint total profit per unit time. An algorithm was developed to obtain the optimal solution for the proposed problem. Several numerical examples are used to demonstrate the proposed model and analyze the effects of parameters changes on the optimal solutions. Finally, management implications for relevant decision makers are obtained from the numerical examples.

scholarly journals Deterministic inventory model for items with Time varying demand, weibull distribution deterioration and shortages

2002 ◽  
Vol 12 (1) ◽  
pp. 61-72 ◽  
Author(s):  
Kun-Shan Wu
Keyword(s):  
Weibull Distribution ◽  
Optimal Solution ◽  
Inventory Model ◽  
Time Varying ◽  
Numerical Examples ◽  
System Parameters ◽  
Eoq Model ◽  
Holding Cost ◽  
Varying Demand ◽  
Weibull Distribution Deterioration

In this paper, an EOQ inventory model is depleted not only by time varying demand but also by Weibull distribution deterioration, in which the inventory is permitted to start with shortages and end without shortages. A theory is developed to obtain the optimal solution of the problem; it is then illustrated with the aid of several numerical examples. Moreover, we also assume that the holding cost is a continuous, non-negative and non-decreasing function of time in order to extend the EOQ model. Finally, sensitivity of the optimal solution to changes in the values of different system parameters is also studied.

scholarly journals A Fuzzy EPQ Model for Non-Instantaneous Deteriorating Items where Production Depends on Demand which is Proportional to Population, Selling Price as well as Advertisement

2019 ◽  
Vol 10 (5) ◽  
pp. 1679 ◽  
Author(s):  
Abhishek Kanti Biswas ◽  
Sahidul Islam
Keyword(s):  
Optimal Solution ◽  
Inventory Level ◽  
Selling Price ◽  
Distance Method ◽  
Defective Items ◽  
Holding Cost ◽  
Epq Model ◽  
Optimal Inventory Level ◽  
Cost Parameters ◽  
Total Average

The inventory system has been drawing more intrigue because this system deals with the decision that minimizes the total average cost or maximizes the total average profit. For any farm, the demand for any items depends upon population, selling price and frequency of advertisement etc. Most of the model, it is assumed that deterioration of any item in inventory starts from the beginning of their production. But in reality, many goods are maintaining their good quality or original condition for some time. So, price discount is availed for defective items. Our target is to calculate the total optimal cost and the optimal inventory level for this inventory model in a crisp and fuzzy environment. Here Holding cost taken as constant and no-shortages are allowed. The cost parameters are considered as Triangular Fuzzy Numbers and to defuzzify the model Signed Distance Method is applied. A numerical example of the optimal solution is given to clarify the model. The changes of different parameters effect on the optimal total cost are presented and sensitivity analysis is given.JEL Classification: C44, Y80, C61Mathematics Subject Classification: 90B05

scholarly journals Integrated multistage supply chain inventory model of multiple retailers with imperfect production and inspection systems

2021 ◽  
Author(s):  
Chi-Jie Lu ◽  
Ming Gu ◽  
Tian-Shyug Lee ◽  
Chih-Te Yang
Keyword(s):  
Supply Chain ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Inventory Model ◽  
Model Complexity ◽  
Supply Chain System ◽  
Imperfect Production ◽  
Proposed Model ◽  
Inspection Systems ◽  
Total Profit

Abstract An integrated multistage supply chain inventory model containing a single manufacturer and multiple retailers is proposed to consider deteriorating materials and finished products with imperfect production and inspection systems. The main purpose is to jointly determine the manufacturer’s production and delivery strategies and the retailers’ replenishment strategies to maximize the integrated total profit. First, the individual total profit functions of the manufacturer and multiple retailers are established and are integrated to form the total profit function of the supply chain system. Then, to address the model complexity, an algorithm is proposed to obtain the optimal solution. Several practical numerical examples are presented to demonstrate the solution procedure, and a sensitivity analysis is performed on the major parameters. From the numerical results, several findings that differ from those in the previous literature were observed. First, retailers with larger market scale, better cost control, and inspection capabilities guarantee higher integrated total profit. Second, increasing the deterioration rates of materials and finished products affect the order quantity of materials in various ways. Third, the manufacturer’s shipping strategy is rigid and not easily adjusted in the proposed model. The performance of the proposed model has several meaningful management implications.

scholarly journals Multi-Objective Inventory Model with Lead-Time and Defective Items

2019 ◽  
Vol 9 (2) ◽  
pp. 2415-2420
Keyword(s):  
Lead Time ◽  
Inventory Model ◽  
Inventory Problem ◽  
Defective Items ◽  
Multi Objective ◽  
Deterministic Demand ◽  
Decision Making Problem ◽  
Holding Cost ◽  
Total Inventory

Inventory problem are generally classified under decision making problem where lead time plays an important role in performance and services to customers during supply and placement of order of an item orders can be placed in shorter lead time with higher price or in longer lead time with lower cost. In this paper we have formulated multi-objective inventory model with one objective of minimizing the total inventory cost and other objective of maintaining the quality of the product by discarding the defective items. The model involved the deterministic demand, lead time dependent lead time cost, holding cost, ordering cost and inspection cost for inspecting defective items. The techniques of priority goal programming and genetic algorithm are applied and the results are compared. The sensitivity analysis is explained due to restriction in cost parameter. The model is finally illustrated with a numerical example.

scholarly journals Inventory Model with Demand Dependent on Unit Price under Fuzzy Parameters and Decision Variables

2019 ◽  
Vol 8 (3) ◽  
pp. 784-788
Keyword(s):  
Numerical Solutions ◽  
Unit Cost ◽  
Optimal Solution ◽  
Unit Price ◽  
Lot Size ◽  
Setup Cost ◽  
Eoq Model ◽  
Decision Variables ◽  
Holding Cost ◽  
Cost Parameters

An EOQ model with demand dependent on unit price is considered and a new approach of finding optimal demand value is done from the optimal unit cost price after defuzzification. Here the cost parameters like setup cost, holding cost and shortage cost and also the decision variables like unit price, lot size and the maximum inventory are taken under fuzzy environment. Triangular fuzzy numbers are used to fuzzify these input parameters and unknown variables. For the proposed model an optimal solution has been determined using Karush Kuhn-Tucker conditions method. Graded Mean Integration (GMI) method is used for defuzzification. Numerical solutions are obtained and sensitivity analysis is done for the chosen model

scholarly journals An Inventory Model based on Imperfect Production with Shortage Backorder

2020 ◽  
Vol 9 (2) ◽  
pp. 89-92
Keyword(s):  
Raw Materials ◽  
Optimal Solution ◽  
Inventory Model ◽  
Production Costs ◽  
Business Strategies ◽  
Optimal Order ◽  
Model Based ◽  
Proposed Model ◽  
Imperfect Items ◽  
Marketing Systems

In this paper, we discussed about the imperfect items. In practice items may get damaged due to production or transportation conditions. Each lot receives some imperfect items. This model also considers the effects of business strategies such as optimal order size of raw materials, production rates and unit production costs, and idle time in different areas on the cooperation of marketing systems. The model can be used in industries such as textiles and footwear, chemicals, food. We develop an inventory model based on imperfect products and shortages. We consider demand is constant and continuous. Purpose of this study is not only to find the retailer`s optimal replenishment policies but also to minimize the total average cost. Finally, a numerical example is presented to illustrate the proposed model and sensitivity analysis of the optimal solution concerning parameters is carried out using the Mathematica 10.0 software.

EOQ Model with Stock-Level Dependent Demand and Different Holding Cost Functions

2017 ◽  
Vol 8 (4) ◽  
pp. 59-75 ◽  
Author(s):  
H.S. Shukla ◽  
R.P. Tripathi ◽  
Neha Sang
Keyword(s):  
Order Approximation ◽  
Optimal Solution ◽  
Optimal Order ◽  
Order Quantity ◽  
Inventory Cost ◽  
Stock Level ◽  
Numerical Examples ◽  
Eoq Model ◽  
Holding Cost ◽  
Dependent Demand

This paper presents EOQ (Economic Order Quantity) model with stock- level dependent demand and different types of holding cost function. We show that the total relevant inventory cost per unit time is convex with respect to cycle time. Mathematical models are established to determine optimal order quantity and total relevant inventory cost. Numerical examples are provided for two different models i.e. (i): Instantaneous replenishment with inventory dependent holding cost and (ii) Instantaneous replenishment with quadratic time dependent carrying cost. Numerical examples are provided to illustrate the proposed model. Sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out. The second order approximation is used for finding closed form optimal solution. Mathematica 5.2 software is used to find numerical results.

scholarly journals Technical Note on(Q,r,L)Inventory Model with Defective Items

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
Cheng-Tan Tung ◽  
Yu-Wen Wou ◽  
Shih-Wei Lin ◽  
Peter Deng
Keyword(s):  
Analytical Approach ◽  
Optimal Solution ◽  
Technical Note ◽  
Inventory Model ◽  
Reasonable Assumption ◽  
Robust Method ◽  
Inventory Models ◽  
Defective Items ◽  
Stochastic Inventory ◽  
Stochastic Inventory Models

Under a reasonable assumption, we derive an analytical approach that verifies uniqueness of the optimal solution for stochastic inventory models with defective items. Our approach implies a robust method to find the optimal solution.

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