scholarly journals Optimal inventory policies for imperfect inventory with price dependent stochastic demand and partially backlogged shortages

2012 ◽  
Vol 22 (2) ◽  
pp. 199-223 ◽  
Author(s):  
Jhuma Bhowmick ◽  
G.P. Samanta
Keyword(s):  
Stochastic Demand ◽  
Optimal Order ◽  
Partial Backlogging ◽  
Order Quantity ◽  
Inventory Policies ◽  
Defective Items ◽  
Proposed Model ◽  
Special Cases ◽  
Total Profit ◽  
Increasing Function

The paper investigates a single period imperfect inventory model with price dependent stochastic demand and partial backlogging. The backorder rate is a nonlinear non-increasing function of the magnitude of shortage. Two special cases are considered assuming that the percentage of defective items follows a truncated exponential distribution and a normal distribution respectively. The optimal order quantity and the optimal mark up value are determined such that the expected total profit of the system is maximized. Numerical example is given to illustrate the proposed model which is compared with the traditional model of perfect stock. Sensitivity analysis is performed to explain the behavior of the proposed model with respect to the key parameters.

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 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 A Single-Stage Manufacturing Model with Imperfect Items, Inspections, Rework, and Planned Backorders

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 446 ◽  
Author(s):  
Chang Wook Kang ◽  
Misbah Ullah ◽  
Mitali Sarkar ◽  
Muhammad Omair ◽  
Biswajit Sarkar
Keyword(s):  
Production System ◽  
Single Stage ◽  
Order Quantity ◽  
Lot Size ◽  
Defective Items ◽  
Long Run ◽  
Proposed Model ◽  
Imperfect Items ◽  
Inspection Process ◽  
Inspection Station

Each industry prefers to sell perfect products in order to maintain its brand image. However, due to a long-run single-stage production system, the industry generally obtains obstacles. To solve this issue, a single-stage manufacturing model is formulated to make a perfect production system without defective items. For this, the industry decides to stop selling any products until whole products are ready to fulfill the order quantity. Furthermore, manufacturing managers prefer product qualification from the inspection station especially when processes are imperfect. The purpose of the proposed manufacturing model considers that the customer demands are not fulfilled during the production phase due to imperfection in the process, however customers are satisfied either at the end of the inspection process or after reworking the imperfect products. Rework operation, inspection process, and planned backordering are incorporated in the proposed model. An analytical approach is utilized to optimize the lot size and planned backorder quantities based on the minimum average cost. Numerical examples are used to illustrate and compare the proposed model with previously developed models. The proposed model is considered more beneficial in comparison with the existing models as it incorporates imperfection, rework, inspection rate, and planned backorders.

Coordination model of supply chain based on deciders’ risk attitudes in a fuzzy decision environment

2021 ◽  
Vol 40 (1) ◽  
pp. 27-41
Author(s):  
Jingjing Wang ◽  
Minli Xu ◽  
Huiyun Jian
Keyword(s):  
Supply Chain ◽  
Fuzzy Numbers ◽  
Optimal Order ◽  
Risk Attitudes ◽  
Order Quantity ◽  
Two Stage ◽  
Quantity Discount ◽  
Risk Seeking ◽  
Proposed Model ◽  
Optimal Order Quantity

This paper considers a two-stage supply chain consisting of one manufacturer and one retailer, exploring the impact of the fuzzy uncertainty of product yield and demand and the deciders’ risk attitudes on the optimal order quantity of the retailer. At the same time, this study tries to analyze the coordination problem in the two-stage supply chain with consideration of the retailer and the manufacturer’s risk attitudes. Firstly, this study develops a supply chain optimal decision model in a centralized decision framework. In the proposed model, the L-R fuzzy numbers are used to depict the yield and demand with fuzzy characteristics. Then, the coordination of quantity discount in a supply chain is studied. Consequently, this research further investigates a special case in which the market demand and yield are assumed to be triangular fuzzy numbers, and the optimal solution of the order quantity and the wholesale price are obtained. At last, this paper utilizes several numerical examples to validate the proposed model. The results show that the quantity discount contract can coordinate the supply chain in a fuzzy environment, and the optimal order quantity decreases with the increasing of the risk bias coefficient of the retailer and the manufacturer. It also suggests that risk-seeking retailer will order more products, in addition, the manufacturer tend to choose a risk-seeking retailer as partner and the retailer is more likely to choose a risk-seeking rather than risk-aversion manufacturer as partner.

scholarly journals An Economic Order Quantity Model with Completely Backordering and Nondecreasing Demand under Two-Level Trade Credit

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Zohreh Molamohamadi ◽  
Rahman Arshizadeh ◽  
Napsiah Ismail ◽  
Amir Azizi
Keyword(s):  
Demand Function ◽  
Trade Credit ◽  
Economic Order Quantity ◽  
Economic Order ◽  
Order Quantity ◽  
Competitive Industry ◽  
Decision Variables ◽  
Proposed Model ◽  
Special Cases ◽  
Optimal Ordering

In the traditional inventory system, it was implicitly assumed that the buyer pays to the seller as soon as he receives the items. In today’s competitive industry, however, the seller usually offers the buyer a delay period to settle the account of the goods. Not only the seller but also the buyer may apply trade credit as a strategic tool to stimulate his customers’ demands. This paper investigates the effects of the latter policy, two-level trade credit, on a retailer’s optimal ordering decisions within the economic order quantity framework and allowable shortages. Unlike most of the previous studies, the demand function of the customers is considered to increase with time. The objective of the retailer’s inventory model is to maximize the profit. The replenishment decisions optimally are obtained using genetic algorithm. Two special cases of the proposed model are discussed and the impacts of parameters on the decision variables are finally investigated. Numerical examples demonstrate the profitability of the developed two-level supply chain with backorder.

scholarly journals An EOQ model with stock dependent demand and imperfect quality items

2010 ◽  
Vol 20 (2) ◽  
pp. 237-247 ◽  
Author(s):  
Shibaji Panda
Keyword(s):  
Optimal Order ◽  
Optimal Solutions ◽  
Order Quantity ◽  
Screening Process ◽  
Imperfect Quality ◽  
Eoq Model ◽  
Total Profit ◽  
Approximate Optimal Solutions ◽  
Single Batch ◽  
Dependent Demand

This paper deals with an economic order quantity model where demand is stock dependent. Items received are not of perfect quality and each lot received contains percentage defective imperfect quality items, which follow a probability distribution. Two cases are considered. 1) Imperfect quality items are held in stock and sold in a single batch after a 100 percent screening process. 2) A hundred percent screening process is performed but the imperfect quality items are sold as soon as they are detected. Approximate optimal solutions are derived in both cases. A numerical example is provided in order to illustrate the development of the model. Sensitivity analysis is also presented, indicating the effects of percentage imperfect quality items on the optimal order quantity and total profit.

scholarly journals Impact of Imperfect Quality Items on Inventory Management for Two Warehouses with Shortages

2020 ◽  
Vol 5 (5) ◽  
pp. 869-885
Author(s):  
Aastha . ◽  
Sarla Pareek ◽  
Leopoldo Eduardo Cárdenas-Barrón ◽  
Mandeep Mittal
Keyword(s):  
Inventory Management ◽  
Storage Capacity ◽  
Inventory Model ◽  
Optimal Order ◽  
Defective Items ◽  
Imperfect Quality ◽  
Inspection Process ◽  
Total Profit ◽  
The Cost ◽  
The Impact

Generally, the majority of the inventory models work on the concept that overall units produced must be perfect in terms of quality and that the storage capacity of the warehouse is unlimited. In fact, under realistic conditions, it is not possible to manufacture products with complete perfection. Furthermore, there are always some limits associated with storage capacity of the warehouse. This paper formulates an inventory model that considers the impact of imperfect quality items and shortages. The cost of storage in rented warehouse (RW) is greater than own warehouse (OW) due to fact there are better preservation facilities in RW. This work considers that defective items are completely withdrawn after the inspection process. The purpose of this inventory model is to establish the optimal order quantity and backorder size that maximize the total profit. Some numerical examples are solved, and a sensitivity analysis is included.

scholarly journals An EPQ model under cash discount and permissible delay in payments derived without derivatives

2007 ◽  
Vol 17 (2) ◽  
pp. 177-193 ◽  
Author(s):  
Yung-Fu Huang ◽  
Chung-Li Chou ◽  
Jui-Jung Liao
Keyword(s):  
Cycle Time ◽  
Optimal Order ◽  
Selling Price ◽  
Order Quantity ◽  
Permissible Delay In Payments ◽  
Special Cases ◽  
Time Optimal ◽  
Optimal Order Quantity ◽  
Cash Discount ◽  
Delay In Payments

The main purpose of this paper is to investigate the case where the retailer?s unit selling price and the purchasing price per unit are not necessarily equal within the economic production quantity (EPQ) framework under cash discount and permissible delay in payments. We establish the retailer?s inventory system as a cost minimization problem to determine the retailer?s optimal inventory cycle time, optimal order quantity and optimal payment time. This paper provides an algebraic approach to determine the optimal cycle time, optimal order quantity and optimal payment time. This approach provides one theorem to efficiently determine the optimal solution. Some previously published results of other researchers are deduced as special cases. Finally, numerical examples are given to illustrate the result and the managerial insights are also obtained.

scholarly journals Multi-Period Age-Discriminated Perishable Inventory

2021 ◽  
Vol 29 (2) ◽  
pp. 97-105
Author(s):  
Wasfi Alrawabdeh
Keyword(s):  
Simulated Annealing Algorithm ◽  
Discrete Event ◽  
Stochastic Demand ◽  
Pharmaceutical Products ◽  
Optimal Order ◽  
Order Quantity ◽  
Event Simulation ◽  
Simulation Based ◽  
Optimal Order Quantity ◽  
Packaged Food

Abstract In this paper, an extremely short shelf-life inventory of age-discriminated stochastic demand is considered. Age discriminated demand can be found in products of high circulation and short shelf-lives such as dairy products, packaged food, pharmaceutical products and medical products of short shelf lives. Simulation based optimization is considered to find the optimal order quantity. The model employs Discrete Event Simulation along with a modified simulated annealing algorithm. To validate the model and the optimization algorithm, the classical newsvendor problem is tested first, later, different experiments are carried out for different product lifetimes. In contrast to the classical newsvendor, this problem tackles a multi-period inventory of different ages and different demand distributions. The objective is to determine the optimal order quantity to satisfy the stochastic demand of all ages such that shortages and expirations are minimized. The results showed remarkable performance and outstanding minimum levels of shortage and expiration.

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