Inventory and pricing decisions for imperfect quality items with inspection errors, sales returns, and partial backorders under inflation

2020 ◽  
Vol 54 (1) ◽  
pp. 287-306 ◽  
Author(s):  
Aditi Khanna ◽  
Aakanksha Kishore ◽  
Biswajit Sarkar ◽  
Chandra K. Jaggi
Keyword(s):  
Optimal Solution ◽  
Selling Price ◽  
Type I ◽  
Discounted Cash Flow ◽  
Screening Process ◽  
Imperfect Quality ◽  
Decision Variables ◽  
Proposed Model ◽  
Price Order ◽  
Inspection Process

In this paper, an optimal replenishment inventory policy for imperfect quality items is presented with a selling price-dependent demand under inflationary conditions using a discounted cash flow (DCF) approach. Due to the presence of defectives in the system, all items go through a 100% inspection process. However, the screening process is also considered to be imperfect and involves errors, namely Type-I and Type-II. In addition, shortages are allowed and are partially backlogged. An optimal solution for the proposed model is derived by maximizing the expected profit function by jointly optimizing three decision variables: selling price, order quantity, and backorder level. To validate the theoretical results, a numerical example along with comprehensive sensitivity analysis is offered. The model has pertinence in industries like textiles, electronics, furniture, footwear, automobiles, and plastics.

scholarly journals Economic production quantity model with backorders and items with imperfect/perfect quality options

2019 ◽  
Vol 17 (4) ◽  
Author(s):  
Behrouz Afshar Nadjafi ◽  
Hamed Pourbakhsh ◽  
Mohammad Mirhabibi ◽  
Hasan Khodaei ◽  
Babak Ghodami ◽  
...  
Keyword(s):  
Optimal Solution ◽  
Screening Process ◽  
Economic Production Quantity ◽  
Economic Production ◽  
Decision Variables ◽  
Proposed Model ◽  
Epq Model ◽  
Production Quantity ◽  
The Impact ◽  
Single Batch

In this paper, an economic production quantity (EPQ) model with backorders considering two options for replenishing of items is proposed; with partially imperfect and perfect quality items. First option assumes a produced shipment contains a fraction of imperfect quality items and supplier does not conduct a full inspection. Therefore, these items are detected by a fully perfect screening process by buyer and are sold as a single batch at a discounted price. While the second one assumes that all items that are produced are fully inspected by supplier and all delivered items are perfect; of course with higher unit production price. Ordering size and backordering level are used as decision variables to derive the closed-form optimal solution. The proposed model is ilustrated and discussed by a numerical example. Finally, a sensitivity analysis is done for identifying the impact of crucial parameters on the optimal solution.

scholarly journals Inventory Modeling for Deteriorating Imperfect Quality Items with Selling Price Dependent Demand and Shortage Backordering under Credit Financing

2017 ◽  
Vol 2 (2) ◽  
pp. 110-124 ◽  
Author(s):  
Aditi Khanna ◽  
Prerna Gautam ◽  
Chandra K. Chandra K.
Keyword(s):  
Trade Credit ◽  
Optimal Order ◽  
Manufacturing Processes ◽  
Selling Price ◽  
Imperfect Quality ◽  
Inspection Process ◽  
Total Profit ◽  
Credit Financing ◽  
Fierce Competition ◽  
Dependent Demand

The production processes throughout the world aim at improving quality by introducing latest technologies so as to perform well in fierce competition. Despite this due to various unavoidable factors, most of the manufacturing processes end up with certain imperfections. Hence, all the items produced are not of perfect quality. The condition tends to be more susceptible while dealing with items of deteriorating quality; therefore an inspection process is must for screening good quality items from the ordered lot. Demand is assumed to be price dependent and it is represented by a constant price elasticity function. Also to endure with the rapid growth and turbulent markets, the suppliers try to engage and attract retailers through various gimmicks and one such contrivance is offering trade credit, which is proved to be an influential strategy for attracting new customers. In view of this, the present paper develops an inventory model for items of imperfect quality with deterioration under trade-credit policies with price dependent demand. Shortages are allowed and fully backlogged. A mathematical model is developed to depict this scenario. The aim of the study is to optimize the optimal order level, backorder level and selling price so as to maximize the retailer’s total profit. Findings are validated quantitatively by using numerical analysis. Sensitivity analysis is also performed so as to cater some important decision-making insights.

Hydrograph-based storm sewer design optimization by genetic algorithm

2006 ◽  
Vol 33 (3) ◽  
pp. 319-325 ◽  
Author(s):  
M H Afshar ◽  
A Afshar ◽  
M A Mariño ◽  
A A.S Darbandi
Keyword(s):  
Genetic Algorithm ◽  
Optimal Design ◽  
Environmental Protection Agency ◽  
Optimal Solution ◽  
Storm Water ◽  
Storm Water Management Model ◽  
Decision Variables ◽  
Proposed Model ◽  
The Us ◽  
Hydraulic Simulator

A model is developed for the optimal design of storm water networks. The model uses a genetic algorithm (GA) as the search engine and the TRANSPORT module of the US Environmental Protection Agency storm water management model version 4.4H (SWMM4.4H) as the hydraulic simulator. Two different schemes are used to formulate the problem with varying degrees of success in reaching a near-optimal solution. In the first scheme, the nodal elevations and pipe diameters are selected as the decision variables of the problem which were determined by the GA to produce the trial solutions. In the second scheme, only nodal elevations are optimized by the GA, and determination of pipe diameters is left to the TRANSPORT SWMM module. Simulation of the trial solutions in both methods is carried out by the TRANSPORT module of SWMM4.4H. The proposed model is applied to some benchmark examples, and the results are presented and compared with the existing results in the literature.Key words: genetic algorithm, optimal design, sewer network, SWMM.

scholarly journals A Novel Prey-Predator Quadratic Harvesting Model via Optimal Control Theory and Hopf Bifurcation

2020 ◽  
Vol 1 ◽  
pp. 1-22
Author(s):  
Prabir Panja ◽  
Dipak Kumar Jana
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Point ◽  
Fish Species ◽  
Interaction Model ◽  
Existence Condition ◽  
Optimal Harvesting ◽  
Selling Price ◽  
Type I ◽  
Functional Responses ◽  
Proposed Model

In this investigation, a predator-prey interaction model among Phytoplankton, Zooplankton and Fish has been developed. In the absence of Zooplankton and Fish, it is assumed that Phytoplankton grows logistically. It is assumed that Zooplankton consumes Phytoplankton and Fish consumes Phytoplankton as well as Zooplankton. Holling type I & II functional responses have been considered to formulate the our proposed model. It is considered that Phytoplankton releases some toxin in the aquatic environment which makes some death in Zooplankton population. Quadratic harvesting is considered on Fish species. Boundedness of the solution of our proposed model has also been studied. Local stability of the system around each equilibrium point has been investigated. Also, the global stability of the interior equilibrium point has been studied. Existence condition of Hopf bifurcation of our proposed system has been studied. It is found that half saturation constant (α) can change the system dynamics. It is also found that the harvesting rate of Fish (E) and consumption rate of Zooplankton (γ1) has a significant role in the stability of the system. Again, it is found that the harvesting of Fish species will be increased if the selling price of Fish (p) and the annual discount (δ1) of Fish production cost increases. It is also found that the optimal harvesting rate of Fish decreases due to the increase of cost (c) of harvesting of Fish. Finally, some numerical simulation results have been presented to verify our analytical findings.

scholarly journals Using system simulation to search for the optimal multi-ordering policy for perishable goods

2019 ◽  
Vol 7 (1) ◽  
pp. 49
Author(s):  
Y.C. Huang ◽  
X.Y. Chang ◽  
Y.A. Ding
Keyword(s):  
Stochastic Demand ◽  
Optimal Solution ◽  
Practical Applications ◽  
Ordering Policy ◽  
Perishable Goods ◽  
Decision Variables ◽  
Proposed Model ◽  
The Cost ◽  
Optimal Ordering ◽  
Computerized System

<p>This paper explores the possibility that perishable goods can be ordered several times in a single period after considering the cost of Marginal contribution, Marginal loss, Shortage, and Purchasing under stochastic demand. In order to determine the optimal ordering quantity to improve the traditional newsvendor and maximize the total expected profits, and then sensitivity analysis is taken to realize the influence of the parameters on total expected profits and decision variables respectively. In addition, this paper designed a multi-order computerized system with Monte Carlo method to solve the optimal solution under stochastic demand. Based on numerical examples, this paper verified the feasibility and efficiency of the proposed model. Finally, several specific conclusions are drawn for practical applications and future studies.</p>

Non-Cooperative Game Theoretic Approach in Supply Chain With Imperfect Quality Items and Credit Financing

2018 ◽  
pp. 215-232
Author(s):  
Rita Yadav ◽  
Sarla Pareek ◽  
Mandeep Mittal
Keyword(s):  
Supply Chain ◽  
Stackelberg Game ◽  
Decision Variable ◽  
Chain Model ◽  
Selling Price ◽  
Theoretic Approach ◽  
Credit Period ◽  
Imperfect Quality ◽  
Inspection Process ◽  
Credit Financing

This paper considers a supply chain model for imperfect quality items in which retail price of the buyer influences the demand of the product. The seller offers fix credit period for the buyer to stimulate his sales. Each delivered lot, goes through an inspection process at the buyer's end. After the inspection, items are separated into two parts, one is perfect quality items and another is imperfect quality items. The perfect quality items are sold at selling price and the imperfect items are sold at a discounted price immediately after the inspection process. The credit period offered by the seller and the selling price of the seller, both are considered as a decision variable. Relationship between seller and buyer is derived from the non-cooperative Seller- Stackelberg game approach. Optimal selling price, credit period and order quantity are determined by maximizing expected total profit of the supply chain. At the end, numerical examples with sensitivity analysis are given to explain the theory of the paper.

Credit Policies for Deteriorating Imperfect Quality Items With Exponentially Increasing Demand and Partial Backlogging

2018 ◽  
pp. 90-106 ◽  
Author(s):  
Chandra K. Jaggi ◽  
Prerna Gautam ◽  
Aditi Khanna
Keyword(s):  
Sensitivity Analysis ◽  
Numerical Analysis ◽  
Trade Credit ◽  
Partial Backlogging ◽  
Inverse Relation ◽  
Screening Process ◽  
Imperfect Quality ◽  
Inspection Process ◽  
Increasing Demand ◽  
Delay In Payments

In retail industries every ordered lot carry some fraction of imperfect quality items which can vary depending upon production and handling conditions. The situation is even more subtle when the items are prone to deterioration. However, an inspection process can spare us from such a criticality by bifurcating the defectives from the good quality lot. Thus, a screening process is mandatory. In the hyper-competitive market, trade-credit is well-known gimmick in order to boost the sales. Keeping in view, an inventory scenario of a retailer is investigated who has to deal with imperfect and “deteriorating items” under “permissible delay in payments”. The demand is assumed to be increasing exponentially. Shortages are permitted to occur and supposed to be “partially backlogged.” Rate of backlogging is assumed to have inverse relation with the waiting time for the subsequent replenishment. In this chapter, shortage point and length of cycle are jointly optimized. Numerical analysis and sensitivity analysis is performed to provide important insights for managerial persistence.

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 BALANCING PUBLIC AND PRIVATE INTERESTS THROUGH OPTIMIZATION OF CONCESSION AGREEMENT DESIGN FOR USER-PAY PPP PROJECTS

2018 ◽  
Vol 24 (2) ◽  
pp. 116-129 ◽  
Author(s):  
Ke FENG ◽  
Shouqing WANG ◽  
Nan LI ◽  
Chunlin WU ◽  
Wei XIONG
Keyword(s):  
Discounted Cash Flow ◽  
Nsga Ii ◽  
Public Funds ◽  
Public And Private ◽  
Private Interests ◽  
Decision Variables ◽  
Proposed Model ◽  
Concession Period ◽  
Public Sectors ◽  
Discounted Cash Flow Method

In user-pay public private partnership (PPP) projects, private sectors collect user fees to cover cost and reap revenue. For projects that cannot be self-financed, public sectors usually invest public funds to make them financially feasible. The concession agreement allocates revenues and risks, and lies in the center of balancing public and private interests. However, stakeholders may have contrary opinions regarding the optimization of concession agreement. While private sectors are concerned about earning money, public sectors pay more attention to the efficient use of public funds. To address this challenge, this paper firstly identifies several key concessionary items, including concession period, concession price, capital structure and government subsidy. Then, a multi-objective optimization model is presented using discounted cash flow method, in which key concessionary items act as decision variables and public and private interests are represented by two sub-objectives. Subsequently, the model is solved using non-dominated sorting genetic algorithm-II (NSGA-II). Furthermore, a numerical case based on Beijing No. 4 Metro Line is provided to demonstrate the application of the model. Results show that the proposed model can produce a series of viable combinations of concessionary items that balance public and private interests, which provides practical references for relative decision making activities.

Effect of inspection errors on imperfect production inventory model with warranty and price discount dependent demand rate

2020 ◽  
Vol 54 (4) ◽  
pp. 1189-1213 ◽  
Author(s):  
Amalesh Kumar Manna ◽  
Jayanta Kumar Dey ◽  
Shyamal Kumar Mondal
Keyword(s):  
Type I Error ◽  
Time Dependent ◽  
Selling Price ◽  
Type I ◽  
Development Cost ◽  
Price Discount ◽  
Dependent Development ◽  
Inspection Errors ◽  
Production Inventory ◽  
Inspection Process

This paper deals with selling price-discount and warranty period dependent demand in an imperfect production inventory model under the consideration of inspection errors and time dependent development cost. Normally, due to long-run, a production process deteriorates with time and here we assume that the process shifts from "in-control" to "out-of-control" state at any random time. A time dependent development cost has been constructed to increase the reliability of the production system i.e., to decrease the deterioration of the system during the production process. As a result, a few items are rejected. Here, two types of inspection errors such as Type-I error and Type-II error, have been considered during the period of product inspection process. In Type-I error, an inspector may choose falsely a defective item as non-defective and in Type-II error an inspector may choose falsely a non-defective item as defective. Due to these phenomena, the inspection process would consist of the following costs: cost of inspection, cost of inspection errors. The purpose of this paper is to investigate the effects of time dependent development cost on the defective items, selling price-discount and warranty policy on the market demand and finally optimize the expected average profit under consideration of such inspection costs in infinite time horizon. Some numerical examples along with graphical illustrations and sensitivity analysis are provided to test the feasibility of the model.

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