A vendor–buyer inventory model with lot-size and production rate dependent lead time under time value of money

2020 ◽  
Vol 54 (4) ◽  
pp. 961-979 ◽  
Author(s):  
Sumon Sarkar ◽  
Bibhas Chandra Giri ◽  
Ashis Kumar Sarkar
Keyword(s):  
Production Rate ◽  
Lead Time ◽  
Demand Uncertainty ◽  
Net Present Value ◽  
Numerical Study ◽  
Optimal Solution ◽  
Integrated System ◽  
Market Demand ◽  
Lot Size ◽  
Regular Production

The paper studies an integrated vendor–buyer model with shortages under stochastic lead time which is assumed to be variable but depends on the buyer’s order size and the vendor’s production rate. The replenishment lead time and the market demand uncertainty are assumed to be reduced by changing the regular production rate of the vendor at the risk of paying additional cost. Shortages are partially backlogged and the backlogging rate depends on the length of the buyer’s replenishment lead time. The proposed model is formulated to obtain the net present value (NPV) of the expected total cost of the integrated system through optimization of (i) the buyer’s order quantity, (2) the buyer’s safety factor, and (3) the vendor’s production rate. Theoretical results are derived to demonstrate the existence and uniqueness of the optimal solution. Through extensive numerical study, some valuable managerial insights are obtained.

scholarly journals Model Persediaan Pemasok-Pembeli Dengan Produk Cacat Dan Kecepatan Produksi Terkontrol.

2016 ◽  
Vol 15 (2) ◽  
pp. 103
Author(s):  
NELITA PUTRI SEJATI ◽  
WAKHID AHMAD JAUHARI ◽  
CUCUK NUR ROSYIDI
Keyword(s):  
Sensitivity Analysis ◽  
Production Rate ◽  
Lead Time ◽  
Demand Uncertainty ◽  
Lot Size ◽  
Defective Items ◽  
Total Cost ◽  
Joint Economic Lot Size ◽  
Demand Rate ◽  
The Impact

Penelitian ini mengembangkan model persediaan Joint Economic Lot Size (JELS) pada pemasok tunggal pembeli tunggal untuk jenis produk tunggal dengan mempertimbangkan produk cacat dan tingkat produksi terkontrol. Tingkat permintaan pada pembeli bersifat stokastik. Pengiriman dilakukan dari pemasok ke pembeli dalam ukuran lot pengiriman yang sama dan lead time pengiriman bersifat tetap. Produk cacat yang ditemukan oleh pembeli pada saat inspeksi disimpan secara sementara di gudang pembeli hingga pengiriman berikutnya tiba untuk selanjutnya produk cacat dikembalikan kepada pemasok. Fungsi tujuan dari model ini adalah meminimasi total biaya persediaan gabungan pemasok pembeli dengan variabel keputusan, yaitu frekuensi pengiriman, periode review, dan tingkat produksi. Analisis sensitivitas dilakukan untuk melihat pengaruh perubahan parameter-parameter tertentu terhadap model. Hasil yang didapatkan dari analisis sensitivitas menunjukkan bahwa total biaya persediaan gabungan sensitif terhadap perubahan nilai parameter persentase produk cacat, ketidakpastian permintaan, dan permintaan. In this paper, we consider a joint economic lot size (JELS) model consisting of single vendor single buyerwith single product. We intend to study the impact of defective items and controllable production rate onthe model. The demand in buyer side is assumed to be stochastic. The delivery of lot from vendor to buyer is conducted under equal size shipment and the lead time is assumed to be constant. The defective items founded by the inspector in buyer side are carried in buyer’s storage until the next shipment and will be returned to the vendor. The goal of the proposed model is to determine optimal delivery frequency, review period and production rate by minimizing the joint total cost. A sensitivity analysis is performed to show the impact of the changes of the decision variables on model’s behavior. The result from the sensitivity analysis shows that the joint total cost is sensitive to the changes of defect rate, demand uncertainty and demand rate. 

An optimal inventory model with interaction of lot size, production rate and lead-time in a fuzzy back-order system

2019 ◽  
Vol 53 (2) ◽  
pp. 517-538
Author(s):  
S. Priyan ◽  
P. Mala ◽  
S. Tiwari
Keyword(s):  
Decision Making ◽  
Production Rate ◽  
Lead Time ◽  
Trade Credit ◽  
Strategic Decision ◽  
Sensitivity Analyses ◽  
Order System ◽  
Lot Size ◽  
Order Rate ◽  
Back Order

This paper examines the decision-making about the interaction of lot size, production rate and lead time between a vendor and a buyer with the consideration of trade credit and fuzzy back-order rate. We assume that the lead time demand is distribution free and the back-order rate is triangular fuzzy number. An economic model is design to determine the optimal lot-size, production rate and lead time while minimizing system total cost. A minimax approach is applied to tackle the model and designed an iterative algorithm to obtain the optimal strategy. Numerical example and sensitivity analyses are given to demonstrate the performance of the proposed methodology and to highlight the differences between crisp and the fuzzy cases. This paper provides optimal decision support tools for managers in the form of mathematical model that improve operational, tactical, and strategic decision making in the fuzzy system. This paper aims to raise the awareness of managers with regard to realistic inventory problems.

scholarly journals Effect of Energy and Failure Rate in a Multi-Item Smart Production System

Energies ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 2958 ◽  
Author(s):  
Mitali Sarkar ◽  
Biswajit Sarkar ◽  
Muhammad Iqbal
Keyword(s):  
Energy Consumption ◽  
Production Rate ◽  
Failure Rate ◽  
Production System ◽  
Optimal Solution ◽  
Development Cost ◽  
Lot Size ◽  
Defective Items ◽  
Unusual Amount ◽  
Control State

To form a smart production system, the effect of energy and machines’ failure rate plays an important role. The main issue is to make a smart production system for complex products that the system may produce several defective items during a long-run production process with an unusual amount of energy consumption. The aim of the model is to obtain the optimum amount of smart lot, the production rate, and the failure rate under the effect of energy. This study contains a multi-item economic imperfect production lot size energy model considering a failure rate as a system design variable under a budget and a space constraint. The model assumes an inspection cost to ensure product’s quality under perfect energy consumption. Failure rate and smart production rate dependent development cost under energy consumption are considered, i.e., lower values of failure rate give higher values of development cost and vice versa under the effect of proper utilization of energy. The manufacturing system moves from in-control state to out-of-control state at a random time. The theory of nonlinear optimization (Kuhn–Tucker method) is employed to solve the model. There is a lemma to obtain the global optimal solution for the model. Two numerical examples, graphical representations, and sensitivity analysis of key parameters are given to illustrate the model.

scholarly journals Two-phase deteriorated supply chain model with variable demand and imperfect production process under two-stage credit financing

2021 ◽  
Author(s):  
Brojeswar Pal ◽  
Anindya Mandal ◽  
Shib Sankar Sana
Keyword(s):  
Supply Chain ◽  
Integrated System ◽  
Chain Model ◽  
Market Demand ◽  
Lot Size ◽  
Credit Policy ◽  
Two Phase ◽  
Quality Improvement Effort ◽  
Promotional Effort ◽  
Imperfect Production

In this article, an imperfect production inventory model consisting of a manufacturer and a retailer with quality improvement effort and the promotional effort sensitive demand pattern is investigated under a two-tier credit policy. We study the model for deteriorating items where the deterioration occurs at different rates in the manufacturer’s and the retailer’s level considering a fixed lifetime of the product. Discussing the six possible cases of credit policy analytically, we analyze the behavior of the model under an integrated system concerning production lot-size, quality effort and promotional effort such that the integrated average profit is maximum. To obtain the optimal solutions of the model, we design an operative solution algorithm. A numerical example is provided to test feasibility of the model, and the effect of the variation of the key parameters is also studied. The outcomes of this proposed model show that the manufacturer and the retailer have to be more careful about their offered credit periods in aspect of the profit. It is observed that the integrated profit is maximum when both credit periods provided by the manufacturer and the retailer belong to the manufacturer’s cycle. Moreover, we identify that the extended product lifetime does not meet with higher profit all times. This study directs that quality effort and promotional effort stimulate the market demand while it is not always economically profitable for the supply chain.

scholarly journals Production rate and lot size-dependent lead time reduction strategies in a supply chain model with stochastic demand, controllable setup cost and trade-credit financing

2020 ◽  
Author(s):  
Monami Das Roy ◽  
Shib Sankar Sana
Keyword(s):  
Production Rate ◽  
Lead Time ◽  
Trade Credit ◽  
Chain Model ◽  
Lot Size ◽  
Setup Cost ◽  
Lead Time Reduction ◽  
Supply Chain Model ◽  
Reduction Strategies ◽  
Credit Financing

This study explores simultaneous reduction strategies of lead time and setup cost in a two-stage supply chain model under trade-credit financing. Lead time depends on avariable production rate and lot size. It consists of setup, production, and transportation time which are shortened to reduce lead time. Although double safety factors are considered to avoid stock-out; but still backorders take place as the demand during the lead time is stochastic.Setup cost is reduced by including an extra investment cost. In addition, the vendor offers a fixed credit period to the buyer to settle the account. The objective is to minimize the integrated expected total cost and optimize the order quantity, number of deliveries, setup and transportation time, setup cost, safety factor for the first batch, and the production rate. A multi-variable optimization technique is used for these purposes. Furthermore, a numerical example together with managerial insights is provided for the establishment and applicability of the proposed model.The numerical results show that the introduction of setup cost reduction and trade-credit financing along with lead time reduction is more beneficial by means of integrated expected total cost reduction.

scholarly journals Production inventory models for deteiorative items with three levels of production and shortages

2017 ◽  
Vol 27 (4) ◽  
pp. 499-519
Author(s):  
Chickian Krishnamoorthi ◽  
C.K. Sivashankari
Keyword(s):  
Production Rate ◽  
Consumer Satisfaction ◽  
Optimal Solution ◽  
Inventory Model ◽  
Lot Size ◽  
Inventory Models ◽  
Total Cost ◽  
Initial Stage ◽  
Production Inventory ◽  
Holding Cost

In this paper, three level production inventory models for deteriorative items are considered under the variation in production rate. Namely, it is possible that production started at one rate, after some time, switches to another rate. Such a situation is desirable in the sense that by starting at a low rate of production, a large quantum stock of manufacturing items at the initial stage are avoided, leading to reduction in the holding cost. The variation in production rate results in consumer satisfaction and potential profit. Two levels of production inventory models are developed, and the optimum lot size quantity and total cost are derived when the production inventory model without shortages is studied first and a production inventory model with shortages next. An optimal production lot size, which minimizes the total cost, is developed. The optimal solution is derived and a numerical example is provided. The validation of the results in this model was coded in Microsoft Visual Basic 6.0.

Optimal production model with quality sensitive market demand, partial backlogging and permissible delay in payment

2018 ◽  
Vol 52 (2) ◽  
pp. 499-512 ◽  
Author(s):  
Brojeswar Pal
Keyword(s):  
Trade Credit ◽  
Integrated System ◽  
Production Model ◽  
Inventory Level ◽  
Market Demand ◽  
Lot Size ◽  
New Production ◽  
Permissible Delay In Payment ◽  
Delay In Payments

In this study, we consider an imperfect production inventory system with quality of the products dependent market’s demand structures and allowable delay in payments. Two alternative approaches of trade credit policies have been discussed when the manufacturer could not pay the due amount to the supplier within the credit period offered. Here, a new cycle is begun with new production when the manufacturer’s inventory touches to a certain level of shortages. The cycle also ends when backlogged inventory level is reached a certain level. The backlogging rate for the player is dependent on waiting time. The production cost of the manufacturer varies with ordering lot size and quality of product. The behavior of the model under integrated system is analyzed. The sensitivity of the key parameters is examined to test feasibility of the model. Finally, a numerical example is provided to investigate the proposed model.

scholarly journals Optimal Decision-Making to Charge Electric Vehicles in Heterogeneous Networks: Stackelberg Game Approach

Energies ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 325 ◽  
Author(s):  
Shijun Chen ◽  
Huwei Chen ◽  
Shanhe Jiang
Keyword(s):  
Electric Vehicles ◽  
Heterogeneous Networks ◽  
Demand Uncertainty ◽  
Stackelberg Game ◽  
Optimal Solution ◽  
Stackelberg Equilibrium ◽  
Optimal Decision ◽  
Charging Station ◽  
Simulation Results ◽  
Grid Operators

Electric vehicles (EVs) are designed to improve the efficiency of energy and prevent the environment from being polluted, when they are widely and reasonably used in the transport system. However, due to the feature of EV’s batteries, the charging problem plays an important role in the application of EVs. Fortunately, with the help of advanced technologies, charging stations powered by smart grid operators (SGOs) can easily and conveniently solve the problems and supply charging service to EV users. In this paper, we consider that EVs will be charged by charging station operators (CSOs) in heterogeneous networks (Hetnet), through which they can exchange the information with each other. Considering the trading relationship among EV users, CSOs, and SGOs, we design their own utility functions in Hetnet, where the demand uncertainty is taken into account. In order to maximize the profits, we formulate this charging problem as a four-stage Stackelberg game, through which the optimal strategy is studied and analyzed. In the Stackelberg game model, we theoretically prove and discuss the existence and uniqueness of the Stackelberg equilibrium (SE). Using the proposed iterative algorithm, the optimal solution can be obtained in the optimization problem. The performance of the strategy is shown in the simulation results. It is shown that the simulation results confirm the efficiency of the model in Hetnet.

Sign in / Sign up

Export Citation Format

Share Document