scholarly journals A Constrained Production System Involving Production Flexibility and Carbon Emissions

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 275 ◽  
Author(s):  
Asif Iqbal Malik ◽  
Byung Soo Kim
Keyword(s):  
Production Rate ◽  
Carbon Emissions ◽  
Production System ◽  
Ghg Emissions ◽  
Real Life ◽  
Lot Size ◽  
Setup Cost ◽  
Defective Items ◽  
Machine Failure ◽  
Decision Variables

The proposed study presents an economic lot size and production rate model for a single vendor and a single buyer setup. This model involves greenhouse gas (GHG) emissions from industrial sources. The carbon emissions in this model are considered as two types: direct emissions and indirect emissions. The production rate affects carbon emissions generation in production, i.e., generally, higher production rates result in more emissions, which is governable in many real-life cases. The production rate also impacts the process reliability and quality. Faster production deteriorates the production system quickly, leading to machine failure and defective items. Such reliability and quality problems increase energy consumptions and supply chain (SC) costs. This paper formulates a vendor-buyer SC model that tackles these issues. It considers two decision-making policies: integrated or centralized as well as decentralized, where the aim is to obtain the optimal values of the decision variables that give the minimum total SC cost. It includes the costs of setup, holding inventory, carbon emissions, order processing, production, reworking, and inspection processes. The decision variables are the production rate, lead time, order quantity, the number of shipments, and the investments for setup cost reduction. In the later sections, this paper compares the numerical outcomes of the two centralized and decentralized policies. It also provides sensitivity analysis and useful insights on the economic and environmental execution of the SC.

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 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

A SINGLE-VENDOR SINGLE-BUYER INTEGRATED PRODUCTION-INVENTORY MODEL WITH QUALITY IMPROVEMENT AND CONTROLLABLE PRODUCTION RATE

2017 ◽  
Vol 80 (1) ◽  
Author(s):  
Wakhid Ahmad Jauhari
Keyword(s):  
Quality Improvement ◽  
Production Rate ◽  
Capital Investment ◽  
Production Capacity ◽  
Success Factor ◽  
Lot Size ◽  
Improvement Program ◽  
Defective Items ◽  
Total Cost ◽  
Single Vendor

In the classical vendor-buyer inventory models, the common unrealistic assumption is that all the items manufactured are in good quality. However, in reality, it can be observed that there may be some defective items produced and then delivered to the buyer. Thus, the existence of defective items would consequently give significant influence to system behavior. In addition, a manufacturing flexibility such as the capability to adjust production capacity becomes a key success factor for increasing system flexibility as well as reducing total cost. Here, we investigate how a quality improvement program and adjustable production rate can help the supply chain to reduce the total cost. This paper studies the effect of quality improvement and controllable production rate in joint economic lot size model consisting of single-vendor and single-buyer under stochastic demand. The model gives allowance to the vendor to adjust production rate and also to invest an amount of capital investment to reduce the defect rate. The lead time is comprised of production time and setup and transportation time. The model also considers a situation in which the shortages in buyer side are assumed to be partially backordered. To solve the model, an iterative algorithm is proposed to determine simultaneously safety factor, delivery lot size, delivery frequency, production rate and process quality for minimizing total cost is proposed. The result from this study shows that allowing the vendor to both adjust the production rate and reduce the defective product by adopting quality improvement policy can reduce the individual and total cost. In the example given, the proposed model gives significant total cost saving of 45.9% compared to the model without controllable production rate and quality improvement.

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.

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. 

scholarly journals Does the Autonomation Policy Really Help in a Smart Production System for Controlling Defective Production?

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1142 ◽  
Author(s):  
Mitali Sarkar ◽  
Li Pan ◽  
Bikash Koli Dey ◽  
Biswajit Sarkar
Keyword(s):  
Production System ◽  
Capital Investment ◽  
Single Type ◽  
Main Theme ◽  
Total System ◽  
Production Rates ◽  
Setup Cost ◽  
Defective Items ◽  
Long Run ◽  
Imperfect Items

This study explains about a serial smart production system where a single-type of product is produced. This system uses an unequally sized batch policy in subsequent stages. The setup cost is not always deterministic, it can be controllable and reduced by increasing the capital investment cost, and that the production rates in the system may vary within given limits across batches of shipments. Furthermore, as imperfect items are produced in long-run system, to clean the imperfectness autonomation policy is adopted for inspection, which make the process smarter. The shipment lot sizes of the deliveries are unequal and variable. In long-run production system, defective items are produced in “out-of-control” state. In this model, the defect rate is random with a uniform distribution which is clean from the system by autonomation. In addition, in the remanufacturing process, it is assuming that all defective products are repaired, and no defective products are scrapped. The main theme of developing this model is to determine the number of shipments and the optimal production lot size to adjust the production rates and decrease the total system cost under a reduced setup cost by considering the discrete investment and make a serial smart production system. A solution procedure along with an advanced algorithm was proposed for solving the model. Numerical examples with some graphical representations are provided to validate the model.

scholarly journals An EPQ inventory model considering an imperfect production system with probabilistic demand and collaborative approach

2019 ◽  
Vol 17 (2) ◽  
pp. 282-304
Author(s):  
Katherinne Salas-Navarro ◽  
Jaime Acevedo-Chedid ◽  
Gina Mora Árquez ◽  
Whady F. Florez ◽  
Holman Ospina-Mateus ◽  
...  
Keyword(s):  
Supply Chain ◽  
Production System ◽  
Inventory Model ◽  
Collaborative Approach ◽  
Lot Size ◽  
Defective Items ◽  
Content Type ◽  
Imperfect Production ◽  
Imperfect Items ◽  
Exponential Probability

Purpose The purpose of this paper is to propose an economic production quantity (EPQ) inventory model considering imperfect items and probabilistic demand for a two-echelon supply chain. The production process is imperfect and the imperfect quality items are removed from the lot size. The demand rate of the inventory system is random and follows an exponential probability density function and the demand of the retailers is depending on the initiatives of the sales team. Design/methodology/approach Two approaches are examined. In the non-collaborative approach, any member of the supply chain can be the leader and takes decisions to optimize the profits, and in the collaborative system, all members make joint decisions about the production, supply, sales and inventory to optimize the profits of the supply chain members. The calculus approach is applied to find the maximum profit related to the members of the supply chain. Findings A numerical example is presented to illustrate the performance of the EPQ model. The results show that collaborative approach generates greater profits to the supply chain and the market’s demand represents the variable behavior and uncertainty that is generated in the replenishment of a supply chain. Originality/value The new and major contributions of this research are: the inventory model considers demand for products is random variable which follows an exponential probability distribution function and it also depends on the initiatives of sales teams, the imperfect production system generates defective items, different cycle time are considered in manufacturer and retailers and collaborative and non-collaborative approaches are also studied.

scholarly journals Optimization of Safety Stock under Controllable Production Rate and Energy Consumption in an Automated Smart Production Management

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2059 ◽  
Author(s):  
Mitali Sarkar ◽  
Biswajit Sarkar
Keyword(s):  
Energy Consumption ◽  
Production Rate ◽  
Production System ◽  
Spare Parts ◽  
Energy Utilization ◽  
Smart Manufacturing ◽  
Defective Items ◽  
Safety Stock ◽  
Random Breakdown ◽  
Optimum Energy

A smart production system is essential to produce complex products under the consumption of efficient energy. The main ramification of controllable production rate, amount of production size, and safety stocks is simultaneously optimized under proper utilization of energy within a smart production system with a random breakdown of spare parts. Due to the random breakdown, a greater amount of energy may be used. For this purpose, this study is concerned about the optimum safety stock level under the exact amount of energy utilization. For random breakdown, there are three cases as production inventory meets the demand without utilization of the safety stock, with using of the safety stock, and consumed the total safety stock amount and facing shortages. After the random breakdown time, the smart production system may move to an out-of-control state and may produce defective items, where the production rate of defective items is a random variable, which follows an exponential distribution. The total cost is highly nonlinear and cannot be solved by any classical optimization technique. A mathematical optimization tool is utilized to test the model. Numerical study proves that the effect of energy plays an important role for the smart manufacturing system even though random breakdowns are there. it is found that the controllable production rate under the effect of the optimum energy consumption really effects significantly in the minimization cost. It saves cost regarding the corrective and preventive maintenance cost. The amount of safety stock can have more support under the effect of optimum energy utilization. The energy can be replaced by the solar energy.

scholarly journals Effect of Unequal Lot Sizes, Variable Setup Cost, and Carbon Emission Cost in a Supply Chain Model

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Biswajit Sarkar ◽  
Sharmila Saren ◽  
Debjani Sinha ◽  
Sun Hur
Keyword(s):  
Supply Chain ◽  
Carbon Emission ◽  
Graphical Representation ◽  
Chain Model ◽  
Lot Size ◽  
Setup Cost ◽  
Defective Items ◽  
Supply Chain Model ◽  
Investment Function ◽  
Optimum Solution

Due to heavy transportation for single-setup multidelivery (SSMD) policy in supply chain management, this model assumes carbon emission cost to obtain a realistic behavior for world environment. The transportation for buyer and vendor is considered along with setup cost reduction by using an investment function. It is assumed that the shipment lot size of each delivery is unequal and variable. The buyer inspects all received products and returns defective items to vendor for reworking process. Because of this policy, end customers will only obtain nondefective items. The analytical optimization is considered to obtain the optimum solution of the model. The main goal of this paper is to reduce the total cost by considering carbon emission during the transportation. A numerical example, graphical representation, and sensitivity analysis are given to illustrate the model.

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.

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