Minimum Production Cost Research Articles

Elimination of Shrinkage in Ductile Iron Castings Using Computer Simulation of Casting and Solidification

The production of high-quality castings without foundry defects at minimal production costs is a constant priority for foundries. Innovation and optimization of production processes are key to achieving this goal. Computer simulation of foundry processes offers a modern alternative to expensive and time-consuming experiments in real foundries and provides a reliable representation and analysis of casting and solidification processes. A detailed analysis of the casting and solidification simulation results allows the prediction of various risks that can cause defects in cast castings, thereby reducing their quality and, last but not least, the cost of their production. This paper deals with the analysis of a computer simulation of the casting of a brake disc in a Slovak foundry. This brake disc has had shrinkages and micro shrinkages that reduce the internal quality of the casting. These defects occurred in the ribs in the upper part of the casting under the feeders. A computer simulation of the casting and solidification of this casting was made according to the real conditions. It turned out that the designed gating system with a system of feeders was not sufficient to eliminate the emerging defects. A new layout for the feeders was proposed, which ultimately eliminated the occurrence of defects based on the results of the computer simulation. The input parameters were set to be as close as possible to the actual needs of the foundry. Moreover, 3D models of the assemblies were designed in SolidWorks Premium 2015 x64 Edition CAD software, and the filling and solidification simulations were performed using the NovaFlow & Solid CV 4.6r42 simulation program.

COST-BENEFIT ANALYSIS OF SELECTED PRE-EMERGENCE HERBICIDES FOR WEED CONTROL IN COCOYAM (Xanthosoma sagittifolium L.) PRODUCTION

Weed control being a very important operation in the production of cocoyam is costly, therefore, there is a need to evaluate the most economically viable method of weed control for the purpose of minimizing production cost to maximize profit. The experiment was conducted in 2018 at the Ido farm settlement in Ibadan, Oyo State. The experiment involved five pre-emergence herbicides (Diuron 3.2 kg a.i/ha, Indaziflam + Ixoxaflutole 300 g a.i/ha, Flumioxazin + Pyroxasulfone 0.32 kg a.i/ha, Sulfentrazone 600 g a.i/ha, S-Metolachlor + Atrazine 2.64 kg a.i/ha), weed free and weed check (control) laid out in a Randomized Complete Block Design with four replicates. Data were collected on corm and cormel yield parameters, inputs, and costs including revenue associated with herbicide and manual weeding treatments used in benefit: cost ratio analysis. Results showed that Diuron (6.7 t/ha) and Sulfentrazone (9.4 t/ha) gave better cormel and corm yield respectively than the other treatments. The highest benefit-cost ratio was achieved from Diuron-treated plots (4.97). Sulfentrazone and Flumioxazin + Pyroxasulfone treated plots also had a benefit-cost ratio of 2.86 and 2.76 respectively. Indaziflam + Ixoxaflutole and Metolachlor + Atrazine had a similar benefit-cost ratio of 2.71. A low benefit-cost ratio (1.99 ) was produced in weed-free plots while a benefit-cost ratio of less than 1 was observed in weedy check plots (0.76). Therefore, the highest net benefit with a high benefit-cost ratio can be achieved by using Diuron, Flumioxazin + Pyroxasulfone, Sulfentrazone as pre-emergence herbicides in cocoyam production.

Application of The Simplex Method and Digital Literacy in Profit Optimization Problems Taufik Tempe

Resource allocation in the production process are important things that need to be considered to achieve optimal production levels. Production optimization problems are still an obstacle for most businesses operating in the food sector. One of them is the “Taufik Tempe” business which produces tempeh in three different sizes, namely large, medium, and small. The business owner finds it difficult to determine the amount of production according to market demand and minimize production costs for maximum profits. This research aims to solve the profit optimization problem of “Taufik Tempe” with appropriate production allocation to achieve maximum profits. The method used is the method of data collection and data analysis. Data collection methods include field studies (observations and interviews) and literature review. Meanwhile, data analysis uses the simplex method and uses MATLAB software. Data analysis techniques using observation and interviews. Meanwhile, the research results show that the maximum profit per month obtained is Rp 750.000,00 by focusing on producing only large-sized tempeh. Furthermore, by using MATLAB software the same results are obtained as using the simplex method but with a simple, effective and efficient algorithm, ofcourse with precise results and the use of this software aims to avoid calculation errors.

An integrated steering approach to improve a phosphate supply chain efficiency

ABSTRACT This paper presents and illustrates an original application of the redesign in the real context of a mining supply chain producing phosphate rock. One of the major challenges is to successfully produce the final products required by the customers, from raw materials whose chemical composition and availability depend on the extraction program and method. Redesign of the mining supply chain consists of considering the impact of extraction, processing, and blending stages in achieving target objectives. The proposed approach, based on a mixed integer linear programming model, allows moving from fixed production flows to dynamic ones by adopting a flexible and reactive management mode that fully satisfies customer requirements at minimum production costs. Numerical results obtained using real data, corresponding to the infrastructure and order books, illustrate (i) the flexibility, quality, and horizontal alignment ensured by our approach and (ii) the impact of the extraction method on the ability of the SC to fulfil the orders book with more efficiency.

Feasibility analysis and Atlas for green hydrogen project in MENA region: Production, cost, and environmental maps

Renewable energy markets in the Middle East and North Africa (MENA) countries are growing quickly. Therefore, the objective of the current study is to investigate the feasibility of green hydrogen production based on the meteorological conditions within each MENAcountry utilizing a water electrolysis system powered by available solar and wind energies. In addition, it shows the opportunities for constructing hydrogen projects in MENA countries based on the available power, system performance, cost, and CO2 emission mitigation. The simulation is conducted using MATLAB/Simulink software. In addition, five degradation rates are examined in economic analysis in the context of hydrogen production from photovoltaic panels and wind turbines due to the unpredictability of the future value of money. The results revealed that the highest hydrogen production density for WT/H2 is 1.29 kg/m2 in Morocco, 1.26 kg/m2 in Egypt, 5.7 kg/m2 in Saudi Arabia, and 5.58 kg/m2 in Egypt for PV/H2. The WT/H2 system is more efficient than the PV/H2 system, with a maximum value of 31.54 %. The minimal production cost is 2.12 $/kg in Morocco and 2.17 $/kg in Egypt for the WT/H2. In the case of PV/H2, it is 3.28 $/kg in Saudi Arabia and 3.35 $/kg in Egypt. MENA countries have significant potential in hydrogen production and hydrogen investment. The range of CO2 mitigation lies between 11.47 and 87.4 kgCO2/m2. Finally, the current investigation revealed that the MENA region has an excellent opportunity to construct green hydrogen production projects based on wind/solar energies.

Optimizing Perishable and Non-Perishable Product Assignment to Packaging Lines in a Sustainable Manufacturing System: An AUGMECON2VIKOR Algorithm

Identifying appropriate manufacturing systems for products can be considered a pivotal manufacturing task contributing to the optimization of operational and planning activities. It has gained importance in the food industry due to the distinct constraints and considerations posed by perishable and non-perishable items in this problem. Hence, this study proposes a new mathematical model - according to knowledge discovery as well as an assignment model to optimize manufacturing systems for perishable, non-perishable, and hybrid products tailored to meet their unique characteristics. In the presented model, three objective functions are taken into account: (1) minimizing production costs by assigning the products to the right set of manufacturing systems, (2) maximizing the product quality by assigning the products to the systems, and (3) minimizing total CO2 emissions of the machines. A numerical example is utilized to evaluate the performance of AUGMECON2VIKOR compared to AUGMECON2. The results show that AUGMECON2VIKOR obtains superior Pareto solutions across all objective functions. Furthermore, the sensitivity analysis explores the positive green impacts, influencing both cost and quality.

Production and Inventory Dynamics in the Mining Supply Chain: The Impact of Extraction Routings

This paper deals with integrated production-inventory-routing decisions in mining industries. It treats the impact of phosphate extraction routings adopted in open pit mines in providing stocks with diversified characteristics, to satisfy customer requirements at a minimum production cost. Those routings aim to control minerals’ characteristics in terms of quality, volume, and delivery time. For planning production activities, there is a need to select the right extraction routings in mines, to enrich (or not) the raw material and then blend ingredients according to their availability and customer requirements. Less attention was given by literature to the impact of extraction routings in production and stock dynamics. The primary focus revolves around filling the gap and recognizing their pivotal impact in open pit mines. While washing and blending ingredients play crucial roles, they alone may not always suffice to meet customer requirements. This paper undertakes an exhaustive study and modeling, using the case study of a Moroccan company specialized in phosphate rock production and its derivatives, aiming to underscore the significance of extraction routings through tangible and real examples. The findings emphasize a crucial need for variating the extraction routings in providing stocks of raw materials with the optimal characteristics regarding customer requirements.

Adaptability Specifications of No-Till Farming in the Krasnodar Territory

Soil cultivation technologies, applied in the farming system of the Krasnodar region and their impact on changes in the soil organic composition, have been analyzed. Advantages and disadvantages of no-till farming technology, the relationship between the mechanic means in-use and agrotechnical requirements, have been substantiated. Strategy for obtaining competitive agricultural products with a minimum production cost, has been stated. Advantage of multifunctional units in applying no-till farming, has been shown. Crop rotations, recommended for no-till farming application in conditions of the Krasnodar Territory, have been analyzed. Fuel economy in applying no-till farming can reach 40...50%.

Machining-Induced Distortion during Peripheral Milling of High Strength Aluminum Parts

In the aerospace and automotive industries aluminum sheet metal components are often produced by forming and post-machining. Due to the change in the complex stress state during manufacturing, part distortion is a major challenge. The overall objective of this work is to streamline the process chain to minimize production costs. For this, a determination of the material properties and analysis of the machining process parameters and their influence on the resulting distortion are required.First, tensile tests of the aluminum alloy EN AW-7075-T651 were performed. Subsequently, a series of machining tests were conducted to examine the effect of the machining process on the resulting part distortion. This paper presents machining-induced part distortion depending on the variation of the process parameters for down milling operations of thick aluminum plate material. It was found that the radial depth of cut and the cutting speed have a high impact on the resulting distortion, while the feed rate has a small influence.

Examining the robustness of selected microalgae to grow in landfill leachate

Microalgae is widely recognized as a leading candidate for future bio-oil production, serving dual purposes: biodiesel generation and bioremediation. Identifying a sustainable cultivation medium is essential, aiming to minimize production costs. Landfill leachate emerges as a prospective growth medium for microalgae. However, due to the diverse substances within landfill leachate that may impede microalgal growth, careful selection of robust species becomes crucial. This study examined the growth of four microalgae species—Chlamydomonas reindhartii, Chlorella vulgaris, Chlorella ovalis, and Nannochloropsis oculata—in landfill leachate. Prior to utilization, the landfill leachate underwent treatment to remove the total ammonium nitrogen (TAN). Cultivation spanned 30 days, during which various parameters, including ammonium removal, growth rate, and oil content, were monitored. Initially, all microalgae exhibited a decline in numbers, succeeded by a subsequent increase in concentration after several days. Results revealed Nannochloropsis oculata to have the highest growth rate, while Chlamydomonas reindhartii displayed the lowest. Generally, the oil content of all species at the end of cultivation was lower than that of their respective inocula. Chlorella vulgaris exhibited the highest oil content, followed by Chlamydomonas reindhartii, Chlorella ovalis, and Nannochloropsis oculata.

Enterprise Ordering and Transportation Scheme Based on Entropy Weight TOPSIS Method

In this paper, we use the entropy weight TOPSIS method to quantitatively analyze the importance of suppliers to enterprises and establish a single objective function supplier selection model. Specifically, by checking the reliability of the data, the validity of the data in the attachment is guaranteed. The supplier's important metric system is constructed by using six indicators, and a single objective function is established to solve it by Lingo programming. In addition, the objective function aiming at the minimum number of suppliers and the objective function aiming at the minimum production cost of the enterprise is established, and the quantitative analysis method is used to consider the value of the transfer plan and the order plan. Furthermore, a dual-objective planning model aiming at enterprise storage costs and transportation costs is established, and the Lingo program is used to obtain the most economical ordering plan for the new enterprise in the next 24 weeks. Finally, the sensitivity of the considered models was analyzed by SPSS.

Optimisation framework of biomass supply chain in southwest Nigeria

The article investigates the development of a biomass supply chain model by studying the logistic, network optimisation, transportation and economic impact as it affects the southwest Nigeria, with a particular emphasis on the conversion of crop residues into bioproducts such as bioethanol and biodigestate for electricity generation. This model compares the energy produced from single and multiple feedstocks using simulation methods implemented in the MATLAB 2022b programming language solver with the linprog function to implement linear programming to investigate the maximum revenue and minimum production costs as they affect biomass supply chain in southwest Nigeria. The sensitivity analysis is performed to examine the impact of key parameters by measuring essential uncertainty features to show the profitability of the supply chain network while employing feedstock such as cassava peel, maize husk, rice straw, and sorghum bran. The study's findings provide insight into the optimal design and operation of the biomass supply chain in Southwest Nigeria, as well as the viability and potential of using various feedstocks for energy generation while taking into account the economic and logistical aspects of the supply chain. The optimisation framework provides decision-makers and stakeholders with practical tools to improve the sustainability of biomass utilisation and efficiency in the region, and research will help to develop a more robust and environmentally friendly energy system in the region, easing the transition to a renewable and sustainable future.

PERENCANAA PRODUKSI PAVING BLOCK DENGAN MENGGUNAKAN MODEL PROGRAM DINAMIS (DYNAMIC PROGRAMMING) DI CV. SHOHAT GORONTALO.

This current research aimed to plan an optimal and scheduled production to minimize defects in production quantities, excess or shortage of production quantities with minimum costs. The method used was Dynamic Progamming to develop optimal scheduling, by forecasting average production using the Autoregressive Integrated Moving Average (ARIMA) model. The ARIMA was employed to forecast the average amount of production data of CV Shohat Gorontalo which were the data for the last 24 weeks or during 6 months. The result obtained was that the minimum cost was always obtained at the inventory figure I = 0, because having less inventory or even no inventory would reduce the total cost due to the small holding costs when compared to production costs. The cost incurred for the production schedule during the July- December of 2023 period was IDR 9,161,954,550. In addition, the data were the optimal result in minimizing production costs using the Dynamic Programming method. Abstract written in English. Abstracts are written in a sequence that contains the purpose of research, the methods used in research, research results, conclusions, suggestions, and research implications. The abstract is concise, concise and written in one paragraph (maximum 200 words) with single space, Times New Roman font and 10 font sizes

Technology and Peculiarities of Production of Large-format Ceramic Stones Based on Opoka-like Rocks

Introduction. One of the urgent tasks of the wall ceramics industry at present is the production of large-format ceramic stones with compressive strength of 10–15 MPa and thermal conductivity less than 0.12 W/(m·оС), while the market cost per 1 m3 should be competitive with gas-concrete blocks and be in the range of 5–6 thousand rubles per 1 m3. This problem can be solved by developing modern energy-efficient production technology and using opoko-like rocks and coal processing wastes as the main raw material as fuel and burnout additive.Materials and Methods. The opoka-like rocks — opokas from the deposits of southern Russia — Nagolnovskoye, Bakanskoye, Shakhtinskoye, Avilo-Fyodorovskoye, and coal cake produced by Pyramida LLC were used for research. The study of chemical and mineral composition was carried out by standard methods on prepared samples. The study of ceramic and technological properties (plasticity, molding moisture, degree of crushing, air and fire shrinkage, compressive strength, water absorption) of raw materials was carried out according to generally accepted methods on samples precrushed to a certain grain composition, since opokas, depending on the type, do not soak or slowly soak in water.Results. Pre-firing technological properties of opokas and their differences from traditional clay raw materials soaked in water were confirmed: increased molding moisture, small air shrinkage, low sensitivity to drying. The dependence of density and strength of samples on the degree of pulverization of opoka, firing temperature and the amount of carbon cake in the raw material mixture has been established. The influence of coal preparation wastes and their optimal amount on physical and mechanical properties of fired samples has been determined. The introduction of carbon cake allows to exclude the use of gas for firing or minimize its introduction. On the basis of the obtained results a simplified technological scheme for the production of large-format stones with minimum production cost has been developed.Discussion and Conclusion. The proposed technological scheme consists of two units of the main mass preparation equipment, molding of products is carried out by semi-rigid extrusion, drying of products is carried out directly on kiln cars, and for firing coal cake is used, which is introduced into the raw mix. These factors and technological methods allow to obtain products with low thermal conductivity, but with strength 3–5 times higher than that of aerated concrete blocks of similar density. The prime cost of ceramic stones will amount to 3–3.5 thousand rubles per 1 m3 of products. Rostov region, possessing opoka-like rocks and unclaimed reserves of technogenic coal raw materials, can become a center of production of large-format ceramic stones with low cost and provide the south and central part of the country with highquality wall materials.

An improved study of near-well zone flooding for polymer solution through the mechanical shearing and forchheimer flow simulation

Polymer flooding is a vital tertiary oil recovery technology that maintains stable oilfield production during high water cut periods. This technique involves improving the viscosity of injection fluids by using polymer solutions, which help reduce the mobility ratio of oil and water, expand sweep efficiency, and increase swept area. However, highly viscous polymer solutions form complex spatial structures between and within molecules, which leads to significant viscosity loss rates in the near-wellbore region at the well injection end. To address this issue, a near-wellbore shear device with nozzle completion was built to study the shear effects of two types of polymers. The study revealed that the polymer solutions destroyed intermolecular and intramolecular structures after shearing, causing the water cut curves to shift up and left. Based on the Brinkman equation of COMSOL Multiphysics's Carreau model, the percolation model of polymer solution in the near-well zone was constructed. COMSOL simulation results also demonstrated that high-speed shearing at the nozzle orifice was the primary cause of shear degradation. Therefore, it is essential to adopt reasonable injection intensities and proper polymer solution concentrations in oilfields to maximize oil recovery and minimize production costs. This is of crucial engineering significance in guiding oilfield production and optimizing injection parameters and processes.

The development of an integrated GIS-based optimization framework for power generation from municipal solid waste-to-energy facilities

Waste-to-energy (WtE) is one of the municipal solid waste (MSW) management pathways that can reduce waste volumes while recovering energy. There has been considerable focus on using MSW for energy production; however, there are few integrated assessments of the optimal location and scale of the conversion of MSW to energy. This research develops a novel framework that integrates the analysis of candidate sites for MSW gasification facilities using a geographical information system (GIS) through a multi-criterion decision-making (MCDM) model with a mixed-integer linear programming (MILP) model to determine optimal scale and location. The most suitable candidate locations were identified through a GIS-based location-allocation analysis. A MILP model integrated with GIS was then used to determine the minimum per-unit electricity production costs by optimizing the numbers, locations, and sizes of the proposed WtE and preprocessing facilities. The key inputs to the optimization model are actual road and railway transportation distances, WtE gasification and preprocessing facility capital and installation costs, operation and maintenance costs, gate fee and tipping fees (the fee for disposal of ash at the landfill), and the municipal guidelines. The proposed integrated framework was applied in a case study for Alberta, a western province in Canada. The results indicate that at a 10% rate of return, electricity production is cost-competitive with current electricity prices. The per-unit cost of electricity production (COEP) was found to be only 16.14 $/MWh when the gate fee was treated as a revenue component. The optimal plant location was in Edmonton and the optimum plant size was 175 MW. Sensitivity and uncertainty analysis was conducted to understand the critical input parameters that impact the COEP. The results indicate that the COEP is most sensitive to changes in tipping fees, plant efficiency, capital cost, discount rate, and transportation cost. The developed framework is critical for investment decisions and policy development, and it can be applied globally with adjustments to data and assumptions.

Chiplets Integration: Simplifying the Landscape

Heterogenous integration and the use of chiplets are the logical outcome of several factors effecting the IC industry’s drive towards higher and higher performance, and to accomplish this at minimum total product cost. This drive to heterogenous solutions has created a new development cycle in the IC Packaging industry to get ready for these product needs. The choice of which package to use for chiplet-based designs is driven by several important factors, most importantly, the type of die-to-die interface that is being used. This bus largely defines the physical structure such as line and space requirements, and the electrical performance which influences the type of materials used as dielectrics and design practices which must be enabled to permit a successfully product design. There are a growing number of package configurations to accommodate these chiplet integrations, but in vast majority of real-world applications, there are only a handful of package types, with clear rationale guiding package selection. This paper will examine the different approaches for heterogeneous packaging and try to simplify the IC packaging selection process, and provide guidance for real-world implimenations. Although there are many different trade names in the industry there are only a few basic categories, and once this is understood the package selection should seem much less daunting.

A Novel Strategy for Whole-Cell Biotransformation Enabling Simultaneous l-Phenyllactic Acid Production and Coenzyme Regeneration.

l-Phenyllactic acid (l-PLA) is a small molecular organic acid that exhibits a powerful capacity for inhibition against foodborne pathogens. In this work, we developed a new cost-effective and environmentally friendly process for the biosynthesis of l-PLA. This strategy designed a novel whole-cell biotransformation system employing two heterologous enzymes, namely, phenylalanine dehydrogenase (PheDH) and l-hydroxyisocaproate dehydrogenase (l-HicDH). The novelty of this strategy lies in the first-time utilization of these two enzymes, which not only enables cascade catalysis for the production of l-PLA but also facilitates the regeneration of the coenzymes (NAD+/NADH) using only two enzymes rather than introducing more heterologous enzymes to the system. Consequently, this strategy can effectively simplify the biosynthesis process of l-PLA and minimize production costs. The initial l-PLA yield using this process achieved 2.53 ± 0.07 g/L. Furthermore, through meticulous optimization of the parameters for inducible enzyme expression and l-PLA biosynthesis, the l-PLA yield was successfully increased to 4.68 ± 0.04 g/L with a yield rate of 64.54 ± 0.29%. Moreover, this novel strategy is versatile in the biosynthesis of other organic acids, which can be achieved by easily modulating the combinations of substrates and enzymes.

A comparative experimental study on hemispheric distillation system integrated with metamorphic fabric materials for efficient and low-cost solar desalination

This work presents a comparative experimental investigation of the potential of low-cost metamorphic fabric materials for augmenting the distilled yield of hemispheric solar distillation systems. The impacts of two various metamorphic layers; namely, a 20 mm thick cement layer and a 20 mm thick slate layer on the distiller thermo-economic performance are studied and compared with a conventional hemispheric solar distiller (CHSD). Three hemispheric solar stills are manufactured and tested under the same climate characteristics. Moreover, a thermo-economic analysis of the three involved hemispherical solar stills is carried out; including cumulative distilled product, daily thermal efficiency, and cost per unit kg of the distilled product. According to the findings, the incorporation of a 20 mm thick slate layer with a saltwater depth of 10 mm into the hemispheric absorber basin with the optimal modification yields the maximal distilled product and minimal production cost of the hemispheric distillers. The daily distilled product augmented and reached 8.35 and 7.60 kg/day⋅m2 for the hemispheric distiller respectively with a layer of slate and cement, in comparison with that of the CHSD (5.65 kg/day⋅m2). The increase in the distilled product with the use of slate and cement metamorphic layers reached 47.80 % and 34.51 %, over the CHSD, respectively. Furthermore, the thermoeconomic findings revealed that the amelioration in the daily energetic efficiency for using the slate and cement metamorphic layers is evaluated as 46.90 % and 34.04 %, respectively, compared to CHSD. Additionally, the reduction in the freshwater cost is estimated as 31.73 %, and 25.24 % over the CHSD, respectively.

A Lagrangian relaxation approach to an electricity system investment model with a high temporal resolution

AbstractThe global production of electricity contributes significantly to the release of carbon dioxide emissions. Therefore, a transformation of the electricity system is of vital importance in order to restrict global warming. This paper proposes a modelling methodology for electricity systems with a large share of variable renewable electricity generation, such as wind and solar power. The model developed addresses the capacity expansion problem, i.e. identifying optimal long-term investments in the electricity system. Optimal investments are defined by minimum investment and production costs under electricity production constraints—having different spatial resolutions and technical detail—while meeting the electricity demand. Our model is able to capture a range of strategies to manage variations and to facilitate the integration of variable renewable electricity; it is very large due to the high temporal resolution required to capture the variations in wind and solar power production and the chronological time representation needed to model energy storage. Moreover, the model can be further extended—making it even larger—to capture a large geographical scope, accounting for the trade of electricity between regions with different conditions for wind and solar power. Models of this nature thus typically need to be solved using some decomposition method to reduce solution times. In this paper, we develop a decomposition method using so-called variable splitting and Lagrangian relaxation; the dual problem is solved by a deflected subgradient algorithm. Our decomposition regards the temporal resolution by defining 2-week periods throughout the year and relaxing the overlapping constraints. The method is tested and evaluated on some real-world cases containing regions with different energy mixes and conditions for wind power. Numerical results show shorter computation times as compared with the non-decomposed model and capacity investment options similar to the optimal solution provided by the latter model.