Optimal Production Quantity Research Articles

Scheme selection with probabilistic multiple objectives optimization

This article presents the scheme/alternative selections with probabilistic multiple objectives optimization (PMOO). In the PMOO assessment, all response objectives (attributes) are divided into beneficial or unbeneficial types according to their function and preference to equivalently contribute their partial preferable probabilities simultaneously, the total preferable probability of an alternative is the multiplication of its all partial preferable probabilities, which determines the optimal evaluation uniquely and comparatively. The application examples contain a personnel selection and a production quantity optimal control. The former is for an engineer position in a software development department from five alternative candidates withstanding seven optimal criteria (response objectives) comparatively, and the latter aims to get an optimal production quantity with a higher profit rate and lower final cost. In the personnel selection, the seven optimal response objectives (criteria) include relevant education, work experience in the field, relevant certificates, level of presentation and communication, ability of personnel management, capabilities of planning and organization, and expressiveness of foreign language. All these seven response objectives are attributed to the beneficial type of attribute to join the assessment. As to the production quantity control, the profit rate belongs to the beneficial type of objective, while the final cost is attributed to the unbeneficial type of attribute. The evaluated results reveal that the optimal alternate for the personnel selection is candidate No. 4, and the optimum production quantity is at x* = 54 items. The achievement of the present article indicates the validity of the corresponding approach and algorithm with rationality. The novelty of this work is to reflect the simultaneity of the response objectives (criteria) in the optimal system by using probabilistic multiple objectives optimization, and all response objectives either beneficial type or unbeneficial type are evaluated separately in an equivalent manner.

OPTIMALISASI JUMLAH PRODUKSI ROTI ADIL BAKERY DI DESA MEUSEE KECAMATAN KUTA BLANG KABUPATEN BIREUEN

The Adil Bakery bread agroindustry is one of the industries that produces bread with contemporary variants, namely; Tiramissu bread, blueberry bread, strawberry bread, chocolate bread and srikaya bread. In the implementation of production and marketing activities, this bread agroindustry does not always run smoothly, there are several obstacles that occur, such as erratic bread sales every day, such as bread not being sold out within a day. Therefore, Adil Bakery requires optimal production quantity planning to determine the number of products that will be produced for each type of bread variant in a day. This research was conducted to analyze the optimal combination of bread production quantities and to determine the maximum amount of profit obtained by the Adil Bakery agroindustry. The data analysis method used is quantitative with a linear programming model using the simplex method with the help of QM For Windows software. The results of the research show that in one production the optimal bread production combination for the Adil Bakery bread agroindustry to produce maximum profits is 460 pcs of tiramissu bread, 750 pcs of blueberry bread, 750 pcs of strawberry bread, 1,080 pcs of chocolate bread pcs and 750 pcs of srikaya bread. Meanwhile, the maximum profit that will be obtained by the Adil Bakery bread agroindustry in one production is IDR 6,541.12 per five variants. If production is under optimal conditions, the profit contribution that Adil Bakery will receive will increase by IDR 3,105,236 per five variants from the profit contribution under actual conditions. Keywords: Agroindustry, Bread, Optimization, Profit

A Sustainable Production Planning Scheme for New Energy Vehicles in China

The carbon emissions of new energy vehicles (NEVs)have transited from the use stage to the production stage, indicating that the environmental impact of NEVs in the manufacturing stage cannot be ignored. To reduce carbon emissions and maintain profits, this study proposes a fuzzy multi-objective optimization model to achieve a sustainable production planning scheme for NEVs. The proposed model not only considers the maximum profits of automobile enterprises but also the minimum target of carbon emissions in the production process, to coordinate the optimal production quantity. The results show that the output of NEVs in different price ranges has different proportions. The market share of blade electric vehicles is the highest, accounting for 39% of the NEV market, and the proportion of plug-in hybrid and blade electric vehicles is increasing. The sensitivity analysis further reflects the impact of government subsidy “recession” and body lightweight on the output, carbon emissions, and annual profits of NEVs in China. Accordingly, this paper provides policy implications for achieving a sustainable production planning scheme for NEVs in China.

Optimum production lot size for a perishable product under exponential demand with partial backordering and rework

The management of inventory significantly impacts an organization's profitability. Numerous researchers have developed the production model tailored for decaying items to boost sales and minimize inventory, thereby increasing turnover ratios. This study focuses on the EPQ model for reworkable items under exponential combined with inventory dynamics. The primary objective is to optimize the production plan to manage maintenance costs effectively, ensuring optimal Leveraging human and technological resources. The research determines the optimal cycle length, backordered quantities, and production quantities to minimize overall costs. Specifically, penalties are incurred for excessive production times during rework and non-rework phases. This model finds applications in industries such as printed circuit board assembly in semiconductor manufacturing, metal parts, and plastic molding. The study concludes with numerical examples comparing total costs under the proposed model, supplemented by sensitivity analyses that explore the impacts of parameter variations on decision-making.

Optimisasi Jumlah Produksi Roti Kacang Dengan Metode Cutting Plane

Abstract. This research aims to optimize the production of peanut bread at UKM Peanut Roti Hj. Eliya Lubis in Tebing Tinggi City. The main challenges faced are fluctuating raw material prices and unstable consumer demand, which affect the production process. The research uses the cutting plane method to complete an integer linear program to determine optimal production quantities. This method was chosen because it is effective in solving optimization problems with integer results, which are relevant for in-house production. The research results show that the cutting plane method is able to produce better optimal solutions than other methods, such as branch and bound, thereby increasing production efficiency and company profits. This research makes a significant contribution in helping SME entrepreneurs face intense business competition by managing resources more effectively and efficiently.

Software locking special features: Optimal marketing and operational strategies for a manufacturer

This paper studies a manufacturer that produces and sells a low-end product and a high-end product. The manufacturer can utilize the operational strategy of producing one uniform product but software lock the special features from the customers who did not pay the premium price for the high-end product. The software lock enables the manufacturer to further invest in marketing efforts to promote the low-end customer to buy the special features well after the purchase and delivery of the product. We provide the necessary and sufficient conditions under which the manufacturer should produce one uniform product and utilize the software lock strategy instead of the traditional manufacturer that produces two distinct products with the possibility of downward product substitution. Our paper establishes the threshold production costs required for the manufacturer to produce one uniform product. The results from our numerical studies confirm the validity of our mathematical models and provide further insights into the impact price, cost, demand uncertainty, and marketing efforts have on the optimal production quantity and total profit. We find that interestingly, when the expected proportion of high-end demand increases, the threshold cost of the low-end product for the manufacturer to produce one uniform product, initially decreases then it increases.

Should live broadcasting platforms adopt artificial intelligence? A sales effort perspective

We analytically investigate a supply chain (SC) that is composed of a manufacturer and a live broadcasting platform, and examine whether the latter should adopt artificial intelligence (AI) considering sales effort. We consider several important factors that affect the SC partners’ decision-making including live broadcasting power, consumer expectations of the product, and unfit probability that the consumer is unsatisfied with the bought product. Specifically, the “live broadcasting power” refers to the power of influencers’ personal influence and fans group to enhance product sales. The results are as follows: First, the optimal production quantity of the offline channel (platform) exhibits a positive (negative) correlation with the retail price of the offline channel in the agency mode with AI. Nevertheless, in the resale mode, the retail price of the offline channel has no influence on the two channels’ optimal production quantities. Second, with low marginal cost of adopting AI, the live broadcasting platform should (not) adopt AI under high (low) live broadcasting power. With high marginal cost of adopting AI, the live broadcasting platform should (not) adopt AI under low or high (moderate) live broadcasting power. In addition, the manufacturer without AI should select the agency mode (resale mode) under high (low) live broadcasting power, while the manufacturer with AI should always collaborate with the live broadcasting platform implementing the agency mode. Finally, the agency and resale modes can achieve coordination between the two firms. We also consider the partial unfit probability, hybrid mode, and “webrooming” behavior to extend our study, and numerically demonstrate our analytical findings’ robustness.

Optimal product quantity linear programming model for profit maximization in plastic small medium manufacturing firms

Planning production and maximizing profits can be difficult tasks for small and medium-sized manufacturing businesses (SMEs). Owing to their difficulties implementing the newest and most advanced Industry 4.0 technologies, small and medium-sized enterprises (SMEs) generally depend more on expert guidance. Thus this study focuses on the development of a Linear programming model for determining the optimum quantities of product in order to maximize profit profits in manufacturing Small medium enterprises. Data spanning over a period of forty five months was obtained from a manufacturing small and medium-sized enterprise. An optimization was developed in the study to determine the optimal product quantity for profit maximization. Based on the developed model and its optimization, it was determined that the optimal production quantity for the plastic factory to be 12000cups resulting in a maximum profit of N456000. This optimization approach provides valuable insights for the plastic factory’s production planning.

Optimizing Concrete Paver Block Production: A Linear Programming Approach for Enhanced Profitability in the Construction Industry

As an operational optimization (maximization or minimization) methodology, linear programming (L.P.) in operation research has proven successful in several areas by offering logical outcomes to challenging issues, including resource constraints. The study aimed to bridge the gap between theoretical applications of L.P. and the practical needs of the construction industry, specifically focusing on determining the optimal production quantities of 60 mm and 40 mm concrete paver blocks for Janta Udhog Pvt. Ltd. as a case study to achieve maximum profitability, offering essential new insights into how L.P. may successfully handle the complex problems encountered by businesses in this industry. An interview with the owner of Janta Udhog Pvt. Ltd. was conducted to obtain the primary data for the study. Secondary data such as sale records, monthly demand of each product, and inventory records were also obtained to formulate a linear programming model. The model was then solved using the LINGO software. This research underscores the optimal production recommendations for Janta Udhog Pvt. Ltd., advising the manufacture of 566.67 units of the 60 mm block and 350 units of the 40 mm block, leading to a maximum daily profit of NPR 2966.67. By applying linear programming techniques, these findings contribute to a more informed and strategic decision-making approach in the construction sector. The study illuminates the benefits of utilizing linear programming in challenging situations, providing valuable insights for academics, business owners, and decision-makers.

Newsvendor model for a dyadic supply chain with push-pull strategy under shareholding and risk aversion

This paper investigates the optimization and coordination problem in the framework of classic push and pull newsvendor models under shareholding and CVaR criterion. A decentralized supply chain consisting of upstream supplier and the downstream manufacturer is considered. Firstly, taking the risk aversion into account, the optimal decision-makings are investigated under shareholding in push, pull supply chain respectively. By comparison it is found that the optimal order or production quantity depends on the degree of member’s risk aversion and shareholding ratio. Furthermore, the combined contracts are designed to coordinate the supply chain and optimal coordination parameters are obtained. Besides, the impacts of risk-averse preference and the shareholding fraction on supply chain performance are also investigated. The results indicate that in push supply chain the optimal ordering increases in the risk-averse parameter of the downstream manufacturer and the percentage of shares held by the upstream supplier in the downstream manufacturer. However, the optimal wholesale price makes the opposite change. In pull supply chain, the optimal production quantity is independent of the shareholding fraction and decreases with regards to the supplier’s risk aversion. Lastly, some numerical examples are given to illustrate the theoretical results and some suggestions to supply chain management are also provided.

Optimizing the Economic Order Quantity Using Fuzzy Theory and Machine Learning Applied to a Pharmaceutical Framework

In this article, we present a novel methodology for inventory management in the pharmaceutical industry, considering the nature of its supply chain. Traditional inventory models often fail to capture the particularities of the pharmaceutical sector, characterized by limited storage space, product degradation, and trade credits. To address these particularities, using fuzzy logic, we propose models that are adaptable to real-world scenarios. The proposed models are designed to reduce total costs for both vendors and clients, a gap not explored in the existing literature. Our methodology employs pentagonal fuzzy number (PFN) arithmetic and Kuhn–Tucker optimization. Additionally, the integration of the naive Bayes (NB) classifier and the use of the Weka artificial intelligence suite increase the effectiveness of our model in complex decision-making environments. A key finding is the high classification accuracy of the model, with the NB classifier correctly categorizing approximately 95.9% of the scenarios, indicating an operational efficiency. This finding is complemented by the model capability to determine the optimal production quantity, considering cost factors related to manufacturing and transportation, which is essential in minimizing overall inventory costs. Our methodology, based on machine learning and fuzzy logic, enhances the inventory management in dynamic sectors like the pharmaceutical industry. While our focus is on a single-product scenario between suppliers and buyers, future research hopes to extend this focus to wider contexts, as epidemic conditions and other applications.

Economic Production Quantity Model Considering Rework of Imperfect Goods under Stock, Advertisement, Selling Price and Replacement Period-Dependent Demand

An economic production quantity (EPQ) system with an imperfect production model in which demand is affected by advertisement frequency, selling price, stock level and product replacement time is discussed in this paper. It is unavoidable to produce only perfect quality goods in a manufacturing operation due to real-life issues like labor problems, machinery faults, etc. Therefore, we consider the production system imperfect and manufacture a fraction of imperfect goods that depend on the production rate. All produced goods are continuously shifted to the screening center, where perfect goods are directly sold to the consumers. After the screening period, the imperfect goods are transferred to the reworking center, where some imperfect goods are reworked at a price. The remaining defective products are sold as a single lot. A profit function is developed for this proposed production inventory model, which is highly nonlinear. The total profit is maximized using the graphical method to get the optimal production quantity and total business time. The profit function’s concavity is shown graphically by using the Mathematica software. To demonstrate the model’s feasibility, numerical examples are provided. Sensitivity analysis is carried out to highlight the findings of the suggested production inventory system and depict the managerial insights.

Platform Operations With Consumer Returns Windows: Reselling Mode Versus Marketplace Mode

In platform operations, consumer returns are common. In this article, considering the consumer returns window (CRW), we analytically study the manufacturer's operational decisions using the marketplace mode and reselling mode. We explore both the exogenous and endogenous CRW scenarios. We uncover several findings: First, with an exogenous CRW, the optimal production quantities using the marketplace mode and reselling mode always decrease with the fitness between the product and consumers’ taste; the optimal production quantity using the marketplace mode increases in the commission rate, and the optimal profits of the manufacturer and platform increase in MRE (i.e., the marketplace relative efficiency). Second, with an endogenous CRW, the manufacturer's optimal profit first decreases and then increases with MRE, while the platform's optimal profit increases with MRE. Third, the manufacturer prefers the reselling mode (marketplace mode) if MRE is low (high) under the case with an exogenous CRW. However, the result is opposite with an endogenous CRW. Last, using an online–offline salvage-revenue sharing contract can always coordinate the platform system under both the reselling mode and marketplace mode.

Optimasi Kapasitasi Produksi Untuk Memperoleh Keuntungan Maksimum dengan Linear Programming Metode Simpleks

This research is a progress report of the project entitled "Optimization of Production Capacitation to Obtain Maximum Profit with Linear Programming Simplex Method (Study on Alltho Beverage UMKM)". This project aims to help the owner of Alltho Micro, Small, and Medium Enterprises (MSMEs) in optimizing the production and profit of their products. In this study, the linear programming method with the simplex method technique was used to find the optimal solution that maximizes the profits of Alltho UMKM. Data on the maximum capacity of raw materials and product selling prices are determining factors in the calculation. The three main products analyzed were Red Velvet Choco Royal, Choco Royal Oreo, and Greentea Choco Royal. The results showed that using the linear programming simplex method, the optimal production quantities of each product were 10.29 Red Velvet Choco Royal drinks and 11.76 Greentea Choco Royal drinks, while the production of Choco Royal Oreo should be temporarily stopped. These results indicate that Alltho MSMEs can achieve maximum profits of around IDR 227,942 by producing these products according to the recommended quantities. This research provides an important contribution to decision-making in MSME production management, helps improve efficiency in resource utilization, and provides an overview of the importance of applying mathematical techniques in optimizing MSME businesses in a competitive era.

An integrated Optimization Model of Product Mix, Assortment Packing, and Distribution in A Fashion Footwear Company

Recognizing the paramount importance of operational effectiveness and resource management in supply chain management (SCM) of the fashion industry, this study addresses a specific challenge faced by a prominent Indonesian fashion footwear company. The inefficiency is due to repetitive sorting and packaging processes during product distribution, which significantly impact optimal production mixes and product distribution from the distribution center to the point of sale. A crucial aspect is also the optimization of the delivery route. To address these challenges and minimize the total cost of ownership, the study proposes an integrated optimization model. This model simultaneously determines the optimal production quantity, assortment packaging, and distribution channels, taking into account decision variables related to distribution in configuration boxes, overload and underload products, as well as production numbers that respond to store-specific demand fluctuations. A notable contribution of this research is the integration of product mix decisions into the assortment packaging and distribution model, which represents a novel approach. The optimal solution determined using the LINGO 18.0 software highlights the significant influence of product penalty costs and product demand parameters on the objective function, while shipping costs have no noticeable influence. By emphasizing the integration of product mix decisions into the optimization framework, this research contributes significantly to improving the understanding and practical application of efficient supply chain management in the fashion industry.

The impact of the COVID-19 epidemic on agricultural production strategy from the perspective of loss aversion

Agricultural products have the characteristics of high perishability, short life cycles, and low salvage, and agricultural production is easily affected by uncontrollable natural conditions. Therefore, farmers will face great risk when making agricultural production decisions. In addition, farmers have a high demand for basic income security, so they are typically loss-averse decision-makers. Simultaneously, the impact of the COVID-19 epidemic has undoubtedly increased their loss aversion. The piecewise utility function is an effective model for investigating decision-making with consideration of loss aversion, in which the loss aversion parameter will be adjusted by the epidemic to a certain degree. We innovatively involve the impact of COVID-19 epidemic by a quantitative correction factor in the loss-averse newsvendor model to deal with the decision-making problem of agricultural production and investigate the influences of the epidemic and farmers’ loss aversion degree on the optimal production quantity and profits as well as the relationship between the epidemic situation and loss aversion. Through model analysis and numerical experiments on a specific agricultural product by Matlab software, it is found that the effect caused by the epidemic and the increased level of loss aversion will reduce farmers’ production and income. Therefore, it is necessary to strengthen regular epidemic prevention and control and formulate corresponding support policies to stimulate farmers’ production motivation. Maintaining relative stability in the agricultural market demand can also alleviate the negative impact of the epidemic to a certain extent. Faced with the impact of the epidemic, farmers need to do their best to control agricultural production costs to relieve their economic pressure.

Model Integrasi Sistem Produksi Single Supllier & Multi Buyer

To compete in a market that continues to grow rapidly, companies need to have the ability to meet market needs. One method that is often used to determine the amount of production in each producer cycle is Economic Production Quantity (EPQ). An integrated inventory model is used to achieve optimal results in the supply chain. In this research, a supply chain network model is developed between one producer and two buyers with the aim of minimizing inventory costs. Producers make simultaneous deliveries to each buyer, and these goods are then sold on the market to consumers. Annual demand from each buyer is assumed to vary, and the inventory cycle is also the same length. The optimal production quantity in one production cycle is found through the use of a simple algorithm. Numerical experiments are carried out to test this algorithm. Numerical experimental results show that the delivery frequency in one production cycle is 4 times. with an optimal production quantity of 1,898 units. The optimal quantity for each shipment to each buyer is 380 units for buyer 1, 285 units for buyer 2, 475 units for buyer 3, 569 units for buyer 4, and 190 units for buyer 5. The total inventory costs in this model, which involving one producer and five buyers, is Rp. 76,757,641.02. This inventory cost is the minimum cost obtained from the numerical experiments that have been carried out.

Minimization Implementation of Fuzzy Logic to Optimize a Cashew Nut Production using Simpleks-Duality Theory

Production control of cashew nuts greatly affects the profits earned by the company. When cashew nut raw materials exceed production needs, it results in storing cashews for an extended period, causing the cashew products to lose freshness, and the quality of processed cashews deteriorates. If the raw materials are damaged, the manufacturer must acquire additional costs to procure raw materials again. Another issue is that cashew nut raw materials are seasonal products and are not always available.To solve these problems, a calculation method is needed to control optimal production inventory to minimize the company's expenditures. The method used is to formulate the problem into a Fuzzy Linear Programming mathematical model using a combination of methods: the Simplex algorithm and Duality Theory. The case implementation focuses on the uncertainty of cashew nut production quantities outside the harvest season. Moreover, the calculation of an optimal production quantity to minimize resulting losses is needed. The output generated is an optimal production prediction using the combination of the Simplex Algorithm and Duality Theory in solving Fuzzy Linear Programming.

Supply chain coordination with financial constraints considering delivery time and cross‐channel spillover effect

AbstractA manufacturer selling its products via an offline channel and a capital‐constrained platform is considered in our work. The agency or reseller mode is operated by the platform. Affected by the delivery time, the offline demand is affected by the online channel, which is called the cross‐channel spillover effect (CCSE). Building game models for analysis, we derive the following major results: First, how the commission rate affects the optimal production quantity depends on CCSE. CCSE has no impact on (decreases) the platform's optimal delivery time in the agency (reseller) mode. Besides, the platform's optimal profit decreases with a positive CCSE but increases with a negative CCSE in the agency mode. But in the reseller mode, it always increases with CCSE. Second, the financial constraint decreases the optimal production quantity and extends the optimal delivery time. Third, the agency mode always leads to a larger market share and longer delivery time than the reseller mode. The manufacturer should choose the reseller mode (agency mode) under a high (low) slotting fee. Last, the manufacturer and platform cannot realize coordination by using only the agency or reseller mode. However, considering the manufacturer‐led Stackelberg game, the reseller mode can do so, while the agency mode cannot. Further, considering a retailer and a third party under the omnichannel strategy, the reseller mode can always coordinate them, and the agency mode can only do so at a low interest rate of the loan.

Sustainable Short-Term Production Planning Optimization

This study proposes a framework for short-term production planning of a Portuguese company operating as a tier 2 supplier in the automotive sector. The framework is intended to support the decision-making process regarding a single progressive hydraulic press, which is used to manufacture cold-stamped parts for exhaust systems. The framework consists of two sequential levels: (1) a Mixed-Integer Linear Programming (MILP) model to determine the optimal production quantities per week while minimizing the total cost; (2) a dynamic production sequencing rule for scheduling operations on the hydraulic press. The two levels are combined and implemented in Excel, where the MILP model is solved using the Solver add-in, and the second level uses the optimal production quantities as inputs to determine the production sequence using a dynamic priority rule. To validate the framework, a proposed optimal plan was compared to a real plan executed by the company, and it was found that the framework could save up to 22.1% of the total cost observed in reality while still satisfying demand. To address uncertainties, the framework requires a rolling weekly planning horizon.