Optimal Production Decisions Research Articles

Optimal joint production and green investment decisions of green credit financing under uncertain demands

Green credit financing (GCF) is a specialized financial service offered by banks, aimed at incentivizing borrowers to engage in environmentally sustainable investments, and thus promote sustainable development. It is worth noting that in the practical economic environment, the ability of enterprises to adapt their production and green investment decisions to unforeseen market demand is critical for their green credit financing. This paper investigates a joint production and green investment optimization problem of manufacturers financed through GCF under uncertain demand. Only the interval bound of the demand are known. The problem is initially formulated as a min-max regret model to maximize robustness. Based on problem characterizations, an optimal joint production and green investment decision is proposed. To determine the effectiveness of the proposed decision, computational experiments are conducted on real-world instances. Besides, sensitivity analysis is conducted to derive managerial insights on the implementation of GCF under uncertain demand.

Research on Production Optimization Based on Simulated Annealing Algorithm and Bayesian Sampling Optimization Model

Simulated annealing algorithm is an optimization algorithm in the field of machine learning that is good at processing high-dimensional complex data and seeking global optimal solutions. In this research, the simulated annealing algorithm is combined with mixed integer linear programming and applied to the production decision optimization scenario. Firstly, the normal distribution and hypothesis testing method and the Bayesian sampling optimization model are used to formulate the corresponding sample sampling scheme. This method provides the most comprehensive possible picture of the yield of a complete batch of parts, semi-finished products, or products with the minimum number of samples and the smallest batch size. Secondly, this paper takes the profit maximization of the enterprise as the objective function to model the production inspection and compensation process of the enterprise and uses the simulated annealing algorithm to solve the corresponding optimal production decision scheme. In general, this research not only expands the application scope of simulated annealing algorithm, but also provides a feasible optimization method and reference for similar multi-objective production decision-making problems.

Green Technology Investment and Production Decisions Considering Stochastic Demand and Firms' Decision Preferences Under Cap‐and‐Trade Regulation

ABSTRACTThis paper investigates how finite rational firms optimally respond to market potential under cap‐and‐trade regulation, considering stochastic demand. Using the mean–variance model framework, we develop an optimization model for green technology investment and production by finite rational firms with different decision‐making preferences. The main results indicate: (1) Under stable demand, firms investing in green technology gain more profits and consumer surplus, however, the effectiveness of carbon emission reduction depends on the market potential size. (2) Under stochastic demand, optimal decisions resulting from firms' varying decision preferences systematically deviate from those of risk‐neutral firms and often demonstrate firms' risk‐averse tendencies that lean towards conservatism. As external factors change, there can even be a reversal in technology investment with an increase in demand uncertainty that amplifies this systematic deviation. (3) Taking firms with different decision‐making preferences as the starting point, this study further analyses the distortion effect of the firm's risk attitude on the optimal technology investment and production decisions, enriching the related research on the joint decision‐making risk model of clean production. And it is more pertinent to the complex situation firms face in the real situation with decision‐making. (4) This study provides a theoretical basis and practical reference for the finite rational firms facing green technology investment choices. Considering the risk‐averse characteristics of firms, this study suggests that the government should establish a risk‐sharing mechanism to weaken the deviation of stochastic demand from the optimal decision‐making of firms or implement certain subsidy policies to protect the profit level of firms.

A strategic optimizing carbon neutrality within profit and emission reduction efficiency: a stackelberg game analysis under a cap-and-trade scheme.

Carbon emissions (CO2e) are a main problem, and many countries are committed to reducing CO2e to attain carbon neutrality. To narrow this gap, this research considers green technology implementation (GTI) and CO2e quota in dual green gaming. The objective is to explore the integration of GTI and CO2e quotas into optimal production and pricing decisions in emission-generating companies (EGCs). To achieve this, a two-party simulation Stackelberg game model involving the CO2e strategy of EGCs and governments is proposed. We formulate a mathematical model and experimental methods to optimize EGCs' decision-making using neutral indicators. EGCs optimize production quantity, achieving CO2e reduction through ERE maximization. EGCs exhibit a strong commitment to ERE enhancement practices, enhancing profit and carbon-neutral goals. Our findings demonstrate the effectiveness of CO2e quotas and GTI as carbon-neutral indicators in EGCs, contributing to global CO2e reduction. Our research provides both literature and inspiration for global CO2e reduction efforts. Moreover, it aids governments in exploring optimal incentives and decisions for pricing and production. Last, this work enables EGCs to maximize profits and move toward a carbon-neutral environment.

A Study on the Production-Inventory Problem with Omni-Channel and Advance Sales Based on the Brand Owner’s Perspective

This study explores a supply chain product-inventory problem with advance sales under the omni-channel strategies (physical and online sales channels) based on the brand owner’s business model and develops corresponding models that have not been proposed in previous studies. In addition, because the brand owner is a member of the supply chain, and has different handling methods for defective products or products returned by customers in various retail channels, defective products or returned products are included in the supply chain models to comply with actual operating conditions and fill the research gap in the handling of defective/returned products. Regarding the mathematical model’s development, we first clarify the definition of model parameters and relevant data collection, and then establish the production-inventory models with omni-channel strategies and advance sales. The primary objective is to determine the optimal production, delivery, and replenishment decisions of the manufacturer, physical agent, and online e-commerce company in order to maximize the joint total profits of the entire supply chain system. Further, this study takes the supply chain system of mobile game steering wheel products as an example, uses data consistent with the actual situation to demonstrate the optimal solutions of the models, and conducts sensitivity analysis for the proposed model. The findings reveal that increased demand shortens the replenishment cycle and raises order quantity and shipment frequency in the physical channel, similar to the online channel during normal sales. However, during the online pre-order period, higher demand reduces order quantity and cycle length but still increases shipment frequency. Rising ordering or fixed shipping costs lead to higher order quantity and cycle length in both channels, but variable shipping costs in the online channel reduce them. Market price increases boost order quantity and frequency in the online channel, while customer return rates significantly impact inventory decisions.

The evolution of two‐stage production and order equilibrium in a random yield supply chain with demand information updating

AbstractThe mismatch between production, order, and demand seriously affects supply chain performance. However, most research focus on the mismatch between the retailer's order and customer's demand, which ignores the influence of the supplier's random yield on supply chain members' decision‐making. This paper investigates a two‐stage optimization problem within a two‐echelon supply chain, featuring a supplier with random yield and a retailer updating demand information in real‐time. Faced with a long production lead time, the retailer can either place advance orders at the production season's onset (first‐stage advance order) or opt for instant orders at the beginning of the sales season (second‐stage instant order). To ensure timely order fulfillment, the supplier initially employs a cost‐effective regular production mode with random yield during the production season. If yields are insufficient during sales, a pricier emergency production mode with guaranteed output becomes available. Utilizing a dynamic programming approach, we formulate the two‐stage optimization problem to derive optimal production and order decisions. Our analysis uncovers how realized random yield and stochastic market signals influence emergency production and instant order quantities in the second stage. We compare expected profits in scenarios with perfect and imperfect market signals, probing the members' preferences regarding order strategies. An intriguing finding emerges: as instant wholesale prices rising, the supplier's preferred order strategy diverges from the retailer. By strategic adjustments to the instant wholesale price, we demonstrate the potential for unanimous agreement on preferred order strategies among supply chain members — a quality enhancing the chain's flexibility and performance. Moreover, we extend the model to hybrid order strategies and identify conditions for unanimous preference among the three strategies. To bolster our theoretical findings, we provide numerical examples, lending practical support to our study.

Navigating Platform-Led Affiliate Marketing: Implications for Content Creation and Platform Profitability

Practice- and Policy-Oriented Abstract Recently, some user-generated content (UGC) platforms have introduced shopping features to generate additional commission-based revenue from in-app transactions. These platforms allow creators to produce shoppable content, where promoted products are tagged with affiliate links, and in return, they earn a percentage of the commission the creators receive from merchants This paper aims to investigate the impact of this platform-led affiliate marketing business model on the key stakeholders. Employing a game-theoretic model, our study demonstrates that platform-led affiliate marketing can create a win-win situation for UGC platforms, creators participating in affiliate marketing, and consumers. Furthermore, even creators not participating in affiliate marketing can sometimes benefit indirectly from other creators’ participation. However, we find that platforms may not necessarily benefit from adopting this emerging business model because of potential losses in traffic revenue. These results carry significant managerial implications for platforms regarding whether and how to leverage affiliate marketing. Moreover, our findings suggest that creators may benefit from reducing their production efforts in the face of intensified competition. More importantly, optimal production decisions for creators can vary significantly, depending on specific factors contributing to heightened competition. These findings offer valuable insights that can guide creators in refining their production strategies.

Optimal production decision of hybrid power generation enterprises in multi-quota policy coupled markets

At present, China is adopting both Carbon Emission Trading (CET) and Tradable Green Certificate (TGC) markets to optimize the resource allocation of its power industry. To mitigate the impacts of the above dual markets, more and more power generation enterprises are adopting hybrid production mode, generating electricity from thermal and new energy units simultaneously. In these complex production and market conditions, enterprises are difficult to arrange their generation activities. This research describes the production decision process of hybrid power generation enterprises with different market positions, obtains their optimal yield, and then offers market equilibrium results. In addition, the consequences of enterprise collusion behaviors and government interventions are also measured. Numerical experiment results confirm the correctness of the production decision model and reveal the following facts: 1) CET and TGC markets effectively control the carbon emission level and promote the consumption of new energy, but magnify the failure of electricity market to a certain extent. 2) CET and TGC markets promote each other in function. The existence of one market can help the other to achieve the anticipated goal. 3) Enterprises first offset the impact of market condition changes by adjusting the share of new energy generation, and then digest the residual influence by adjusting the total power generation. 4) Enterprise collusion behaviors aggravate the welfare loss of electricity consumer and then lower the expected effects of CET and TGC markets.

Design and selection of government regulations for vehicle supply chains: A Chinese perspective

New energy vehicles (NEV) have become a major trajectory changer for the global auto industry and an important catalyst for global sustainable economic growth. The implementation of carbon cap and dual credit regulations has altered the competitive environment and strategy of conventional vehicles (CV) and NEV, and has attracted extensive scholarly attention. However, the collaborative governance of the two regulations is relatively limited. This paper constructs two stylized production models based on Cournot game to examine the impacts of different combinations of two regulations, including no regulatory intervention (NC, ND), consideration of dual credit regulation without carbon cap regulation (NC, D), consideration of carbon cap regulation without dual credit regulation (C, ND), and consideration of both regulations (C, D), on vehicle production decisions, and determine the optimal regulatory scheme and intervention intensity under varying conditions. The Lagrange functions and Karush-Kuhn-Tucker (KKT) optimization conditions are employed to solve for the optimal CV and NEV production decisions. The results show that carbon cap regulation not only reduces carbon emissions but also expands the NEV market size. Different regulatory combinations are applicable in different contexts, while collaborative efforts between carbon cap and dual credit regulation can enhance social, economic, and environmental potential within the auto industry under specific conditions. These findings provide important theoretical guidance for expanding NEV market and improving government intervention mechanism.

Optimal production decision and supply chain coordination under different capital conditions

Optimal production decision and supply chain coordination under different capital conditions

Social influencer spillover effects under cap-and-trade and carbon tax regulation: the choice between marketplace or reseller mode

PurposeThe purpose of this paper is to analyze manufacturers' production decisions and governments' low-carbon policies in the context of influencer spillover effects.Design/methodology/approachThis paper investigates the impact of the social influencer spillover effect on manufacturers' production decisions when they collaborate with intermediary platforms to sell products through marketplace or reseller modes. Game theory and static numerical comparison are used to analyze our models.FindingsFirstly, under low-carbon policies, the spillover effect does not always benefit manufacturer profits and changes non-monotonically with an increasing spillover effect. Secondly, in cases where there are both a carbon emission constraint and a spillover effect present, if either the manufacturer or intermediary platform holds a strong position, then marketplace mode benefits manufacturer profits. Thirdly, regardless of business mode used when environmental damage coefficient is high for products; government should implement cap-and-trade regulation to optimize social welfare while reducing manufacturers’ carbon emissions.Practical implicationsThis study offers theoretical and practical research support to assist manufacturers in optimizing production decisions for compliance with carbon emission limits, enhancing profits through the development of effective influencer marketing strategies, and providing strategies to mitigate carbon emissions and enhance social welfare while sustaining manufacturing activities.Originality/valueThis paper addresses the limitations of prior research by examining how the social influencer spillover effect influences manufacturers' business mode choices under government low-carbon policies and analyzing the social welfare of different carbon emission restrictions when such spillovers occur. Our findings provide valuable insights for manufacturers in selecting optimal marketing strategies and business modes and decision-makers in implementing effective regulations.

A comparative analysis of government intervention under the EPR system: Eco-design and authorized remanufacturing

The extended producer responsibility system and government intervention are among the essential requirements for constructing sustainable economies. In a closed-loop supply chain consisting of an original equipment manufacturer (OEM) and a third-party remanufacturer (TPR), this paper develops four Stackelberg game models for four modes of government intervention under patent licensing: no intervention, tax and subsidy, tax and subsidy plus eco-design tax deduction, and eco-design tax deduction only. The impacts of the different government interventions on the optimal production decision, social welfare, and environment are analyzed and compared. The results indicate that, compared with no government intervention, government tax and subsidy decrease the supply of new products, increase supply of remanufactured products, and raise recycling rates of end-of-life products; on top of tax and subsidy, the government’s eco-design tax deduction can further increase OEM and TPR profits; the environmental impact under different government intervention depends on the ratio of the environmental impacts of remanufactured to new products and the level of eco-design effort. This study provides decision makers (i.e., OEM and TPR) and policy makers (i.e., governments) with new managerial insights on the benefits of eco-design and effective mechanisms to promote it.

Optimal production and carbon reduction investment decision for manufacturers with leasing–selling strategies considering financing

AbstractFor a capital‐constrained manufacturer, in the context of carbon reduction, whether products should be sold or leased and which financing mode is more beneficial are usually debated. By considering Carbon Emission Permits Repurchase Financing (CEPRF) and Green Credit Financing (GCF), the optimal decision‐making models with different strategies are presented. The Karush–Kuhn–Tucker theorem is applied and the results are compared. Meanwhile, the influence of initial capital and interest rates on the manufacturer's decision‐makings, profits, and environment are explored. The results show that: under the selling strategy, when the initial capital is small, GCF is better for the manufacturer; otherwise, CEPRF is better; under the leasing strategy, both optimal production and carbon reduction investment with CEPRF are lower than that with GCF, but their profits are higher. With CEPRF, the leasing strategy would bring more economic and environmental benefits to the manufacturer; with GCF, the selling strategy would result in more economic and environment benefits.

Consignment contract in a supply chain with price, demand and yield randomness: A distributionally robust approach

We investigate a supply chain consisting of a supplier and an e-commence platform who sign a consignment contract with uncertainty in price, demand, and yield. Due to the challenges of actually determining the joint distribution of random variables, we assume that only the partial distributional information is available for these three uncertainties. To address the issue of distributional ambiguity and to more accurately account for arbitrary correlations among these uncertainties, we introduce a moment-based distributionally robust optimization (DRO) approach that assumes only the first and second moments of these three uncertainties are known. Given an exogenous consignment rate, we derive the closed-form expression for the supplier’s optimal production decision and her worst-case expected profit. We study the impact of random price and random yield within the ambiguity set on the supplier’s production decision and the worst-case expected profit. From the e-commerce platform’s perspective, we further examine the contract design problem when the consignment rate is endogenous and analyze equilibrium solutions for both contracting parties. Our results show that the additional consideration of price or yield uncertainty within the ambiguity set does not always mitigate or enhance the degree of conservatism of the contracting parties, which is closely related to the correlation between any two types of uncertainty, as well as the degree of uncertainty itself.

A hybrid trade-old-for-new and trade-old-for-remanufactured supply chain with carbon tax

Facing serious environmental problems, governments and manufacturers are taking action to reduce carbon emissions. Among these endeavors, carbon tax policy are widely adopted by governments, trade-old-for-new (TON) and trade-old-for- remanufactured (TOR) are offered by manufacturers and subsidized by governments. To explore the effects of remanufacturer competition and carbon tax on the manufacturer’s TON and TOR decisions and the environment, we formulate three profit maximization models and present some theoretical and numerical analyses. The results show that, under the remanufacturer competition and carbon tax, the manufacturer’s optimal price and production decisions mainly depend on consumer willingness and carbon tax rate. A higher consumer willingness to manufacturer’s remanufactured products will decrease the demand for the manufacturer’s TON, but it always increases the demand foe the manufacturer’s TOR. A higher consumer willingness to remanufacturer’s products will not affect the demand for the manufacturer’s TON; however, it will reduce the demand for manufacturer’s TOR. In addition, we find that a higher carbon tax rate always reduces total carbon emission reduction, and it may increase the manufacturer’s profit due to the increase in TOR demand.

Optimal production and predictive maintenance decisions for deteriorated products under advance-cash-credit payments

In the 4th industrial revolution era, manufacturers tend to integrate predictive maintenance into production systems to maximize the lifespan of equipment and avoid costly disruptions. Using internet of things sensors and data analyses, predictive maintenance can significantly reduce the production downtime by detecting and predicting system problems before they become uncontrollable, resulting in a lower defective rate. Additionally, an advance-cash-credit (ACC) payment scheme is commonly applied in real-world business transactions to enhance cash flow flexibility among supply chain members. In this study, we developed a supplier–manufacturer chain, wherein a predictive-maintenance-adopting manufacturer received an ACC payment from a supplier, to demonstrate a supply chain management situation within the imperfect economic production quantity framework. The inventory system of the manufacturer was modeled as a cost minimization problem to determine the optimal replenishment cycle time and predictive maintenance effort for deteriorated products. The proposed model also adopted a discounted cash-flow analysis to consider the time value of the cost function, which was proven to be strictly convex in the replenishment time and predictive maintenance effort. Furthermore, a numerical and sensitivity analysis was conducted to illustrate the effectiveness of the proposed model and gain management insights.

The interaction between manufacturer-encroachment and information sharing in a closed-loop supply chain under technology licensing

This paper investigates the interaction between a retailer’s information sharing behaviour and a manufacturer’s encroachment strategies in a closed-loop supply chain in which the manufacturer licenses a third party to remanufacture. We apply the Stackelberg game to obtain the optimal pricing and production decisions and show that, information sharing always brings a profit increase to the manufacturer while a profit loss to the retailer. The retailer may be willing to share information in presence of manufacturer encroachment. We also show that, no matter whether the manufacturer remanufactures by himself or licenses the third party to remanufacture, the encroachment case is always profitable to the manufacturer due to the dual revenues from both the producing and marketing activities. In addition, whether the encroachment case is beneficial for the retailer is contingent on the encroachment cost. Specifically, when the encroachment cost is high enough, the encroachment case dominates the no-encroachment case because the manufacturer prefers to sell more products through the traditional retail channel rather than the direct selling channel. These results provide a new insight into information sharing and manufacturer-encroachment in a closed-loop supply chain.

Is carbon asset pledge financing contributing to the operation of emission-dependent engineering machinery remanufacturing with emission abatement?

As a new financing strategy in the carbon trade market, carbon asset pledge financing (CAPF) provides a new financing channel for capital-constraint firms. For the carbon emission-dependent engineering machinery remanufacturer, how to formulate an optimal production plan under CAPF is still an unsolved problem. In this study, we suppose the emission-dependent remanufacturer adopts the pure carbon asset pledge financing (PCAPF) to solve capital shortage problem, and then study the optimal production and carbon emission reduction (CER) decisions of remanufacturers under PCAPF. The results show that: i) Only when the remanufacturer's initial capital is below a certain threshold can it benefit from PCAPF, and the threshold is different under all remanufacturing strategies. ii) Compared with no CER, the yield of new products increases when CER is implemented. However, whether remanufactured products increase depends on different remanufacturing strategies. iii) Under PCAPF, a high carbon asset pledge rate is not conducive to the production and profit of remanufacturers regardless of CER, and the increase of carbon price fluctuation coefficient negatively affects the production and environment without CER. However, the correlation among them is related to the threshold of the CER rate. iv) With/without CER, the yield of new/remanufactured products, environmental impact, and profit decrease sequentially with the choice of complete remanufacturing, partial remanufacturing, and non-remanufacturing under PCAPF. Meanwhile, although the increase of the CER rate increases environmental impact, whether it can improve the profit of remanufacturers is related to the threshold of unit emission of remanufactured products. Thus, the remanufacturer should balance the trade-off when implementing CER.

How to Choose the Refueling of New Energy Vehicles under Swapping vs. Charging Mode: From the Consumers’ Perspective

Battery charging mode (CM) is a prevalent method of trans-shipping power to new energy vehicles (NEVs). Unfortunately, due to the limited capacity of batteries, typical NEVs can only travel for approximately 350 miles on a single charge and require hours to be recharged. Battery swapping mode (SM), as a novel alternative, can offer an ideal solution by exchanging depleted batteries for recharged ones at swapping stations in the middle of long trips, inevitably influencing potential consumers’ purchase behaviors. To examine the impact of SM and CM on consumers’ purchase intention, this paper examines a duopolistic market consisting of two new energy vehicle manufacturers (i.e., a NEV-SM manufacturer and a NEV-CM manufacturer), who adopt SM and CM to service consumers, respectively. Considering SM is characterized by low initial investment and ease of use for consumers, NEV-CM manufacturers capitalize on extended battery warranty services in response to rivals’ utilization of SM. Thereby, non-cooperative game models are formulated, in which government subsidies are taken into account. The optimal production decision for both the NEV-SM manufacturer and the NEV-CM manufacturer are analyzed under three scenarios: without extended warranty service, with extended warranty service, and with extended warranty service and subsidy. The results show that the two manufacturers’ market dominance relies on the ratio of the swapping station’s convenience to the extended warranty service and the valuation incremental rate. Additionally, we also find that the government subsidy can dramatically improve the NEV-SM manufacturer’s performance at the initial stage, but if the subsidy is insufficient in size at the subsequent stage, this will lead to policy failure and inefficiency in propelling the diffusion of swapping mode.

Downstream firm's equity financing for capacity expansion in a supply chain

AbstractIn this research, we investigate a supply chain consisting of a downstream firm who purchases a component from an upstream firm and then transforms it into a final product. The downstream firm has a production capacity constraint and considers to raise capital from an investor through equity financing. The raised capital not only enables the downstream firm to expand the capacity but also allows the investor to hold equity shares in the downstream firm. We derive the optimal pricing and production decisions of the two firms and discuss the optimal equity financing strategy of the downstream firm. We consider two distinct models: the external equity financing model, where the capital is raised from an outside institution, and the internal equity financing model, where the capital is raised from the upstream firm. We show that because the cooperative relationship between the two firms can be improved in the internal equity financing model, the production quantity in this model may be even higher than that in a benchmark model with no capacity constraint and no equity holding by the investor in the downstream firm. In addition, the original shareholder of the downstream firm gets more benefit from the internal equity financing activity than from the external equity financing activity. We also analyze the impacts of the key model parameters on the equity financing strategy and find that the dependence of the financing strategy on the initial asset of the downstream firm is quite different in the two models. Moreover, when the production cost of the downstream firm is changed, less capital raised for expanding capacity may create more value for the original shareholder of the downstream firm in each model. Finally, we show that the key finding remains unchanged when deterministic demand is changed to stochastic demand.