Optimal Production Quantity Research Articles

Retailer Information Sharing Strategy with Counterfeiter Encroachment

In this paper, we examine the retailer’s information sharing decision in an authentic supply chain with a single supplier and a single retailer under different counterfeiter encroachment situations. We propose a Stackelberg game model to analyze the optimal wholesale price of the supplier, the optimal order quantity of the retailer and the optimal production quantity of the counterfeiter. We obtain the information sharing strategies of the retailer and analyze the impact of the counterfeiter on the authentic supply chain. It is revealed that: (1) under certain conditions, the retailer will voluntarily share information with the upstream supplier and (2) the existence of the counterfeiter may increase the profit of the authentic supply chain.

Sustainable circular economy production system with emission control in LED bulb companies.

Mother Earth has a completely sustainable circular life cycle pattern. In its life cycle, there is no harm created to any living creature or to the environment. In this paper, a sustainable circular economic production and consumption system for a LED bulb firm that follows the same cycle pattern as our planet is developed. The circular economy concept, green technology, and carbon cap-and-trade policy are introduced in this model to control the carbon emission rate and resource depletion in LED firms. The profit function is maximized by Lagrange's multipliers method and Karush-Kuhn-Tucker (KKT) criteria. This paper determined the optimal production quantity and circularity index of the LED bulb for a wise manufacturing process. The concavity of the optimal profit function is proved by using the Hessian matrix method. Different linear and non-linear combinations of demand and profit functions were discussed. This article claims that the circularity level of LED bulbs has influenced their selling price, cost, and demand. Green technology and carbon cap-and-trade policies improved the sustainability of LED bulb companies. Numerical examples, results discussions, and an optimal solution table are provided to show the implication of this model for LED bulb companies. Sensitivity analysis is presented for key parameters. Managerial implication explained in terms of arrived results. Limitations and possible future extensions of this model are given in the conclusion section.

Optimal Acquisition and Production Policies for Remanufacturing with Quality Grading

Core acquisition is essential to the success of the remanufacturing business. The value of sorting and grading cores into nominal-quality classes has been certified in industry and academia. In this paper, we investigate how many unsorted cores of uncertain quality should be acquired and how many sorted cores should be remanufactured by a third-party remanufacturer (3PR) before the demand is realized. We first develop analytically tractable solutions to the acquisition and production model under deterministic demand, and then we extend it to the model under the stochastic demand by fully characterizing the structure of the optimal policy. Subsequently, we investigate the impact of core quality fraction uncertainty on the solutions. Finally, numerical analyses are conducted to further verify the proposed models. The results are as follows. First, the optimal quantity of acquisition/production and minimum expected profit increase with an increase in the selling price and decrease with an increase in the uncertainty of demand and acquisition cost. Second, the optimal production quantity does not decrease in acquisition quantity, and the rate of utilization of the recycled parts (the ratio of production quantity to acquisition quantity) increases with a decrease in the acquisition cost. Third, the growth stage is most profitable stage, so the remanufacturers should pay more attention to remanufacturing activities early in the life of products. The proposed models and solutions can not only solve the core acquisition and production problem in remanufacturing, but also solve the combinatorial optimization problem.

Live streaming platform operations and coordination under the cap-and-trade regulation: Platform-enabled mode versus platform-agency mode

We consider a supply chain consisting of a supplier and a manufacturer where the manufacturer sells its products directly or through a live streaming platform (LSP). Operating in either the platform-enabled and platform-agency mode under the cap-and-trade regulation, the platform has platform power that reflects its ability to expand the market size. We find that the optimal production quantity in the platform-agency mode may decrease with the cap and platform power. The supplier and manufacturer can always be coordinated under the wholesale price contract in the platform-enabled mode. However, in the platform-agency mode, the two firms can be coordinated under low or high platform power, but whether coordination is achieved under moderate platform power depends on the unit carbon emissions of the products. If the platform power is low or high, the platform-enabled mode yields more total production quantity; otherwise, the platform-agency mode yields more total production quantity. Whether the platform-enabled or platform-agency mode generates a higher profit for the manufacturer highly depends on the promotion cost. By considering product investment and sales effort, we find the following: (i) When considering product investment, the supplier and manufacturer cannot be coordinated under the wholesale price contract in either mode. (ii) When considering sales effort, the firms can be coordinated in the platform-enabled mode, while in the platform-agency mode, whether they can be coordinated under the wholesale price contract depends on the cost coefficient and the unit carbon emissions of the products.

The choice between the agency and reselling modes considering green technology with the cap-and-trade scheme

Given an online platform and a manufacturer, we research the platform mode choice where the two firms' cooperative mode is either the reselling or agency mode. With the cap-and-trade scheme, green technology is used to comply with this scheme and cater to consumers' environmental consciousness. We consider agency inefficiency and platform-enabled power, the platform's inherent characteristics in e-commerce, in our models. In addition, given the power structure, we consider three cases, namely the agency, manufacturer-led reselling, and platform-led reselling modes. Analyzing the optimal operational decisions, platform mode choice, and coordination problems in the three cases, we derive new and interesting findings. First, we uncover that increasing the cap weakens the optimal green level. However, increasing the cap first weakens and then enhances the optimal production quantity. Second, we uncover that the platform-led reselling mode is always more conducive to the production quantity and green level but the manufacturer-led reselling mode is more conducive to the manufacturer's profit. In addition, increasing agency inefficiency gradually enhances the market share, green level, and manufacturer's profit in the agency mode. Lastly, the manufacturer-led reselling mode can coordinate the two firms. Extending our models to consider the delivery time, we uncover that the agency and manufacturer-led reselling modes can coordinate the two firms.

Optimization of bakery production by using branch and bound approach

Mommy Ai Kitchen is one the businesses specializing in the bakery business, producing cupcakes, birthday cakes, brownies, and donuts. However, it does not optimally determine each bakery’s production quantity, so it offers fewer profits and becomes a problem. This research aims to find the optimal production quantity so that this business maximizes profits. The method used was integer programming using the branch and bound approach, which counts the decision variable value using the simplex method. This research was based on the number of raw materials on hand wheat flour, sugar, eggs, modal, and the profits of each bakery. Based on the analysis of the branch and bound approach, it was known that the maximum profit value was IDR 253,200, with eight alternative options for the bakeries that were produced. One of them was Mommy Ai Kitchen, which could produce three cupcakes, five birthday cakes, one brownie, and nine donuts to get that maximum profit. Meanwhile, Mommy Ai Kitchen’s estimation could produce one cupcake, one brownie, and six donuts using available materials with a profit of IDR 78,800. As a result, the profit difference before and after integer programming was IDR 174,400.

Optimization of bakery production by using branch and bound approach

Mommy Ai Kitchen is one the businesses specializing in the bakery business, producing cupcakes, birthday cakes, brownies, and donuts. However, it does not optimally determine each bakery’s production quantity, so it offers fewer profits and becomes a problem. This research aims to find the optimal production quantity so that this business maximizes profits. The method used was integer programming using the branch and bound approach, which counts the decision variable value using the simplex method. This research was based on the number of raw materials on hand-wheat flour, sugar, eggs, modal, and the profits of each bakery. Based on the analysis of the branch and bound approach, it was known that the maximum profit value was IDR 253,200, with eight alternative options for the bakeries that were produced. One of them was Mommy Ai Kitchen, which could produce three cupcakes, five birthday cakes, one brownie, and nine donuts to get that maximum profit. Meanwhile, Mommy Ai Kitchen’s estimation could produce one cupcake, one brownie, and six donuts using available materials with a profit of IDR 78,800. As a result, the profit difference before and after integer programming was IDR 174,400.

The Joint Decision-Making Support through Piecewise Objective Optimization Model for Integrated Supplier Selection, Inventory Management, and Production Planning Involving Discounts

The decision-makers in manufacturing industries continuously optimize every supply-chain part to achieve optimal profit. In this paper, three crucial activities in the supply chain are observed as profit contributors: supplier selection, inventory management, and production planning. Decision-making support is needed to optimize those activities, especially when prices/costs involve discounts. Therefore, this study aims to develop integrated decision-making support for supplier selection, inventory management, and production planning involving discounted prices. The problem was considered with multi-supplier, multi-raw material, multi-product, and multi-observation time instant. The objective was based on maximizing the profit for the entire activity, i.e., from the raw material procurement and storage to the production. This supply chain was modeled as mixed-integer linear programming with a piecewise objective function representing the profit, which was maximized. It was also modeled with a bunch of constraint functions, including product demand satisfaction. The proposed model was tested with computational simulations using randomly generated supply chain data. The primal simplex algorithm was also employed to calculate the real value of the optimal decision, which was combined with the Branch-and-Bound approach to calculate the appropriate integer solution. The results showed that the optimal decision was achieved, namely (1) The optimal quantity of raw materials ordered to each supplier, (2) The optimal production quantity, and (3) The optimal inventory level, which provided the maximal profit for the whole optimization time horizon. This indicated that the proposed decision-making support model is implementable for industrial decision-makers.

When Is It Wise to Use Blockchain for Platform Operations with Remanufacturing?

Blockchain technology has been widely used in many industries. One current application is in remanufacturing. In this paper we consider the combination of remanufacturing and blockchain, and model a supply chain composed of a manufacturer, a third-party firm, and an online platform. Among them, the manufacturer faces the cap-and-trade regulation and adopts blockchain to record the information on the used products and then remanufactures products. The platform has the power to expand the potential market size and can operate in the marketplace or reselling mode. The third-party firm collects used products for the manufacturer. We conduct a Stackelberg game analysis and obtain the following major findings: First, the optimal production quantities and optimal collection rates with and without blockchain in the marketplace and reselling modes increase with the allocated cap and platform-enabled power. Second, in the reselling or marketplace mode, the manufacturer should not adopt blockchain if the emissions intensity is low; otherwise, it should adopt blockchain. Third, selecting the reselling (marketplace) mode is more profitable for the manufacturer if the platform-enabled power is low (high). Fourth, for quantity coordination, the reselling mode under the wholesale price contract can always coordinate the manufacturer and platform, and the manufacturer, online platform, and third-party firm. However, the marketplace mode with a commission rate can only coordinate the manufacturer, online platform, and third-party firm. For social welfare coordination, the manufacturer, online platform, and third-party firm can achieve coordination in the marketplace or reselling mode. Finally, extending the work to consider the cross-channel effect, we find that the major findings for both quantity coordination and social welfare coordination in the reselling and marketplace modes still hold.

Coordination of a platform-based supply chain in the marketplace or reselling mode considering cross-channel effect and blockchain technology

We consider a supply chain consisting of a manufacturer and an online platform. The manufacturer produces products under the carbon cap-and-trade policy, and sells them through its own offline channel and the platform, which operates in either the marketplace or reselling mode. While enlarging the potential retail market size through the “platform power”, the platform provides logistics service for the online sales. We also consider the cross-channel effect concerning the impact of online sales on offline demand. The manufacturer can adopt blockchain technology to improve demand forecasting. We study the optimal production, pricing, delivery time decisions, and the coordination problem of the two firms under various scenarios. We compare the optimal decisions of the two firms and the manufacturer's profits with and without blockchain in each operation mode of the platform. We find that the cross-channel effect and blockchain have significant impacts on the optimal decisions and coordination results. In the marketplace mode, the optimal production quantity increases (decreases) with the commission rate if the cross-channel effect is high (low). The optimal delivery time increases (decreases) with the cross-channel effect and the cap in the marketplace (reselling) mode. The reselling mode can coordinate the manufacturer and platform regardless of whether delivery time or strategic inventory is considered, while the marketplace mode can coordinate the two firms only when delivery time is considered. If the cross-channel effect is low (high) and the platform power is high (low), adopting blockchain can generate more profit for the manufacturer. Furthermore, adopting blockchain promotes the coordination of the manufacturer and the platform.

Call option contract in a supply chain with random yield and random demand using downconversion approach

PurposeThis study aims to examine the value of the call option contract in hedging the risks in the supply chain. The decentralized supply chain without call option contract is first studied as the criterion model for evaluations. This paper addresses several questions: What will be the optimal manufacturer’s production quantity, retailer’s ordering and pricing policies in the presence of random demand and random yield by applying the downconversion approach? How will the call option contract influence the optimal decisions for the members of the supply chain? Can the risk from randomness be divided among the members in the supply chain through the call option contract?Design/methodology/approachThis paper considers a two-level decentralized supply chain under random yield and random demand in which the manufacturer takes advantage of the downconversion approach with two scenarios, with and without option contract. To the best of the authors’ knowledge, no article or study uses the downconversion approach in a supply chain regarding random yield and random demand. Furthermore, the paper considers pricing with option contract in the supply chain, which makes this article stands out significantly from other articles in the literature.FindingsThis study shows that the downconversion approach would reduce the risk caused by the random yield, which appears to be the appropriate method for the environmental goal of the supply chains. Moreover, adopting a call option contract can increase flexibility and mitigate risks, resulting in more expected members’ profits.Research limitations/implicationsTo simplify the model, the authors assume one manufacturer and one retailer, so extending the model to consider multiple retailers instead of one retailer and inventory sharing between them would be interesting. Considering the option and exercise prices as decision variables would be important future research topics. Put option and bidirectional option contracts could be investigated in the future. Another extension is modeling asymmetry of information in supply chain.Originality/valueThis paper provides managerial insights on dealing with both demand and yield risks in a manufacturer–retailer supply chain. The manufacturer has a random yield production and produces two types of vertical products: low-end and high-end. To reduce waste caused by the random yield, the manufacturer uses a downconversion approach in which low-end products are made by converting the defective high-end products. The manufacturer purchased a shortage of high-end products from the secondary market (i.e. emergency sourcing). High-end products are sold through the retailer, and low-end products are sold directly by the manufacturer. The customer demand for high-end products in the end market is random and depends on the selling price, and the customer demand for the low-end products in the secondary market is independent and random. The retailer contracts the manufacturer with the call option to obtain high-end products to meet a random demand; in fact, by using the call option contract, the authors try to balance the risks between two members. Two scenarios of with and without call option contract are proposed. After the high-end product demand is observed, the retailer would exercise the option order quantity in the call option contract scenario and then place an instant order with the manufacturer if necessary. In each scenario, the manufacturer and the retailer make their decisions simultaneously (static game) to determine the retailer’s optimal ordering and pricing policies and the optimal production quantity of the manufacturer (Nash equilibrium) by maximizing their expected profits. Finally, the impact of the model parameters on the supply chain is expressed through numerical examples. The numerical analysis shows that the call option contract provides greater profit than the wholesale price contract.

A novel stochastic fuzzy decision model for optimizing decision-making in the manufacturing industry

In unpredictable and imprecise production environments, this research introduces a stochastic fuzzy decision model for the manufacturing industry. Decision-makers can use the stochastic and fuzzy logic model to capture uncertainties, variability, and language representations of industrial factors. The choice problem, fuzzy input variables, and crisp outcome variables are identified to start the research. Linguistic terms related with fuzzy input variables are represented by fuzzy sets and membership functions. Fuzzy rules link fuzzy input variables to crisp output variables based on expert knowledge or historical data. Objective function, restrictions, and fuzzy rules are incorporated into the stochastic fuzzy decision model's mathematical formulation. Decision-makers can maximize outcomes by considering stochastic factors and fuzzy logic with the model. The model uses an optimization technique to find the optimal choice variable values. A numerical example of manufacturing production planning illustrates the model's use. The results show that the stochastic fuzzy decision model may minimize production costs by calculating optimal production quantities depending on demand. The research concludes that the proposed approach helps manufacturing companies make decisions. Decision-makers can use the model to make educated judgments despite uncertainties and inaccurate information. Future study will explore additional aspects and integrate the model into decision support systems or industrial software. In dynamic and uncertain manufacturing contexts, the stochastic fuzzy decision model empowers manufacturing decision-makers to make optimal decisions

Fuzzy Production Inventory Model considering Imperfect Quality and Shortage: A Case Study in a Goat Milk SMEs

Goat milk powder is one of the perishable processed products. The decreasing quality of goat milk powder can cause financial losses to the company if not regulated properly. So far, the company is also faced with the problem of consumer demand uncertainty. When demand for powdered goat's milk is high, the company experiences stockout but can be overcome by backorder. When demand is low, there will be overstock. Overstock conditions, in addition to causing high holding costs, are also at risk of product quality degradation or expiration. In this study, an inventory model of goat milk powder was developed that considers the uncertainty of demand, product quality, and backorder to determine the optimal production quantity so that the total inventory cost incurred is minimum. The basic model used is economic production quantity. Uncertainty in demand and the percentage of products declining in quality is approached using a triangular fuzzy. While the defuzzification technique used is signed distance.

Building a Mathematical Model to Determine the Optimal Production Quantity based on a Fuzzy Time Series: A Case Study

Building a Mathematical Model to Determine the Optimal Production Quantity based on a Fuzzy Time Series: A Case Study

When is it wise to use artificial intelligence for platform operations considering consumer returns?

We consider a supply chain comprising a manufacturer and a platform, where the former sells its products through an offline channel and the latter. The platform has two operational modes, namely the marketplace and reselling modes. Platform power refers to the platform's ability to increase the market size, while network effects concern the platform's effect on the offline channel. Consumers may return dissatisfied products brought from the platform within a return window. Without artificial intelligence (AI), the optimal production quantities in both the marketplace and reselling modes increase (decrease) with the platform power under low (high) network effects. The optimal profit of the manufacturer in the marketplace mode increases with the platform power and the direction may be positive in the reselling mode. With AI, the optimal profits of the manufacturer in the two modes always increase with the platform power. Comparing the cases with and without AI, we find that using AI in the marketplace mode increases (decreases) the manufacturer's profit under low (high) network effects. And using AI in the reselling mode increases (decreases) the platform's profit under low (high) network effects. With and without AI, the marketplace mode cannot coordinate the supply chain, while the reselling mode can. We also extend our work by considering several cases to check the robustness of the results.

Values of blockchain for risk-averse high-tech manufacturers under government's carbon target environmental taxation policies.

Today, high-tech industries such as consumer electronics commonly face government rules on carbon emissions. Among the rules, carbon emission tax as well as extended producer responsibility (EPR) tax are two important measures. Using blockchain, the policy makers can better determine the carbon target environmental taxation (CTET) policy with accurate information. In this paper, based on the mean-variance framework, we study the values of blockchain for risk-averse high-tech manufacturers who are under the government's CTET policy. To be specific, the government first determines the optimal CTET policy. The high-tech manufacturer then reacts and determines its optimal production quantity. We analytically prove that the CTET policy simply relies on the setting of the optimal EPR tax. Then, in the absence of blockchain, we consider the case in which the government does not know the manufacturer's degree of risk aversion for sure and then derive the expected value of using blockchain for the high-tech manufacturers. We study when it is wise for the high-tech manufacturer and the government to implement blockchain. To check for robustness, we consider in two extended models respectively the situations in which blockchain incurs non-trivial costs as well as having an alternative risk measure. We analytically show that most of the qualitative findings remain valid.

Robust contract design and coordination under consignment contracts with revenue sharing

We study a classical supply chain consisting of a supplier and a retailer in which the former can sell the product through the latter under a consignment contract with revenue sharing. In this case, the supplier faces both uncertain yield (supply) and demand. In practice, it is difficult to precisely elicit the joint probability distribution of random demand and yield. Therefore, we investigate how to match demand with supply for supply chain when only partial distribution parameters, such as the first-two moments, are known. We use a distributionally robust approach to solve this challenge within the framework of a stylized two-stage Stackelberg game model. Under centralized and decentralized settings, a simple closed-form expression of the optimal robust production quantity that can properly match supply and demand can be completely characterized. Then, by comparing the performance of the two settings, we show that a supply chain double-marginalization issue exists. As such, we propose a subsidy mechanism based on a revenue-sharing contract to improve supply chain performance, and also prove the existence of a Pareto-improvement set, which can plausibly overcome the low efficiency of the supply chain. Our numerical studies further observe the impact of demand and yield uncertainty on the double-marginalization effect, the Pareto-improvement set, and both contract parties' expected profit loss. We also extend our model to consider the case of endogenizing pricing and asymmetric demand information.

An EPQ Model for Delayed Deteriorating Items with Two-Phase Production Period, Exponential Demand Rate and Linear Holding Cost.

The economic production quantity (EPQ) model for delayed deteriorating items considering two-phase production periods, exponential demand rate and linearly increasing function of time holding cost is proposed to solve a production problem similar to the one caused by the Covid-19 pandemic. Without shortages, the necessary and sufficient conditions for optimality of this model are characterized through a theorem and lemmas while a solution methodology based on differential calculus is adopted. This paper determines the best replenishment cycle length corresponding to the optimal total variable cost and production quantity of imperfect production industry. To illustrate this model, a numerical experiment is conducted. The results demonstrate that a higher carrying charge decreases the production quantity and a longer demanding period decreases the total variable cost of an industry with a distracted production period. Finally, managerial insights are discussed using sensitivity analysis and future research directions are exposed.

Analisis Kontribusi Keuntungan Atas Produk- Produk Pada CV. Salim Tailor Di Tenggarong (Penerapan Linear Programming Metode Simplek)

The main objective of this study was to find out whether the production amount of CV. Salim Tailor In Tenggarong has been at the optimum point to generate maximum profit contribution and to know which type of products that generate maximum profit contribution from various products produced by CV Salim Tailor in Tenggarong.The research result is indicated that business well get maximal profit from product Pants (X1) with respective optimal production quantities are rounded to 24,4253 unit it’s mean that 24 unit plus 1 unit product on process productions 42,53% and also product PDL (X5) with respective optimal production quantities are rounded to 13,472% unit it’s mean that 13 unit plus 1 unit product on process productions 4,72% with the maximum profit Rp. 29.188.950 for 1 month.For the time of measurement and cutting or process 1 (S1) still leave time during 5,0833 minute, this is indicated that the company have a lost time on the process 1 for more or less 0,08 hours for 1 month. Keywords: Profit Contributions (Application of Linear Programming Simplex Method)

Marketplace or reselling: the pricing decisions and face value of the coupons under the Cap‐and‐Trade regulation

AbstractThis paper considers a manufacturer selling his products with the marketplace or the reselling mode under the cap‐and‐trade regulation. Coupons are allocated when selling the products. We explore the optimal decisions, the selection and the coordination with the two modes. First, we analytically find that the increase of the cap and platform power (commission rate) increases (decreases) the total production quantity and the optimal production quantity for coupon‐sensitive consumers, and interestingly find that it reduces (increases) the production quantity for coupon‐insensitive consumers when the sensitivity of the coupons is high. Furthermore, the optimal profit of the manufacturer first increases and then decreases with the cap when the emission intensity is low, and it increases with the cap when the emission intensity is high. Second, the marketplace mode creates more (less) profits for the manufacturer if the order‐fulfillment cost is low (high). Whether the marketplace mode or the reselling mode will generate more carbon emission depends on the commission rate and the platform power. Finally, the marketplace mode is not capable of coordinating the manufacturer and the platform at all times, while the reselling mode can coordinate the two firms after considering a coupon‐sharing contract under considerable platform power, and they can achieve Pareto improvement with a two‐part tariff contract under the generalized Nash bargaining framework.