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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.21 No.2 pp.220-227

A Systematic Literature Review on Quantity Flexibility Contracts in a Supply Chain System

Kyunghwan Choi, Seongam Moon*
Department of Defense Management, Korea National Defense University, Korea
*Corresponding Author, E-mail:
July 12, 2021 ; October 11, 2021 ; October 11, 2021


This is the first to comprehensively review the issues such as contract parameters and research models/methods of Quantity Flexibility Contract (QFC) in a supply chain system. We are experiencing a low-frequency-high-impact (LFHI) event such as coronavirus (COVID-19), and rapid technological changes, bringing about a rapid change in customer demand now. Matching supply with demand is one of the biggest challenges in Supply Chain Management (SCM). That is because a sudden rise or drop in customer demand makes it difficult to coordinate objectives between a manufacturer and a retailer. Meanwhile, a QFC has been highlighted as an intensive method in response to this rapid change by gaining time for better observing the market demand before placing its final orders. The intention of this paper is twofold. First, we classify QFC’s articles into contract parameters, comparison and composition of QFC with other strategies and contract types, research models, and methods up to the present point. Second, we guide the future research directions and developments of QFC so that many researchers start easily approaching and studying it. We hope that our discovery from the review provides opportunities to spot gaps in the literature that could be accomplished and values for further future research directions.



    Low-frequency-high-impact (LFHI) events such as coronavirus (COVID-19) or September 11 attacks pose a substantial challenge to supply chains (Hosseini et al., 2019). As LFHI came up with ways to deal with the impact, some industries were destroyed, others were transformed, and brand-new industries were created. Moreover, we have experienced enough in history such as the Spanish flu, the first/second World war, the 911 terrorist attacks, MERS, and SARS infection, which have been unpredictable in general due to performance verification of relief products and vaccines, rapid decrease in demand after using them, and ripple effects from other services associated with them.

    Apart from LFHI, rapid technological growth/ changes as well as ever-changing buying behaviors of the customers, which are driven by various industries like fashion and electronics, cause the customer’s demand a wider variety of products. This fact compels the enterprises to accommodate different supply chain models rather than classical ordering and purchasing models.

    Supply Chain Management (SCM) is to efficiently centralize suppliers, buyers, warehouses, and shops so that merchandise is made and distributed at the right time, locations, and quantities in order to maximize global profits while satisfying service level requirements (Simchi- Levi et al., 2000).

    In decentralized supply chains, managing the optimal costs is even more difficult since the parties act with regard to their individual profits rather than the overall supply chain profits.

    One of the intensive contract methods to address this uncertainty and coordination in supply chains is Quantity Flexibility Contracts (QFC). The QFC is a settlement between a manufacturer (s) and a retailer (s) such that the retailer pledges to first orders with a certain level of flexibility, and the manufacturer makes an appointment to deliver the retailer’s order in full. Therefore, it can be considered an SCM implement that allows the retailer to obtain time to observe the market demand before placing its final orders to the manufacturer. The retailer takes advantage of waiting for the market condition information to be revealed before placing its final orders, thanks to the flexibility of revising its initially committed order up-to a predefined level called flexibility limit (Heydrai et al., 2020). See Figure 1 for the sequence of events in QFC.

    A QFC may be of service to content two channel members, a manufacturer and a retailer. It sanctions retailers to update its primary order both downwards and upwards in a restricted volume. In a such way, the retailer is engrossed in buying a minimum agreed amount while the manufacturer offers up an extra amount if required. We encapsulate much advantage to the manufacturer and the retailer in Table 1.

    During LFHI events or rapid technical growth and after that, we are experiencing a sharp change in customer demand now and will face more of that soon. That’s why we have to deal with QFC now.

    In this paper, we try to respond the following questions:

    • (1) What discussion and evolution of trends have been made in the area of QFC so far?

    • (2) What research models and methods have solved the problems of QFC?

    • (3) What are the research directions and opportunities for development for QFC in the future?

    To answer the above research questions, we focused on gathering and analyzing a great deal of research on the QFC to give insights to many scholars interested. This paper is organized as follows; In Section 2, we show review methodology. In Section 3, we categorize a variety of circumstances and terms parameters, and a comparison and composition with other strategies or supply contracts are presented in QFC studies. Research models and methods are discussed in Section 4. In Section 5, we discuss the future study directions. Finally, conclusion is drawn in Section 6.


    We review and create this paper motivated by the significance of QFCs and a lack of comprehensive literature review on this topic. We employ a systematic litera-ture review, as a valid methodological approach (Basnet and Seuring, 2016) and specific procedures are as follows. First, we locate some articles published in Management Science, Operations Research and, Production Economics. When investigating this survey, we thoroughly and religiously searched the following electronic databases and search engines for related literature: Google Scholar, Elsevier, JSOR, ScienceDirect, Tayor & Francies, IEEE, INFORMS, Springer, Wiley, and so on in English. Second, we identify search terms and citation researches. The keywords used in the search process were ‘supply contracts’ and ‘quantity flexibility contract.’ Third, we extract some articles due to special issues and editorials (2), not focused or unrelated QFC (3), not in the area of SCM (4). Finally, we supply a review of peer-reviewed 50 papers released in leading journals from 1985 to 2020. The journals and the number of publications on QFC in each journal and year are given in Table 2.


    In this section, we classify QFC’s articles in accordance with contract parameters such as contract environment, contract terms, a combination and composition with other strategies and contract types so that we can obtain the goal of research question 1. We could also affirm the evolution of QFC’s research. There were many analyses of influence relation between contract environment and terms at the beginning of the study, i.e., how the demand, information, lead time, flexibility, price, and contract period affect the expected revenue or between them. The research paradigm has begun to change since 2011. A comparison with other contract types or a composition with other strategies and contract types has been mainstream since then. Refer to the below section for more details.

    3.1 Contract Environment

    Contract environment parameters that we mainly discuss include types of agents (a manufacturer-a retailer), echelon (2-stages, 3-stages, multi-stages), products (single, multi), demand (deterministic, stochastic) and its forecast (Bayesian), lead time (deterministic, stochastic, zero).

    3.1.1 Types of Agents

    The supply chain that forms one manufacturer (supplier) and one retailer really rarely exists in the real world. However, many researchers have assumed one manufacturer - one retailer (1-1) QFC model and used it for analysis to identify the influence relation of variables more concisely. These days, research on analyzing QFC with multiple manufacturers and retailers is gradually increasing, adding to the reality. Nevertheless, this still remains attractive to analyze the utility of variables that affect the QFC model. The classification by the number of agents is one-one (Bicer and Haspiel, 2016;Li et al., 2021;Liu, 2015;Tsay, 1999;Wu, 2005), one-multi (Plambeck and Taylor, 2007), multi-one (Chung et al., 2010;Sethi et al., 2004), multi-multi (Karakaya and Bakal, 2013;Kim et al., 2014;Nikkhoo et al., 2008) QFC model.

    3.1.2 Echelon

    Echelon is also an important component of the contract environment, most of which are a 2-echelon model made up of one manufacturer and retailer (Li et al., 2021;Lian and Deshmukh, 2009;Liu, 2015;Wu, 2005), but few a 2-echelon model or more (Nikkhoo et al., 2018) were studied.

    3.1.3 Products (or items)

    Whether there is only one product or a variety of products can also be major variables for analyzing contract performances. Most studies were investigated one item (Bicer and Haspiel, 2016;Nikkhoo et al., 2018), but sometimes two or more items (Miltenburg and Pong, 2007a, 2007b) were shown. Multi-product types can be included in the model in order to reflect more realistic supply chains.

    3.1.4 Lead Time

    Lead time is the time elapsed between the publication and delivery of the retailer’s final order at the QFC model is defined (Bicer and Haspiel, 2016). The Lead time was assumed to be deterministic (Chan and Chan, 2006), not specification (Heydrai et al., 2020), or just long (Li et al., 2021) in many studies. Bicer and Hagspiel (2016) analyzed the influence of lead-time decrease on the worth of quantity flexibility for the retailer and found that the briefer the lead time, the higher the sense of quantity flexibility. Their results indicated that reducing lead times can make contracts more profitable, less risky, and disintermediation problems.

    3.1.5 Demand and its Forecast

    Demand is the quantity of products that customers need in the future. The settings of demand distribution and its forecast are especially essential for QFCs which normally have to order twice. Demand distribution was assumed as uniform distribution (Heydrai et al., 2020), normal distribution (Bicer and Haspiel, 2016), random (Mahajan, 2014;Zhou and Li, 2007), unknown (Chung et al., 2014;Miltenburg and Pong, 2007a, 2007b). Sethi et al. (2004) examined the impact of information quality and flexibility on optimal decisions. Bicer and Haspiel (2016) considered a QFC model that demand forecasts are updated over time, and their forecast accuracy evolves as time goes by. Wu (2005) proposed a QFC model with Bayesian information updating, which is essentially a risk-sharing contract, the manufacturer and the retailer share the benefits from information updating. Miltenburg and Pong (Miltenburg and Pong, 2007a, 2007b) also analyzed the QFC model with multi-products using Bayesian estimation demand information to improve the accuracy of the demand forecast.

    3.2 Contract Terms

    Suppliers often crave a long time to put up capability for retailers. Therefore, the supply chain parties demand to bargain the contract terms and conditions to realize customer demand (Novak and Eppinger, 2001). The uncertainty in the price, cost, and future demand make both the supplier and the retailer in a supply chain incapable of writing a thorough contract that strictly specifies the obligations of the parties in every imaginable situation.

    3.2.1 Flexibility

    Flexibility is the core of QFC. That is because this leads to the performance of supply chain members. Tsay (1999) showed that by itself, the QFC does not guarantee efficiency. He mentioned we could achieve our goals only when there is a trade-off between flexibility and unit price, with the retailer willingly paying more for increased flexibility. Tsay and Lovejoy (1999) proposed a framework for performance analysis and design of quantityflexibility contract and investigated the relationship between inventory management and flexibility. Bicer and Hagspiel (2016) studied that although the quantity flexibility helps the retailer to reduce supply-demand mismatch, it may also cause supply chain disintermediation problems for retailers. They approved the benefit of quantity flexibility is steeper for shorter lead times. Therefore, retailers are likely to turn to their advantage more from limited flexibility used when demand is known than from considerably huger flexibility that needs to be utilized well before the request is known. Wang (2008) investigated the performance of the quantity flexibility as well as lead time flexibility. Wallace and Choi (2011) approved that flexible decisions help supply chain managers adjust to uncertainties and shocks. Kim (2011) verified flexibility does not certainly result in better supports for the clients. Sethi et al. (2004) measured the value of flexibility and provided conditions when this value is positive. Chung et al. (2010) found that the flexibility level is moderately high; the buyer’s action can align with the system’s objective.

    3.2.2 Price (or cost)

    The biggest issues in the price of the QFC is that of final orders, retail, transaction, return, salvage, and so on. Chopra and Meindl (2001) proved that the QFC might be more effective than the return decision if the return cost is high. Li et al. (2021) considered that the situation with the stochastic retail price. They confirmed the correlation between retail price and demand. Bicer and Hagspiel (2016) explored the relationship between supply chain disintermediation expenses and lead time. In addition, they demonstrated that the higher the critical ratio, the less important the disagreement problem. When the supplier’s first investment cost is relatively inadequate, the supply chain disintermediation hazard becomes less significant, and thus, the contract becomes more fruitful for the retailer. Zhou and Li (2007) experimented manufacturer may induce the retailer to order the coordinated quantity by adjusting the unit return price.

    3.2.3 Contract Period

    The determination of the contract period, whether the order quantity is decided at one time or religiously, has a significant impact on the supply chain. That is because a buyer receives discounts for committing to purchase in advance, i.e., the longer the forecast period, the lower the price. A one-period contract model was investi gated by Chung et al. (2014). A two-period dynamic model was developed and obtained an optimal replenishment strategy for the retailer and the supplier’s optimal pricing scheme by Milner and Rosenblatt (2002) and Li et al. (2016). A multi-period version of the QFC was introduced by Sethi et al. (2004), in which they examined single and multi-period QFC that included one demand update per period and a spot market. As an extension of the multi-period QFC, a rolling horizon control method has been examined by Knoblich et al. (2015).

    3.3 A Comparison with Various Contract Types

    Much research has compared the types of contracts that bring the greatest benefit to supply chain members under certain circumstances and conditions, even QFC itself. Tsay (1999) characterized each party’s preferences towards the QFC parameters. However, as the QFC does not guarantee efficiency by itself, he defined certain conditions that system-wide efficiency can be achieved with an appropriate choice of the contract parameters. Finally, he mentioned that there is a trade-off between flexibility and unit price; the retailer prefers to pay more for increased flexibility. Taheri et al. (2015) compared two cases, no coordination, and coordination with QFC. They clearly showed that QFC could increase the profit of supply chain members. Pasternack (1985) is the first to analyze the BBC and QFC. He showed that neither full returns with full buyback credit nor no returns system is optimal. Brusset (2005) compared the minimum purchase contract (MPC), QFC, and spot procurement in a supply chain. He found that the players would determine to transact their business through the spot market instead of MPC or QFC if the information was costly. In addition, the provider chooses the QFC if the buyer chooses the MPC and vice versa. The only possible equilibrium is for both to choose the same contracts when both contracts have to offer the same expected profits to each player. Li et al. (2016) approved by comparing it between models with and without quantity adjustment, the numeric analysis is, and their case application supported their theoretical model proclamation that the synergy of attaining global optimal pricing scheme for the supplier. Li et al. (2021) showed that for a given reservation quantity, the manufacturer constructs greater capacity in the QFC than in the CRC. Moreover, they also find that when coordination is achieved, the retailer prefers QFC because his profit split is higher. The contract preference of the manufacturer and retailer in Table 3.

    A composition with other strategies and contract types Only the QFC is enough to achieve the performance of the supply chain. However, many researchers have begun to create a new research genre by combining diverse strategies and other supply chain contracts to achieve greater expected profits.

    Xiong et al. (2011) proposed a composite contract (CPC) by originally jointing two popular contracts: buyback contracts (BBC) and QFC. They showed that CPC is more flexible for profit and risk allocation among supply chain members than the BBC and QFC. Lumsakul and Luong (2013) developed a composite revenue sharing and quantity flexibility contract. Their research led us to conclude that the combination of revenue sharing contracts (RSC) and QFC can better cooperate with the supply chain than the component contracts. Specifically, there exists the case where the proposed CPC can coordinate the supply chain when the RSC cannot. Chung et al. (2010) designed a new contract that combines the quantity and price-only discount incentives. They find that the contract can coordinate the supply chain without knowing the demand distribution, and a win-win consequence occurs for the buyer and supplier under certain settings. Liu (2015) showed that the exchange rate risk increases the its expected profit with the RSC while decreasing the supplier’s expected profit with the QFC. He suggested the optimal order quantity with the combined QFC and RSC in the global supply chain with the exchange rate fluctuation. Li et al. (2021) advanced that the combination of QFC and capacity reservation contracts (CRC) can coordinate the supply chain so that the total profit in high technology industries such as semiconductors with a short life cycle, high capacity cost, long lead time, and highly volatile demand. Heydari et al. (2020) combined them with an outsourcing strategy to overwhelm the primary shortcomings of classic QFC. However, reserving objects from the outer supplier is more highly-priced than in-house production, and therefore it is not economical for the manufacturer to outsource a huge amount. Indeed, the manufacturer wants to solve the trade-off between the cost of residual scrap goods and outsourcing cost to decide on a proper outsourcing amount. This study addresses this problem by proposing a QFC with outsourcing. Comparing the QFC with outsourcing and the QFC without outsourcing revealed that considering outsourcing opportunity can notably enhance the supply chain’s revenue as well as the group members’ profit.


    In the following section, we focus on approaching and addressing issues on QFC to achieve the goal of research question 2. Various and efficient research models and methods have been applied to juggle in the area of QFC. The newsvendor model was mostly used in the research. Because it is an encouraging approach to optimize the supply and handle the trade-off between the service levels and costs under uncertain demand, attracting great attention in QFC. Dynamic programming, an influential method for solving optimization problems, was employed by many researchers, including Lian and Deshmukh (2009), Sethi et al. (2004), Wu (2005), Chan and Chan (2006), Taheri et al. (2015) and Li et al. (2021) utilized game theory to investigate QFC’s performance between supplier and retailer. Other than these models and methods, the scenario aggregation method (Kim and Wu, 2013), otherwise called the progressive hedging algorithm (Karakaya and Bakal, 2013), simulation (Kim et al., 2014), Game theory (Li et al., 2021;Taheri et al., 2015), Markov chain (Qian et al., 2018), multiplicative martingale (Bicer and Haspiel, 2016), and so on were employed to obtain the optimal quantity and the expected revenue in QFC issues. We could not discover any significant evolution in research models and methods.


    In this section, we make a table to summarize the reviews based on the contract parameters and any other criteria in Table 4. And then we discuss and propose future research directions based on our reviews to attain research question 3. Earlier, we mentioned any tendency movements from contract parameters to comparison and combination with others. However, we detect that there are still many opportunities to develop all two areas. We need to grant contract settings and terms parameters such as batch order, the second delivery timing, fuzzy random demand, redundancy, trade-off relationship between flexibility, upper limit, and price. We also require to compare and combine QFCs with other strategies such as Enterprise Resource Planning (ERP), Vendor Management Inventory (VMI), Behavioral Operational Management (BOM: reference point, various bias such as Pull-to- Center bias, risk aversion bias, status quo bias, immediacy bias, optimal ordering quantity decision, regret, regret aversion, and so on) and contract types such as sales rebate, a quantity discount, pay-back, cost-sharing, and so on. Lastly, we have to apply various research models and methods such as queueing theory, system dynamics simulation, empirical experiments in laboratory or application on the mobile, field case study, survey, etc.


    Our paper’s leading contribution is to distribute a comprehensive review of the previous practical and logical studies of the peer-reviewed journal 50 issues appearing between 1985 and 2020 that examine the QFC and further research directions. The massive literature has been discovered and classified largely into three major sections of contract parameters, a combination or composition with other strategies and contract types, research models/methods, and even the evolution of it.

    Low-frequency-high-impact (LFHI) events such as coronavirus (COVID-19) and rapid technical growth are changing a lot now in every field, and that change will only be the beginning. In particular, we need to overcome and cope with the unexpected change in customer demand now. We want to stress that the QFC can be an alternative to address this chaos by gaining one more time to judge the customer’s demand for the remaining period before positioning the supplier’s final order quantity. Therfore, the industries apply to the QFC so that a manufacturer and a retailer can adjust the quantities and lower risk and cost when the COVID-19 unfolds or ends.

    As far as we know, this paper is the first in the QFC literature framework which potentially contributes to discussions on this zone. We hope that many researchers will revisit the slots identified herein to create much required empirical and conceptual work in the QFC.



    The sequence of events in quantity flexibility contract.


    Advantages to manufacturer and retailer in quantity flexibility contract

    Distribution of the articles with respect to journals

    The contract preference of the manufacturer and retailer

    The summary of quantity flexibility contracts in a supply chain system


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    2. Bicer, I. and Hagspiel, V. (2016), Valuing quantity flexibility under supply chain disintermediation risk, International Journal of Production Economics, 180, 1-15.
    3. Brusset, X. (2005), Comparison between Minimum Purchase, Quantity flexibility Contracts and Spot Procurement in a Supply Chain, University of Louvain.
    4. Chan, F. T. S. and Chan, H. K. (2006), A simulation study with quantity flexibility in a supply chain subjected to uncertainties, International Journal of Computer Integrated Manufacturing, 19(2), 148-160.
    5. Chopra, S. and Meindl, P. (2001), Supply Chain Management: Strategy, Planning, and Operation, New Jersey: Prentice Hall.
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    24. Nikkhoo, F. , Bozorgi-Amiri, A. , and Jafar, J. (2018), Coordination of relief items procurement in humanitarian logistic based in quantity flexibility contract, International Journal of Disaster Risk Reduction, 31, 331-340.
    25. Novak, S. and Eppinger, S. D. (2001), Sourcing by design: Product complexity and the supply chain, Management Science, 47(1), 189-204.
    26. Pasternack, B. (1985), Optimal pricing and returns policies for perishable commodities, Marketing Science, 4(2), 166-176.
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