Production, Manufacturing, Transportation and Logistics
Lead-time quotation and hedging coordination in make-to-order supply chain

https://doi.org/10.1016/j.ejor.2021.07.045Get rights and content

Highlights

  • Nash and manufacturer-led Stackelberg models yield shorter quoted delivery times.

  • Each participant benefits from the production time hedging under multiple sourcing.

  • A manufacturer obtains more profit in a supply chain with fewer competitors.

  • The retailer's profit increases with the manufacturer's holding cost.

  • Multiple sourcing mitigates the negative effects of individual parameter changes.

Abstract

In the Make-To-Order (MTO) supply chain, for enticing the retailer to choose a shorter delivery lead-time, which improves the manufacturer's wholesale prices, the manufacturer adopts the Production Time Hedging (PTH) strategy as an incentive. Since the profit of the retailer depends not only on the Quoted Delivery Lead-Time (QDLT) but also on the Realized Delivery Lead-Time (RDLT), effectively hedging production time uncertainty reduces tardy delivery. We build an analytical model to investigate how PTH affects the retailer's QDLT decision and the supply chain performance. We consider models for four scenarios, namely (I) the centralized model, (II) the Nash model, (III) the manufacturer-led Stackelberg model, and (IV) the retailer-led Stackelberg model. We derive close-form results on the optimal hedging and QDLT decisions. In models II and III, PTH reduces the QDLT under all the conditions. However, in model IV, PTH can only coordinate the retailer when the hedging cost is low, or the holding cost/tardiness penalty is high. Besides, we find that model III is the dominant scenario for both players. Extending model IV to consider the case where the retailer sources from multiple manufacturers, we show that multiple sourcing is the dominant strategy when a manufacturer's hedging cost is high, or its holding cost/lead-time sensitivity factor is small. From the numerical study, we are interesting to find that the retailer's profit increases with the manufacturer's holding cost/lead-time sensitivity factor.

Introduction

We investigate the lead-time quotation and Production Time Hedging (PTH) coordination problem in a Make-To-Order (MTO) supply chain with fixed demand quantity under a single period. The MTO model is increasingly popular in industries such as home furniture and electronics manufacturing (Glock, Rekik & Ries, 2020; Li & Womer, 2012). For example, home furniture firms such as Ikea and Red Star Macalline offer MTO furniture to their customers. Electronics firms such as HP and Dell offer customization programs to consumers to meet their specific requirements. Although the MTO supply chain has the potential to generate more profit by providing customers with reliable services and customized products, the profit may be compromised by decentralization among the supply chain members (Hammami, Frein & Albana, 2020). The self-interested decisions of a party might conflict with other parties’ interests, resulting in a less profitable supply chain. One of the conflict areas among the MTO supply chain arises out of delivery lead-time quotation and production scheduling (Li, Wang & Sawhney, 2012). Although some recent literature on lead-time quotation suggests the importance of jointly optimizing the delivery lead-time decision with other supply chain decisions, the optimal decisions are usually determined subject to fixed capacity/production resource constraints without consideration of the role of the MTO manufacturer. Striving to fill this gap, we build an analytical model to examine the effect of controlling production time on delivery lead-time quotation in a decentralized MTO supply chain.

Specifically, the retailer receives orders from consumers directly and then assigns the customization tasks to the MTO manufacturer. The retailer has the freedom to set the Quoted Delivery Lead-Time (QDLT) and announces it to the consumer. Although consumers are willing to pay a higher price for a shorter QDLT, their satisfaction depends on the realized delivery lead-time (RDLT), which is usually uncertain due to production instability (Kingsman, Tatsiopoulos & Hendry, 1989; Talay & Özdemir-Akyıldırım, 2019). The production time uncertainty is often caused by machine breakdown, shortage of raw material, bad weather condition and festival season (Leng & Parlar, 2009). If the RDLT exceeds the QDLT, the retailer needs to compensate the consumer's waiting time, which incurs a tardiness penalty. Increasing the QDLT reduces the probability of tardy delivery and the selling price, and vice versa. Thus, there is a trade-off between the QDLT and the tardiness penalty. The optimal QDLT decision maximizes the retailer's profit, but does not necessarily increase the manufacturer's and the supply chin's profits. Indeed, the manufacturer's wholesale price is decreasing in the QDLT for the retailer will pay a lower wholesale price when the remaining production time is long. Thus, the manufacturer prefers a short QDLT, which incurs a heavy tardiness penalty to the retailer. As a result, there is a conflict between the retailer and the manufacturer over the QDLT decision.

To resolve this conflict, we propose a PTH mechanism to coordinate the retailer's QDLT decision and the manufacturer's decision. Specifically, the PTH strategy adopted by the manufacturer is to invest more in the MTO production process to improve production time reliability. In an MTO supply chain, production time uncertainty is often caused by unreliable production facilities or unskillful workers, which lead to a longer RDLT that hampers the on time delivery of customized products i.e., the RDLT exceeds the QDLT (Heydari, 2014, 2018; Hu, Guan & Liu, 2011). Unfortunately, tardy delivery in the MTO supply chain not only incurs a heavy tardiness penalty but also affects customers’ goodwill, which decreases profit in the long run. In practice, production time uncertainty can be reduced by hiring more skilled workers and experienced managers, using more reliable equipment, or improving progress controlling and information sharing by applying advanced technologies (Zhai, Choi, Shao, Xu & Huang, 2020). Evidently, being unable to meet the QDLT is a challenge in the MTO supply chain, so reducing the RDLT by controlling production time uncertainty could provide a good incentive for the retailer to participate in the coordination effort. To the best of our knowledge, our work pioneers exploration of the interaction between production time control and delivery lead-time quotation.

Our study aims to develop a theoretically sound and implementable PTH mechanism to address the lead-time quotation problem. Specifically, we set out to address the following research questions.

  • (1)

    What is the effect of PTH on the QDLT decision and whether it can be an incentive for the retailer to participate in the coordination effort?

  • (2)

    What are the optimal strategies for the manufacturer and retailer under the PTH mechanism?

  • (3)

    How do the profits of the manufacturer and retailer depend on different modeling scenarios and the major model parameters?

For the extended model, we address the following additional questions.

  • (1)

    What is the effect of multiple sourcing on the profits of the participants?

  • (2)

    Under what conditions the single sourcing or multiple sourcing is the dominant strategy for the retailer?

To answer the first question, we integrate the effect of PTH on the RDLT into the profit function of each party, and explore the interaction between PTH and the QDLT. To answer the second question, we study the centralized model and three game models, namely the Nash model, the retailer-led Stackelberg model, and the manufacturer-led Stackelberg model. Besides, we use the model without PTH as the benchmark. To address the third question, we conduct extensive numerical studies and find that PTH brings more profits to both parties in the Nash model and the manufacturer-led Stackelberg model under all the conditions. However, in the retailer-led Stackelberg model, both parties’ profits are enhanced only when the hedging cost is low, or the holding cost/tardiness penalty is large. To analyze multiple sourcing, we consider the extended retailer-led Stackelberg model comprising one retailer and multiple manufacturers. Under multiple sourcing, the retailer first announces the QDLT to each manufacturer, which then chooses the optimal PTH amount based on its own objective. To answer the last question, we explore and compare the outcomes of parameter changes under the single and multiple sourcing scenarios. We find that all the parties benefit from PTH under all the conditions.

We organize the rest of the paper as follows: In Section 2 we review the related literature to identify the research gaps and position our study. In Section 3 we introduce the notation and discuss the assumptions. We analyze the benchmark model and the centralized model in Sections 4 and 5, respectively. We study three game models in Section 6. We extend the retailer-led Stackelberg model to consider multiple sourcing in Section 7. We present and discuss the results of the numerical studies and sensitivity analysis to study the effect of PTH on the performance of the MTO supply chain in Section 8. Finally, in Section 9, we conclude the paper and suggest topics for future research. We present all the proofs of the results in the Appendix.

Section snippets

Literature review

This research is related to lead-time quotation, operational hedging method, and multiple sourcing. In the following we review the related literature on these topics.

Model assumptions and notation

Consider an MTO supply chain consisting of a retailer and a manufacturer. The consumers order specific products from the retailer that has full freedom to set its QDLT. This research focus on the delivery time from the manufacturer to the retailer while the shipping time from the retailer to the consumer is assumed negligible and thus omitted. The retailer announces its delivery lead-time decision to both consumers and the manufacturer. In this research, we focus on the MTO supply chain, which

Benchmark model

In this section we study the benchmark model in which the retailer aims to maximize its profit as follows:πR=(PRαLPW+βL)QTQL(tL)dP(t).

The first component denotes the fixed revenue for each order. Specifically, the first term denotes the unit revenue for each product, which is calculated by subtraction the unit wholesale price from the unit sales price, and the second term denotes the order quantity. The second component represents the expected tardiness penalty if the order delivered

Centralized model

In this section we investigate the centralized setting, in which the retailer makes all the decisions with a view to maximizing the system's profit. The manufacturer's profit isπM=(PWβLCM)QHQ0L(Lt)dP(t)CH(eΔl1)Q.

The first component denotes the fixed revenue for each order. It is calculated by subtraction of the production cost from the wholesale price. The second component represents the holding cost for the products that are produced before the actual due date. The last component is the

Decentralized model

In this section we consider three different game models representing different power structures between the retailer and the manufacturer, namely the Nash model, retailer-led Stackelberg model, and manufacturer-led Stackelberg model. The retailer's profit is characterized by Eq. (4), while the manufacturer's profit is characterized by Eq. (6).

Model extension: Multiple sourcing

In order to avoid the failure and production uncertainty of a single manufacturer, the retailer sometimes splits the entire MTO order to a set of manufacturers. In this situation, the retailer acts as the market leader and decides the unique QDLT for all the manufacturers. How to react to the retailer's QDLT decision as well as other manufacturers’ PTH decisions is a critical challenge for each manufacturer. In the extended model, we assume that the entire order is equally divided to n

Numerical studies

In this section we first examine the performance of the hedging coordination mechanism under the single sourcing scenario. We analyse three parameters, namely the hedging cost, holding cost, and tardiness penalty. The first two parameters are endogenous variables, which can be controlled by the manufacturer, so the manufacturer has to know how the system performance is influenced by these parameters. The last parameter is determined exogenously, which varies from order to order. Hence, the

Conclusions

We consider a lead-time quotation and hedging problem in a MTO supply chain comprising a retailer and a manufacturer. In order to entice the retailer to set a short QDLT, the manufacturer adopts the PTH strategy to improve its production reliability, which provides an incentive for the retailer to participate in the coordination effort because the retailer's profit depends not only on the QDLT but also on the RDLT. We propose a PTH mechanism to coordinate the retailer's QDLT decision and the

Acknowledgments

This research was supported in part by the National Natural Science Foundation of China under grant number 71901023, and Beijing Social Science Foundation under grant number 20GLC057. Cheng was also supported in part by The Hong Kong Polytechnic University under the Fung Yiu King - Wing Hang Bank Endowed Professorship in Business Administration.

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