Optimal price and quality decisions of a supply chain game considering imperfect quality items and market segmentation

doi:10.1016/j.apm.2020.10.034

Applied Mathematical Modelling

Volume 91, March 2021, Pages 1227-1244

https://doi.org/10.1016/j.apm.2020.10.034 Get rights and content

Highlights

•
We examine a supply chain game in which the manufacturer’s production process is imperfect.
•
Imperfect quality items can be distributed to a secondary market. Primary and secondary demands are considered simultaneously.
•
Optimal price and quality decisions are determined and compared with the case of an unrestricted secondary market.
•
A numerical example and sensitivity analysis emphasize the relevance of the model and give managerial insights.

Abstract

Imperfect production processes are frequently investigated in supply chain literature. Many recent articles assume that items that do not meet the quality requirements can be sold on a secondary market at a reduced price. Due to simplification, these papers ignore the demand of the secondary customers and assume instead that all imperfect quality items are salable. In this paper, we show that this ignorance can lead to unrealistic results as an unrestricted secondary market may reduce the manufacturer’s incentive for an error-free production process. By introducing a price- and quality-dependent demand for both the primary and secondary markets, we obtain the following main insights: (i) a restricted secondary market leads to more realistic results compared with the unrestricted case; the secondary demand is only ignorable under certain conditions; (ii) quality decisions are mainly influenced by the market parameters of both market segments as well as quality cost parameters; (iii) in some cases, it is advantageous not to serve the secondary market and to concentrate the sales process on primary customers.

Introduction

Today, due to rising customer requirements, product complexity, and global competition, quality decisions have a significant impact on the long-term economic success of every enterprise. Quality is considered to be a key factor not only for a single firm, but within the whole supply chain. Not surprisingly, researchers as well as practitioners show steadily growing interest in quality management issues.

In the past few years, numerous studies have been published that address practical problems in this context, such as the prevalence of defective items in the production process. These papers typically underline different strategic settings that deal with these products. For example, it can be assumed that goods that do not meet quality requirements have to be reworked or sold on a secondary market.

This last variant, that of selling on a secondary market, is a scenario that we would like to address in our article. It is used for product types for which reworking is not possible nor economical, e. g., articles of clothing. Thereby, this scenario is interesting not only within the literature, but also in practice as firms become increasingly aware of the potential benefits of secondary markets.

Many companies today use certain platforms on which they offer imperfect quality products. For example, Amazon sells returned or slightly damaged products at a reduced price on their platform, ”Amazon Warehouse.” Other companies, like Yamaha and AEG, occasionally sell products as B-stock that may have, for example, small cosmetic defects. The company B-stock Solutions (http://bstock.com) is considered to be the world’s leading auction platform for items that are returned, do not meet quality requirements, or are a result of overproduction. They consider themselves to be experts at connecting their clients, such as Amazon, Lowe’s, and Walmart, to the secondary market [1]. Other companies (see, e. g., https://www.avides.com) also specialize in exporting residual items such as excesses, returns, and faulty production on request. For example, manufacturers might want to prevent such inferior or damaged products from entering the core market at dumping prices in order to protect the brand image. Another reason is that they want to protect their own distribution channels, especially their retailers, from low-cost operators.

So, although this option of selling B-stock to secondary customers seems like a profitable way to get rid of this stock, recent theoretical papers ignore an important aspect: the demands of the secondary market. They typically merely assume that all imperfect quality items are sold to secondary customers at a given fixed price (see, e.g., [2], [3], [4]). Depending on the mathematical model, this assumption can lead to questionable results in which the actors in the supply chain are tempted to be careless with the quality they provide. In practice, it is also essential to include the demands of both markets in the decision making, as the demand for imperfect quality items is normally as limited as the primary demand.

Hence, some interesting research questions arise:

•
What is the impact of the assumption of an unlimited secondary market on the results compared to a restricted model? In which cases should the secondary demand never be ignored?
•
How do the market characteristics of both market segments influence the pricing and quality decisions of the firms?

In order to answer these questions, we analyze a supply chain setting in which the channel members are faced with different market segments. On the primary market, only products of perfect quality can be sold, whereas B-stock is transferred to the secondary market. In contrast to existing literature, we introduce a price- and quality-dependent demand for both market segments and allow the case in which not all imperfect items are sold. This way we can show that the manufacturer’s incentive to have a production process as error-free as possible is much increased compared to the case of an unrestricted secondary market.

The remainder of this paper is organized as follows. In Section 2, we present the theoretical background of the paper, including relevant literature. In Section 3, we formulate two game-theoretic models, where one of them (Model 1) assumes that all imperfect quality items are salable, whereas the second model (Model 2) considers a price- and quality-dependent demand for both market segments. We solve the models in Section 4 and illustrate the results with a numerical analysis in Section 5. Since it becomes clear that Model 1 is certainly less complex but significantly less realistic, we present a sensitivity analysis only for Model 2 in that section. Section 6 concludes the paper.

Section snippets

Background

Due to their practical relevance, new contributions are continuously published in the area of quality management. Thereby, ”quality” is a term which might be used and defined individually and in different ways. For example, Garvin [5] considers eight different dimensions of quality: performance, features, reliability, conformance, durability, serviceability, aesthetics, and perceived quality. When using the term ”imperfect quality” authors refer typically to conformance quality issues, meaning

Model formulation

We consider a two-echelon supply chain in which a manufacturer produces a single type of product and sells it through a retailer on the primary market. The manufacturer’s production process is imperfect. Items that are not of sufficient quality are distributed to a secondary market. We underline a game-theoretic setting in which the manufacturer acts as the Stackelberg leader and the retailer as the follower. We distinguish between two model variants that consider either an unrestricted or a

Model 1 – unrestricted case

In the following, we derive the Stackelberg equilibrium for the case in which the demand of the secondary market is assumed not to be restricted. Since we consider a dynamic game-theoretic model, the problem is solved via backward induction. The retailer acts as the Stackelberg follower, hence determining the margin $m_{R}$ that maximizes its profit, given any decisions made by the manufacturer: $\max_{m_{R}} π_{R} = q_{p} m_{R} .$ The problem is solved by taking the first order derivative with respect to $m_{R}$ and setting it

Numerical examples and comparison of the models

Model 1:

In this section, a numerical example is proposed. For that, we set the values of the parameters as follows:

$α_{p} = 100$ ; $β_{p} = 0.5$ ; $θ_{p} = 5$ ; $c_{m 0} = 3$ ; $c_{m} = - 4$ ; $η = 0.7$ ; $σ = 0.6$ ; $f_{0} = 15$ ; $f = 30$ ; $y_{0} = 0.25$ ; $g = 3$ .

We apply Eqs. (17), (19), (20) and (21) and vary the quality level $A$ from 0 to 1.0 to determine its optimal value. We gain the following results for the manufacturer:

$w = 103.832$ ; $m_{R} = 51.584$ ; $q_{p} = 25.792$ ; $A = 0.7$ ; $π_{M} = 2947.098$ ; $π_{R} = 1330.456$ .

The quantity of

Conclusions and future research

This paper considers a supply chain with an imperfect production process where B-stock items are sold on a secondary market. First, we consider Model 1 which follows common assumptions in the literature and ignores secondary demand. We show that this simplification can lead to unrealistic results in which the manufacturer’s quality level is as low as possible in many cases. This leads to our first main finding and answers the first research question, namely, that demand in the secondary market

Declaration of Competing Interest

No potential conflict of interest was reported by the authors. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Optimal price and quality decisions of a supply chain game considering imperfect quality items and market segmentation

Highlights

Abstract

Introduction

Section snippets

Background

Model formulation

Model 1 – unrestricted case

Numerical examples and comparison of the models

Conclusions and future research

Declaration of Competing Interest

Int. J. Prod. Econ.

Appl. Math. Model.

J. Manuf. Syst.

Appl. Math. Model.

J. Manuf. Syst.

Int. J. Prod. Econ.

Appl. Math. Model.

Eur. J. Oper. Res.

Appl. Math. Model.

J. Clean. Prod.

Appl. Math. Model.

Int. J. Prod. Econ.

Eur. J. Oper. Res.

Appl. Math. Model.

Int. J. Prod. Econ.

J. Clean. Prod.

J. Retail.