Over the last decades, supplier development has become an increasingly important concept to remain competitive in today’s markets. Therefore, manufacturers invest resources in their suppliers to increase their abilities and, ultimately, to reduce their product prices. Thereby, most approaches found in the literature focus on longterm supplier development programs. Nevertheless, today’s volatile and dynamic markets require flexible approaches to deal with this complexity. We apply Model Predictive Control to optimize the number of supplier development projects in order to achieve flexibility while maintaining a certain level of security for all parties. Thereby, the article focusses on a multimanufacturer scenario, where two manufacturers aim to develop the same supplier. These manufacturers can establish different levels of horizontal collaboration. While previous results already show the benefits of applying this approach to a static scenario, this article extends this formulation by introducing market dynamics in the numerical simulations as well as into the optimization approach. Thus, the article proposes to derive regression models using realworld data. The article evaluates the effects of realworld market dynamics on two use cases: an automotive use case and a use case from the mobile phone sector. The results show that assuming market dynamics during the optimization leads to increased or at least closetoequal revenues across the involved partners. The average increase ranges from approximately 1% to 5% depending on the type and magnitude of the dynamics. Thereby, the results differ depending on the selected collaboration scheme. While a fullcooperative collaboration scheme benefits the least from regarding dynamics in the optimization, it results in the highest overall revenue across all partners.
Rapid development and advancement of technologies lead to frequent product changes and short production life cycles [
Research on this topic has shown that extended programs increase the reliability of such relationships, while shortterm contracts provide higher flexibility, in particular in turbulent markets. Therefore, companies may be reluctant to engage in longterm agreements, which possibly reduce their tendency to invest in supplier development activities [
Consequently, this article aims to extend the approach by enabling an integration of market dynamics into the mathematical model. The primary objective is to evaluate how market dynamics influence the overall benefits of different settings of collaboration between manufacturers. Therefore, the remainder of this paper is structured as follows. Section
In the current literature, several authors deal with the topics of supply chain collaboration and supplier development. Nevertheless, only a few approaches combine both aspects. This section presents a summary of related previous studies below.
Today is the age of adaptive and intelligent supply chains, which is a new generation of networks and communications across the different partners to deal with dynamics, such as supplier failures or demand uncertainty [
Looking back on nature [
Supply chain interaction formation [
The first phase,
In supply chain collaboration, partners collaborate to share information, logistics facilities, and resources to improve cost efficiency without compromising service levels. Supply chain collaborations categorize as vertical, horizontal, or lateral, according to the collaboration scope [
Following this classification, this study focuses on lateral collaboration in terms of supplier development. In particular, it focuses on the horizontal collaboration between manufacturers in combination with vertical supplier development programs.
To compete effectively in the world market, a company must have a network of competent suppliers. Supplier development enables companies to create and maintain such a network and improve various capabilities of their suppliers to deal with increasing competitive challenges [
Supplier development generally defined as “any effort by a buying firm to improve a supplier’s performance and capabilities to meet the manufacturing firm's shortterm and/or longterm supply needs” [
Supplier development aims to increase a partner’s capabilities or performance, e.g., in terms of responsiveness, product or service quality, reliability, or generally in terms of cost [
Over the last decades, supplier development received increasing attention in research and practice as a new concept. Most literature focusses on qualitative concepts, such as the use of certain operations in the supplier development context [
Apart from these basic concepts of supplier development, several studies focused on the investigation of practical applications in various industries, e.g., [
In terms of quantitative evaluations of supplier development, some authors proposed models to evaluate the efficiency of supplier development programs. Bai and Sarkis applied various gametheoretic models, to reveal how profits of supplier development investments are affected by multiple relationships among manufacturers and suppliers. The results illustrate that a cooperative relationship is more economically beneficial to the supply chain. However, it requires more capital resources and knowledge investments than a noncooperative relationship [
Dastyar and Pannek provided a set of optimization models to address the risk of supplier development [
Meanwhile, the presented models investigate the efficiency of supplier development in various constellations, and they generally assume fixed market conditions and neglect the influence of market dynamics. Since decision makers should be aware of the gained profit of their investment in supplier based on the dynamic market situation, the everchanging markets’ conditions have to be taken into account. To tackle the mentioned issue, we applied two use cases to study the profitability of the supplier development investment for manufacturers implementing realworld data. Section
This article builds upon the model presented in [
The MPC scheme combines shortterm closedloop control of the realworld system with a modelbased, longterm openloop optimization, as shown in Figure
MPC control scheme [
The proposed algorithm relies on three different components: First, the system model, which describes the state of the realworld system. MPC’s open loop uses the system model to simulate the effects of controls. Second, to derive optimal solutions given a specific system state, the optimizer uses a cost function. Finally, the proposed approach uses one of the four collaboration schemes, which determine the order of decisionmaking, and the information available for each manufacturer in each time instance
Dastyar and Pannek propose four collaboration schemes, each differing in the sequence of decisionmaking and the manufacturers’ system models. These schemes describe different information available to each manufacturer during decisionmaking [
In this equation,
The collaboration schemes differ primarily in the order of decisionmaking and in the system model, which the openloop optimization applies to simulate the effects of controls. In contrast, the closedloop system model always records all supplier development projects conducted by all manufacturers to initialize a new openloop iteration. Figure
Order of decisionmaking and information exchanges based on different collaboration schemes.
For the
In the
The
The
Finally, the
The presented model and its derivative collaboration scheme provide a useful tool to optimize supplier development programs. Nevertheless, besides other actors, i.e., additional manufacturers, changes in the current market situation impose additional dynamics, which cannot be handled by these models. Consequently, Section
Extending the cost function provided in Section
In this study, we select two types of products to investigate the effect of price dynamics on the revenue gained by supplier development. We assume Samsung smartphones’ market as a short lifecycle (hightechnology) product and MercedesBenz Aclass cars as a middle lifecycle product, as these markets show very distinct characteristics.
A large number of manufacturing technologybased industries have evolved at an impressive speed, showing rapid transitions in terms of both product features and manufacturers’ competitive dynamics. The mobile phone industry is one of the most prominent examples. The global mobile phone industry has faced radical changes since its birth [
Similarly, many researchers studied the automotive life cycle [
To compare the market situation for mobile phones and automobiles, they have different life cycles and very different market dynamics. The market price of mobile phones generally declines significantly after the new model releases to the market. This condition is not valid for automobile market prices. In the car market, the prices change slowly when a new model presents to the market. Moreover, car prices remain comparably stationary when compared to the high dynamics of mobile phone prices.
This section first presents current drivers of market dynamics by analyzing the structure of incurring costs for each company. Afterward, it describes the modifications required to include market dynamics into the proposed approach.
Variable manufacturing costs divide into three broad categories: direct materials costs, direct labor costs, and manufacturing overhead [
As a result, only the supplier’s revenue (
We analyzed data corresponding to the described use cases and derived generalized regression models to simulate realistic market dynamics. The datasets for the
For the
We created two distinct models as part of each use case to obtain an estimation of market dynamics concerning the price development. The first model (
We split the time series into two distinct datasets to characterize the functions
Regression models for release price (
Figure
Comparison between the estimation of
As described earlier, production costs generally split into material costs, labor costs, and overhead costs. For this study, we also include the energy cost as one of the primary factors; thus, consider it separately from the overhead. The cost functions given in equations (
Thereby, vector
We obtain the time series from the DESTATIS database of Germany’s Federal Office for Statistics [
By aggregating the values provided in this table, we characterized vector
Price indices provide the relative development of a specific value over the years. As a result, these relative values were used directly to obtain a regression model for the development of energy prices without further normalization and preprocessing. Moreover, we assumed that the dynamics in energy costs did not differ between the different sectors and used the same model in all calculations.
This table contains various information about the number of employees, turnovers, and labor costs for each sector. By dividing the amount of paid labor costs by the reported number of working hours, we calculated the monthly average wage in each industry sector. This value was again normalized by dividing through the initial value to achieve the multiplier required for equations (
Similar to the price index for energy, this time series represents the relative change in reported manufacturing costs for each sector. While these values can serve as a benchmark for the estimation of
By combining these regression models, we estimate the production costs as given in equations (
Comparison between the manufacturing price index obtained by Germany’s Federal Office of Statistics in each industry sector with the estimation calculated by equations (
This section presents the results for a set of numerical simulations. These simulations aim to evaluate the difference in the presented optimization approach with and without assuming market dynamics. Thereby, we optimize each use case twice: once we include the models described in the last section (equation (
Table
Experimental setup.

Description  Automotive  Mobile phones  

M1  M2  M1  M2  

Initial willingnesstopay  10,000  10,000  500  500 

Cost for SD projects  3,000,000  2,000,000  13,000  9,000 

Initial prod. cost for manuf.  4,500  5,400  225  270 

Initial prod. cost for supplier  4,050  3,240  202.5  162 

Price elasticity  0.01  0.01  0.01  0.01 

Revenue of supplier  450  360  22.5  18 

Learning rate  −0.1  −0.1  −0.1  0.1 

Maximum number of SD projects per period  20  10  10  5 
—  Sampling horizon  6 months  1 month  
—  Openloop horizon  54 months (4.5 years)  12 months  
—  Closedloop horizon  240 months (20 years)  84 months (7 years) 
To calculate the parameters in the table, we first assume an arbitrary value for the customer’s willingnesstopay
Figures
Results and for the static automotive use case.
Results for the static mobile phone use case.
Control
Control
While in this study we applied realworld data, the results of the static scenarios show the same behavior as the results of Dastyar and Pannek [
The results and behaviors in Figure
Both use cases show very different behaviors when the openloop simulation assumes market dynamics, as shown in Figures
The dynamic mobile phone use case again shows a very different behavior than the previous one. Both manufacturers delay their first investments approximately for the first two years in all collaboration schemes. Therefore, the optimizer determines that the price for investments is too high for the gained benefit of the supplier development program. The comparably low parameter values can explain this behavior for the supplier’s manufacturing cost. It is to mention that, for this use case, the relation between the monthly costs for a supplier development project and the willingnesstopay is approximately half of the automotive use case (factor: automotive 50, mobile phone 26). With this lower relation, we would have assumed to see more substantial investments, as each project only costs approximately half (related to the willingnesstopay), while the effects remain the same (state increased by one per month with the same learning rate). Thus, the lower number of conducted projects originates from the low value for
Table
Comparison of static and dynamic model assumptions.
Noncooperative  Sequential  Simultaneous  Fullcooperative  Mean  

Automotive  
Sum of revenue  5.70%  6.00%  6.14%  2.25%  5.02% 
Switching point  31 months  37 months  43 months  43 months  38.5 months 
Last year (2 instances)  9.59%  10.07%  10.54%  5.70%  8.98% 
Last instance  10.42%  10.92%  10.93%  6.33%  9.65% 


Mobile phones  
Sum of revenue  1.45%  1.27%  1.59%  −0.24%  1.02% 
Switching point  60 months  60 months  60 months  Never  60 months 
Last year (12 instances)  2.30%  2.29%  2.31%  2.25%  2.29% 
Last instance  1.03%  1.03%  1.03%  0.99%  1.02% 
The results for the automotive use case show an increased profit of approximately 5.0% across all four collaboration schemes, considering the sum of the profits for all instances. Comparing the global profit for each time instance, the results show that, for early time instances, a static assumption results in higher profit, while an increasing horizon shows an increasing benefit for the dynamic assumption. This is given by the denoted switching point. The dynamic model assumptions begin to provide a higher global profit starting at 38.5 months into the project on average. When considering the average difference in revenue at the end of the simulation time, the dynamic assumption archives an average of 9.0% more profit compared to the static assumption when considering the last year and even 9.7% when only considering the final instance.
In contrast, the results for the mobile phone use case show no huge difference between the assumptions. The results show a minimal increase of 1.0% in the total profit across all collaboration schemes, again, considering the sum of profits for all instances. Comparing the relative difference in the global profit by time instance, the results show the same behavior as before for the first three collaboration schemes in Table
Even though the comparison shows a lower relative increase in revenue for the fullcooperative scheme when the algorithm considers dynamics, the absolute numbers still show that the fullcooperative scheme achieves the highest total revenue in all cases. Figure
Absolute sum of profits for the (a) automotive and (b) mobile phone use cases.
The results show that assuming dynamics during the optimization results in higher or at least closetoequal revenues for most of the scenarios. Only the fullcooperative mobile phone use case shows a slight decrease in revenue compared to a static assumption. Generally, the results show that the advantage of assuming dynamics depends on the planned runtime of the overall supplier development program. For short programs, a static assumption yields better revenues, as the optimizer issues investments quickly at the beginning of the project. Nevertheless, for more extended programs of more than three years for the automotive use case and more than five years for the mobile phone use case, the integration of dynamics shows higher revenues consistently. Generally, the number of projects funded ties to the supplier’s production costs and the current market price (willingnesstopay
The fact that the fullcooperative schemes benefited the least from assuming dynamics while simultaneous schemes benefitted the most shows an interesting result. This fact, combined with the overall higher revenue of fullcooperative schemes, shows that the combination of cost functions generally provides higher potential to increase revenue in such multimanufacturer scenarios. The sequential scenarios benefit highly from dynamic assumptions but still fall short in the comparison of the overall revenue. As described above, this setting tends to support opportunistic behavior by the second manufacturer. This manufacturer is not as dependent on the supplier as the first one and often tends not to invest and rely on the first manufacturer’s investments. While this optimizes its profit locally, both manufacturers generate less revenue globally. The same holds for the sequential collaboration scheme, which also falls short on total revenue even behind the noncooperative scheme.
The results further show a drastic difference between the two selected use cases. These use cases show very distinct characteristics: a monotone increase in the willingnesstopay and a decrease in the supplier’s production costs for the automotive scenario, compared to a highly volatile willingnesstopay and an increased production cost for the mobile phone use case. While the automotive use case benefits strongly from the inclusion of dynamics, the mobile phone use case only benefits slightly. The general magnitude of the dynamics can explain this difference. Even though the mobile phone use case shows high fluctuations in the willingnesstopay, the general magnitude of the changes only amounts to a fraction of the magnitude for the automotive case (∼2% of the corresponding increase of the willingnesstopay over the simulation time). To evaluate this theory, we conducted several additional optimizations with uniformly scaled values for the willingnesstopay and different prediction and sampling horizons. All of these optimizations showed very similar results (approximately ± 2%) when comparing the sum of the total revenue. While this in itself is no proof for this assumption, it indicates only a minor dependence on the actual parameters used in the experiments but a vital influence of the underlying market dynamics.
This article aims to evaluate, if assuming market dynamics within supplier development programs proves advantageous for the application of a dynamic contract extension. Therefore, the article first presented the used optimization approach, applying Model Predictive Control to optimize supplier development programs for different collaboration schemes in a multimanufacturer setting. The article then presents an extended version of the used cost function, which allows the integration of market dynamics for the parameters
In general, these results show increased efficiency of the supplier development program if considering current market dynamics. Thereby, the extensions to the approach for optimizing investments in supplier development proposed in this article allow practitioners to render decisions using comparably simple models of the assumed market dynamics. As described in Section
Future work will focus on the evaluation of different types and magnitudes of dynamics. The current results show an advantage of including dynamics, but this article also shows that obtaining suitable models for market dynamics is not an easy task. A more detailed analysis of different types of dynamics will support companies in deciding if it is worthwhile to establish such models. Moreover, future work will focus on extending the current formulation of the optimization problem. For example, the current results show a decrease in investments before a new product generation emerges. While this behavior is currently unintended, it is sensible from an economic point of view to cease investments in “old products.” We can facilitate such behavior by including different types of supplier development projects. As stated in the state of the art, projects can have different aims, e.g., to provide additional training or resources of general nature, or they can support specific products or components. By implementing this difference, we can apply advanced mechanics to estimate the effect of such projects. On the one hand, it is possible to weigh their effects differently; on the other hand, we could reset productspecific investments on generation changes. Moreover, such differentiation could also help to gain further insights into the interaction of manufacturers. Therefore, we can assume that productspecific investments do not, or only marginally, benefit the other partners, while general projects will benefit both partners to a certain degree.
The data used to support the findings of this study can be obtained from the website of Germany’s Federal Office of Statistics or the provided references.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
The authors would like to show their gratitude to Prof. Dr. Jürgen Pannek for his support in developing the idea. The first author’s work was supported by the FriedrichNeumannStiftung für die Freiheit under Grant no. ST8224/P612. The Staats und Universitätsbilothek Bremen funded the APC.