Digital Supply Chain through Dynamic Inventory and Smart Contracts
2. Technical Differences between Static and Dynamic Games
3. Characterization of the Static Game
3.1. Centralized Solution of the Static SC Game
3.2. Decentralized Solution of the Static SC Game
3.3. Comparison between Centralized and Decentralized Solution of the Static SC Game
4. Characterization of the Dynamic Game
4.1. Centralized Solution of the Dynamic SC Game
4.2. Decentralized Solution of the Dynamic SC Game
4.3. Comparison between Centralized and Decentralized Solutions of the Dynamic SC Game
5. Numerical Analysis
- The marginal production and purchasing costs, as well as the inventory costs, are the same; therefore, each player is indifferent with respect to producing or holding stocks.
- Nevertheless, by producing and purchasing, each player can reach the optimal production and purchasing quantity. This represents the optimal amount of goods to attain in order to exploit the economies of scale and minimizing the total production and purchasing costs. Also, those quantities are assumed equal for both players.
- The transferring price under RSC is equal to the production cost. The manufacturer does not increase his profit directly by selling but receives a compensating quota of the retailer’s income. The parameter describes that proportion.
- While the existing contributions successfully assessed that the RSC is preferred to the WPC for coordinating SCs, this statement fails when comparing the WPC under dynamic settings with the RSC under static settings. In particular, the cumulative profits obtained by using WPC under dynamic settings result higher than those generated by implementing RSC under a static environment. Accordingly, SCs should be coordinated by simultaneously evaluating the contract schemes and the setting and converging toward an optimal decision. An artificial intelligence system, along with blockchain and big data, should be implemented according to these targets rather than as mere smart tools to write lines of orders.
- Existing contributions clearly highlight the preference for the centralized SC to the decentralized one. We compare the cumulative profits finding that the decentralized SC under dynamic settings obtains higher profits than those obtained by the centralized SC under a static framework. This statement is true independent of the contract scheme adopted for SC coordination. This result suggests that the decision-maker cannot disregard the setting when choosing the SC configuration. Static and dynamic settings suggest an important innovation in the literature when evaluating centralized and decentralized SC compositions. Figure 6 reports the summary of our findings showing the convenience when going from one configuration to another. The bold arrows reflect the innovation due to this research, while the others concern the results already known and well established in the literature and confirmed here.
- The choice of the sharing parameter and the transferring price w determines the convenience for each player in adopting one configuration rather than another. This is particularly true for the manufacturer. When is low enough and the transferring price is equal to the marginal production cost, the RSC totally mitigates the double marginalization effect, and it is found to always be highly preferred with respect to the WPC. When the values (, w) change, the results are not obvious. The smart contracts that firms use should aim at searching for the optimal combinations of these two parameters to make SCs better off with digitalization. Our findings suggest that, beyond the choice of setting, the adequate combination of the parameters (, w) plays an important role in choosing the optimal configuration for maximizing the manufacturer’s cumulative profit.
- Finally, the choice of the parameters (, w) substantially influences the retailer’s cumulative profits. Nevertheless, the retailer shows more stable and interesting results with respect to the comparison between static and dynamic settings. The implementation of the RSC is always preferred to the WPC for the higher cumulative profits generated by each combination of (, w). Notwithstanding, this result is true as long as the comparison between the two contract schemes uses the same settings. When evaluating the results of the WPC under dynamic settings with the RSC under static settings, the previous statement fails for each combination of (, w) used in the sensitivity analysis. The retailer incurs higher economic benefits by adopting WPC in dynamic settings than RSC in static settings. This result introduces a novelty in the literature. When coordinating the SC, the choice of the setting matters considerably, and the adoption of the contract scheme depends on the selection of the setting. Figure 7 reports the summary of the firms’ convenience in shifting from one configuration to another. While the results concerning the retailer are quite stable and clear, the choice of the parameters (, w) impacts the manufacturer’s decisions, which is the leading firm in terms of implementing an artificial intelligence system. Non-bold arrows illustrate the well-assessed findings in the literature, while the findings of this paper are shown in bold. Bold and double arrows represent the relationships that need further future investigations, as the results obtained are not at all definitive.
Conflicts of Interest
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|Planning horizon||One-shot game (t = 1)||The games have starting (t0) and ending (t) periods, or are even infinite|
|Types of games||Cooperative and non-cooperative||Cooperative and non-cooperative over open- and closed-loop frameworks|
|Mathematical computations required||System of first-order conditions||System of ordinary (partial) differential equations in open (closed)-loop games|
|Equilibrium||Best response function||Optimal control variable|
|General objective||Player payoff maximization according to the best response function||Player payoff maximization according to the optimal control variable and the optimal trajectory of the state variables|
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De Giovanni, P. Digital Supply Chain through Dynamic Inventory and Smart Contracts. Mathematics 2019, 7, 1235. https://doi.org/10.3390/math7121235
De Giovanni P. Digital Supply Chain through Dynamic Inventory and Smart Contracts. Mathematics. 2019; 7(12):1235. https://doi.org/10.3390/math7121235Chicago/Turabian Style
De Giovanni, Pietro. 2019. "Digital Supply Chain through Dynamic Inventory and Smart Contracts" Mathematics 7, no. 12: 1235. https://doi.org/10.3390/math7121235