With increasing aesthetic awareness and emphasis on time costs in today’s society, monolithic multilayer precolored zirconia ceramics (M-Zr) facilitate aesthetic restorations in a convenient and straightforward manner without the need for veneering porcelain to modify the color. However, the effect of abutment materials on the final color of M-Zr remains unclear. Herein, we placed Vita A1 Shade M-Zr on six different abutment materials, zirconia (Y-TZP), 3D printed composite resin (CR), dental model resin (MR), polyetheretherketone (PEEK), polyetherketoneketone (PEKK), and cobalt–chromium alloy (Co–Cr), to evaluate their effect on the color accuracy of M-Zr. The color attributes (L*, a*, and b*) were measured using a dental spectrophotometer. The translucency parameter (TP), contrast ratio, color difference (ΔE) between each background substrate and the Vita A1 Shade Guide, and chroma values (C) were calculated to evaluate the color accuracy of M-Zr. A statistical analysis was performed using one-way analysis of variance and post hoc Tukey’s HSD tests (α = 0.05). The experimental results indicate that the TP values and contrast ratio of the M-Zr samples were 14.85 and 0.83, respectively. Co–Cr had the highest ΔE (6.08) and lowest C value (7.52); PEKK had the lowest ΔE (2.60), and PEEK had the highest C value (12.23) (p < 0.05). Notably, the ΔE values of CR (3.13), PEEK (2.86), and PEKK were within clinical indicators (ΔE < 3.7). Based on these results, it can be concluded that the abutment material has a significant effect on the final color of the M-Zr, and PEEK or PEKK resulted in good color accuracy. When choosing the dental MR, traditional zirconia, or metals as abutment materials, colored or opaque cement might be required to eliminate color distortion and achieve desirable optical properties.

This study focuses on an enterprise that wants to expand its business to multiple cities in global and to be one of well-known multinational enterprises (MNEs). Suppose the enterprise utilizes the wholly owned market entry strategy, as well as the decentralized synchronized (market) advancement strategy (DSAS) to achieve the purpose. DSAS refers to expanding business by decentralizing the available amount of capital budget into each planning investment location and investing them concurrently. Consider the MNE hopes each planning investment subsidiary gleans a specific target return within a constant time horizon. Under DSAS, this paper proposes an optimization model to find the optimal allocation policy of capital investment, which minimize the time required to realize the MNE's concerned objective. Due to the nonlinear characteristics of the proposed models, a solution procedure developed upon the piecewise-linear approximation and fraction programming approaches is used for resolving the proposed model.