<p>Edge computing enables service providers to deploy service instances on edge servers, thereby delivering low-latency services to nearby users. Under budget constraints, the effectiveness of a service placement scheme is primarily determined by two key metrics: user coverage and service takeover capability, referred to as coverage and robustness. Existing studies either focus on single-objective optimization or attempt to jointly optimize coverage and robustness. However, due to the magnitude difference between these two benefits, achieving a well-balanced joint optimization remains challenging. To address this issue, this paper formulates the Coverage-Robustness Joint Optimization Problem for K-budget Edge Service Placement (CR-KESP) and proves it to be NP-hard. Building upon this, a Weighted Tchebycheff-based Coverage-Robustness Benefit model (WT-CRB) is introduced. By mitigating the magnitude difference between coverage benefit and robustness benefit, this model unifies the two into a single joint benefit metric, thereby enabling a more interpretable and comprehensive assessment of joint optimization outcomes. Guided by the WT-CRB model, a greedy approximation algorithm, termed ESP-KCR, is developed to maximize the joint benefit of coverage and robustness. Experimental results on a real-world dataset demonstrate that, compared with five representative baseline approaches, the ESP-KCR approach consistently achieves superior performance in terms of coverage, robustness, and their combined benefit. In addition, the approach exhibits strong adaptability across diverse deployment scenarios, validating its effectiveness and feasibility in solving the CR-KESP problem. This study provides an effective modeling and solution framework for coverage–robustness joint optimization in edge service placement, offering valuable insights for both future research and practical implementations.</p>