Analyze a real$-$world case where an organization faced a significant dilemma and utilized management science methodologies to address it$.$ Detail the following aspects in your response:

Identification of the Dilemma: Describe the nature of the dilemma faced by the organization, including the key challenges and stakeholders involved.

Decision$-$Making Framework: Outline the specific management science techniques and decision$-$making frameworks employed by the organization. Include any relevant tools used.

Implementation Process: Detail the steps taken from the initial analysis to the final resolution. Discuss how the management science approach guided the decision$-$making process and led to a resolution.

Outcome and Evaluation: Evaluate the effectiveness of the chosen solution. Analyze the impact on the organization and discuss any limitations or unexpected outcomes of the decision$-$making process.