Part 1 Machine Learning for Operations Inc. (MLO) is a consulting firm that develops customized machine learning software to support operational decisions (e.g., for forecasting, procurement, scheduling, etc.). On average, MLO receives 1.6 new project requests per week. These arrivals follow a Poisson process. On each project, the firm's consultants work jointly in teams of two - a domain expert and a modeler. The same two individuals work as a team throughout the year. On average, each project requires one team working, on average, for 50 business days (from the time the consultants begin working on the project to handing over the results to the client). Historical data reveals that the standard deviation of project work time is 45 business days. MLO assigns projects in first-come-first-served order to the first available consultant team. Each team works on at most one project at a time. MLO currently employs 36 consultants, working as 18 teams. The firm pays each consultant $ 12,000 per month in salary and benefits, whether or not they are working on a project. On average, MLO charges $ 150,000 per project, based on its consulting rate of $ 3,000 per day of work on the project. Assume that each week consists of five business days, every month has four working weeks, and consultants work for all 12 months in a year.

(e) MLO and OpsAI are discussing the possibility of merging. The merged company, to be called OMAnalytix Inc. (OMAx), will benefit from lower overhead and management costs by consolidating some functions (e.g., accounting, legal, and marketing) and dismissing some top executives. The boards of both companies recognize that the firms do not cannibalize each other's markets (i.e., the total demand for the consolidated firm's services will not diminish) and their client requests are independent. OMAx's new CEO wants to ensure that its promise times conform to OpsAI's norm of 14 weeks or less. Of course, she would also like to see as high Billable % as possible. For the execution of consulting projects by the merged company, OMAx is considering two options:

Option 1: Designate MLO and OpsAI as two separate divisions, with each division managing its own consultant teams, directly receiving requests from their current clients, and assigning their own teams to work on these projects (i.e., status quo); or

Option 2: you are required to develop a central department that receives requests from all (MLO & OpsAI) clients, and assign each request to any team (from either original firm). In this case, although the consultants from both firms are well-qualified to handle all projects, OMAx will incur additional "integration" costs, for training, coordination, and travel, of around $ 600,000 per year to standardize the systems and deliverables. You are asked to recommend which among these two options OMAx should select and why. The firm is willing to consider hiring or laying off some consultants under either option to meet its promise time goals (i.e., no more than 14 weeks). OMAx seeks to minimize the total annual cost of consultants and integration (if applicable).