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 firms 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.

1. OpsAI Inc. is another firm that does work very similar to that of MLO, but in a different geographical region (so they do not compete directly). Both firms are organized along similar lines with teams of two consultants working on each project, comparable project work times (same mean and standard deviation of work time per project), and the same approach for quoting promise time. OpsAI is a somewhat smaller operation than MLO; on average, it receives a project request from a client once every 6 business days, with a coefficient of variation of 1. It charges clients the same rate as MLO.

The CEO of OpsAI is customer-oriented. In particular, he wants to ensure that the promise time does not exceed 14 weeks. What is the minimum number of consultants OpsAI needs to employ to meet this norm?

2. Consulting firms closely monitor their cost-efficiency which is the total monthly salaries for consultants expressed as a % of the firms total monthly revenue. What is the cost-efficiency of MLO (with its proposed 90% billable target)? Of Ops AI?

Compare the customer responsiveness and cost-efficiency of the two firms, and comment on the factors that underlie the differences. Are there strategies that either firm can adopt to maintain good cost-efficiency (low values preferred) while also ensuring good customer responsiveness? Explain.

3. 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 others markets (i.e., the total demand for the consolidated firms services will not diminish) and their client requests are independent. OMAxs new CEO wants to ensure that its promise times conform to OpsAIs 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: Create 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).

Which option do you recommend: Option 1 or Option 2?

Show all your calculations to justify your recommendation. Summarize the rationale for your recommendation and give intuitive (managerial) explanations of the factors underlying your results