Staffing at a Distribution Center

A large distribution center is open for business from 8AM to 5PM on Mondays through Fridays. The center has a number of full-time workers. In addition, the manager of the center wants to increase the quality of customer service by adding some part-time workers. Based on her estimates, the minimum number of part-time workers needed varies hour-by-hour as summarized below.

Part-time workers will work 4-hour shifts.

State the decisions to be made, the objective and the constraints in words using = or = in the constraints. (Handwrite answer, 5 points)

Set each of your decisions in (a) equal to 10 and then compute the corresponding numerical values for your objective and constraints. Is this solution feasible and what is the corresponding value of the objective? (Handwrite answer, 5 points)

Define your decisions in part (a) algebraically as decision variables. Then, using your objective and constraints in part (a), formulate the problem as an algebraic linear optimization model. (Handwrite answer, 5 points)

Write your algebraic model from (c) as an EXCEL model. (Submit answer via Blackboard, 5 points)

Using your Excel model with a value of 10 for each decision cell, compute the values for the objectives and the constraints. Do you get the same values as in part (b)? (Submit answer via Blackboard, 5 points)

Using your EXCEL model and Solver, optimize the staffing. What is the minimum number of part-time workers required? What hours would you recommend that each part-time person works? (Handwrite answer, 5 points)

In your optimized model, what hours of the day have surplus workers? What hour of the day has the largest surplus? (Handwrite answer, 5 points)

Time | Minimum # required 8-9 9 10 10-11 11-12 12-1 1-2 2-3 3-4 4-5 5 12 15 12 18 17 19 14 Time | Minimum # required 8-9 9 10 10-11 11-12 12-1 1-2 2-3 3-4 4-5 5 12 15 12 18 17 19 14