Staffing at a Distribution Center $(35$ points$)$

A large distribution center is open for business from $8$AM to $5$PM on Mondays through

Fridays. The center has several 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.

Hint: See Unit $4$A Practice Problem #$2$ & $3$

a$.$ State the decisions to be made, the objective and the constraints in words using $<=,>=$

or $=$ in the constraints. $($Submit copy of Handwritten answer, $5$ pts$)$

b$.$ 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? $($Submit copy of Handwritten answer, $5$ pts$)$

c$.$ 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. $($Submit copy of Handwritten answer, $5$ pts$)$

d$.$ Write your algebraic model from $($c$)$ as an EXCEL model. $($Submit answer in an Excel

file, $5$ pts$)$

e$.$ 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 in an Excel file, $5$ pts$)$

f$.$ 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? $($Submit copy of Handwritten answer, $5$ pts$)$

g$.$ In your optimized model, what hours of the day have surplus workers? What hour of the

day has the largest surplus? $($Submit copy of Handwritten answer, $5$ pts$)$

Note: If you are adventuresome, you could try to equalize the surplus by building an

optimization model to minimize the largest surplus.