A high-volume call center must determine how many customer service representatives (CSRs) to schedule each day of the week to cover the call volume. CSRs work a five-day week with two days off but can start their week on any day. For example, CSRs who start their week on Wednesday work Wednesday through Sunday with Monday and Tuesday off. Average call volumes (in units of CSRs) are given in the following table (actual call volume is normally distributed, with a standard deviation given by 10 percent of the mean.)

The regular daily wage for a CSR is $400. However, if on a given day volume is such that the regular staff is inadequate, the call center will bring in extra CSRs for all or part of a day. The wage for this emergency work is equivalent to $800 per day. (In other words, if 0.5 CSR units of work are needed on an emergency basis, the cost is $400.)

a. If the call center’s objective is to minimize the total cost, including emergency staffing cost, what is the optimal number of CSRs to hire each day and what is the resulting cost?
b. How much emergency staffing will be required under the optimal plan?
c. How would the staffing plan and the minimum cost change if overtime costs were either $600 or $1,000? 

d. Working on weekends is unpopular, which leads to higher than normal absenteeism on Saturdays and Sundays. Would it be advantageous for the call center to pay a $100 bonus (a daily wage of $500) for work on Saturdays and Sundays?A

Transcribed Image Text:

Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday Call volume 22 45 37 33 34 40 29