Logistics Assignment 10

Problem 1 on page 397 The Barberton Municipal Division of Road Maintenance is charged with road repair in the city of Barberton and the surrounding area. Cindy Kramer, road maintenance director, must submit a staffing plan for the next year based on a set schedule for repairs and on the city budget. Kramer estimates that the labor hours required for the next four quarters are 6,000, 12,000, 19,000, and 9,000, respectively. Each of the 11 workers on the workforce can contribute 500 hours per quarter. Payroll costs are $6,000 in wages per worker for regular time worked up to 500 hours, with an overtime pay rate of $18 for each overtime hour. Overtime is limited to 20 percent of the regular-time capacity in any quarter. Although unused overtime capacity has no cost, unused regular time is paid at $12 per hour. The cost of hiring a worker is $3,000, and the cost of laying off a worker is $2,000. Subcontracting is not permitted. a. Find a level staffing plan that relies just on overtime and the minimum amount of undertime possible. Overtime can be used to its limits in any quarter. What is the total cost of the plan and how many undertime hours does it call for? To find a level staffing plan that relies just on overtime and the minimum amount of undertime possible while using overtime to its limits, let's first outline the given data and constraints: Quarterly Labor Hour Requirements: 6,000, 12,000, 19,000, and 9,000 hours. Workforce: Each of the 11 workers can contribute 500 hours per quarter. Overtime Limit: Overtime is limited to 20% of the regular-time capacity per worker, per quarter. This means each worker can work an additional 100 hours (20% of 500) as overtime each quarter. Costs: Regular Pay: $6,000 per worker for up to 500 hours. Overtime Pay: $18 per hour. Undertime Pay: $12 per hour for unused regular hours. Hiring Cost: $3,000 per worker. Layoff Cost: $2,000 per worker. Since subcontracting is not permitted and we're looking for a level staffing plan that only relies on the existing workforce and overtime, we will not consider hiring or layoffs in our calculations. To calculate: - The total regular and overtime hours available per quarter. - The total overtime and undertime required. - The total cost of the plan considering regular pay, overtime pay, and undertime pay. Step 1: Total Available Hours Per Quarter Total Regular Hours = Number of Workers * Hours per Worker = 11 * 500 Total Overtime Hours = Number of Workers * Overtime Hours per Worker = 11 * 100

Step 2: Calculate Overtime and Undertime Needed For each quarter, we need to calculate if the labor hours required exceed the total available regular hours and by how much, to determine overtime. If less, calculate undertime. Step 3: Total Cost Calculation - Regular Pay = Number of Workers * Regular Pay Rate - Overtime Pay = Total Overtime Hours * Overtime Pay Rate - Undertime Pay = Total Undertime Hours * Undertime Pay Rate - Total Cost = Regular Pay + Overtime Pay + Undertime Pay Let's perform these calculations now. The level staffing plan that relies just on overtime and the minimum amount of undertime possible results in the following: - Total Overtime Hours Needed: 3,800 hours - Total Undertime Hours: 0 hours (since we're utilizing all available regular hours efficiently) - Total Cost of the Plan: $332,400 This plan utilizes the maximum allowable overtime to meet the labor hours required for each quarter, ensuring no undertime is needed. b. Use a chase strategy that varies the workforce level without using overtime or undertime. What is the total cost of this plan? Step 1: Required Number of Workers per Quarter Calculate the number of workers needed for each quarter to meet the labor hours required without overtime or undertime. The required number of workers is the labor hours required divided by the regular hours each worker can contribute. Step 2: Workforce Adjustments For each quarter, calculate the difference in the workforce required from the previous quarter to determine the number of hires or layoffs needed. Step 3: Total Cost Calculation Regular Pay: Calculated for each quarter based on the current workforce. Hiring Costs: Number of Hires * Hiring Cost per Worker Layoff Costs: Number of Layoffs * Layoff Cost per Worker Total Cost: Sum of Regular Pay, Hiring Costs, and Layoff Costs for all quarters. Let's proceed with these calculations. Using a chase strategy that varies the workforce level without using overtime or undertime, we find the following:

The company currently has 10 associates. No more than 10 new hires can be accommodated in any month because of limited training facilities. No backorders are allowed, and overtime cannot exceed 25 percent of regular-time capacity on any month. There is no cost for unused overtime capacity. Regular-time wages are $1,500 per month, and overtime wages are 150 percent of regular-time wages. Undertime is paid at the same rate as regular time. The hiring cost is $2,500 per person, and the layoff cost is $2.000 per person. a. Prepare a staffing plan utilizing a level workforce strategy, minimizing undertime. The plan may call for a one-time adjustment of the workforce before month 1. Level workforce strategy minimizes undertime by maintaining a constant level of staff throughout the year. This may result in overstaffing during low periods but avoids the cost of hiring and layoffs. Here’s a level workforce plan for Tax Prep Advisers: Staffing Level: Since the highest demand is 20 associates in months 5, 6, and 7, the company needs to staff at least 20 associates throughout the year Hiring: In month 1, the company needs to hire 10 additional associates (20 - 10 = 10) Cost: The cost of hiring 10 associates is $25,000 ($2,500 x 10) Overtime: No overtime would be required under this plan Advantages: Minimizes undertime and ensures all clients are served on time Provides stability and continuity in staffing Disadvantages: Higher costs due to overstaffing during low periods (months 1, 2, 3, 4, 8, 9, 10, 11, and 12) May lead to underutilization of staff during low points in the demand cycle b. Using a chase strategy, prepare a plan that is consistent with the constraint on hiring and minimizes use of overtime. A chase strategy matches staffing levels closely with demand, adjusting as needed. This often involves hiring and layoffs (within constraints). Here's how to create a chase strategy plan for Tax Prep Advisors:

Staffing Plan Month Required Associates Current Associates Hires Layoffs Overtime Hours 1 12 10 2 0 0 2 14 12 2 0 0 3 16 14 2 0 0 4 18 16 2 0 0 5 20 18 2 0 0 6 20 20 0 0 0 7 20 20 0 0 0 8 18 20 0 2 0 9 16 18 0 2 0 10 14 16 0 2 0 11 12 14 0 2 0 12 10 12 0 2 0 Overtime Calculation: Overtime is needed only when the current workforce cannot meet the demand within the 25% overtime capacity limit. Assumptions: Associates can work up to 25% overtime upon their regular work time (we'll need to calculate the number of hours this represents, see below). Hiring constraint (max 10 per month) is already considered in the table Costs Calculation: Hiring: $2,500 x 8 hires = $20,000 Layoff: $2,000 x 8 layoffs = $16,000 Overtime: (This requires more calculation, covered in detail below) Overtime Cost Calculation Let's assume a standard 40-hour workweek: Regular Time Capacity: 10 associates * 40 hours/week = 400 hours/week Overtime Capacity: 400 hours * 0.25 = 100 hours/week Overtime Pay: $1,500/month * 1.5 = $2,250/month Limitations of this plan:

Potential disadvantages of a mixed strategy: Overtime: Still likely to incur some overtime costs, depending on the severity of peaks in demand. Complexity: Balancing hiring, laying off, and possible overtime requires more careful management. To fully evaluate this plan, we'd need to calculate overtime costs and compare the total expense (hiring, layoff, overtime) across these three strategies (level, chase, mixed). d. Contrast these three plans on the basis of annual costs. Estimated Overtime Calculations Chase Strategy: No overtime appears necessary based on the staffing plan we created earlier. Let's assume, for the sake of being conservative, that there are an additional 20 hours of overtime across the entire year due to unforeseen circumstances. Overtime Cost: 20 hours * ($2,250 / 160 regular hours) * 12 months = $3,375 Mixed Strategy: Similarly, the mixed strategy plan doesn't show a need for overtime. Let's conservatively assume an additional 20 hours of overtime are incurred over the year. Overtime Cost: 20 hours * ($2,250 / 160 regular hours) * 12 months = $3,375 Cost Comparison Table Plan Hiring Cost Layoff Cost Overtime Cost* Total Cost Level $25,000 $0 $0 $25,000 Chase $20,000 $16,000 $3,375 $39,375 Mixed $20,000 $16,000 $3,375 $39,375 Analysis Lowest Cost: The level workforce strategy has the lowest annual cost. Chase and Mixed: The chase and mixed strategies have the same total cost in this scenario. This is likely due to our conservative overtime estimates. In situations with higher demand fluctuations, the overtime would likely be more substantial for the chase plan. Considerations Beyond Cost While the level strategy is the most cost-effective here, it's important to consider other factors: Customer Service: The level strategy ensures everyone is served promptly. If delays have extremely high costs (loss of clients, etc.), it could be worth the extra cost of the other strategies. Morale: Frequent hiring/layoffs in the chase strategy can be detrimental to team morale.

Flexibility: If demand forecasts are uncertain, the mixed or chase strategies offer more flexibility for adjustments. Recommendation Based purely on cost, the level strategy is ideal. However, the company should carefully weigh the impact of customer service, morale, and demand uncertainty factors before making the final decision. Problem 14 on page 402-3 14. Cara Ryder manages a ski school in a large resort and is trying to develop a schedule for instructors. The instructors receive little salary and work just enough to earn room and board. They receive free skiing and spend most of their free time tackling the resort’s notorious double black-diamond slopes. Hence, the instructors work only 4 days a week. One of the lesson packages offered at the resort is a 4-day beginner package. Ryder likes to keep the same instructor with a group over the 4-day period, so she schedules the instructors for 4 consecutive days and then 3 days off. Ryder uses years of experience with demand forecasts provided by management to formulate her instructor requirements for the upcoming month. Day M T W Th F Sa Su Requirements 7 5 4 5 6 9 8 a. Determine how many instructors Ryder needs to employ. Give preference to Saturday and Sunday off. (Hint: Look for the group of 3 days with the lowest requirements.) To figure out the minimum number instructors Cara needs, let's follow a step-by-step approach: 1. Identify Lowest 3-Day Requirement: ● Look for consecutive groups of 3 days and find the one with the lowest total instructor requirement. ● We see that Tuesday, Wednesday, and Thursday form a group with the lowest demand (5 + 4 + 5 = 14 instructors). 2. Find the Greatest Instructor Need Among These 3 Days: ● In this group (Tue, Wed, Thu) the highest demand is on Tuesday (7 instructors).

Tuesday 0 Wednesday 0 Thursday 0 Friday 0 Saturday 9 Sunday 8 The schedule assigns instructors to work 4 consecutive days followed by 3 days off. This way, each instructor gets their weekend days off as much as possible. The slack column shows how many extra instructors are available on each day. For example, on Tuesday (the busiest day), all 7 instructors are assigned to work, resulting in no slack. On Saturday, however, there is a slack of 9, meaning 9 more instructors could be assigned to work on that day if needed.