You are a planner at a small distribution warehouse. Historically, the warehouse has targeted fulfilling 10 orders per hour for planning purposes. However, as the diversity of products has expanded, as well as the size of orders, this target has proven to be unreliable, as the orders are continually behind schedule and customers are complaining about late deliveries. Your supervisor has tasked you with determining a better target so that the warehouse may provide better delivery estimates to customers for their orders. Over the past week you gathered data for the number of orders fulfilled each day. This data is shown in the following table. Day Monday Tuesday Wednesday Thursday Friday Orders 88 64 72 56 80 A. Assuming 8 hours of operations each day, what is the mean and standard deviation for orders fulfilled per hour? The following table may help with these calculations. N is the total number of observations (days in sample) and Ȳ is the mean orders per hour over the last week. Interpret the results. What could the new target be for the orders per hour based on these results? Observation (Day) Orders per hour (Y) (Ȳ-Y)^2 1 (Monday) 11 4 2 (Tuesday) 8 1 3 (Wednesday) 4 (Thursday) 5 (Friday) Total Mean (Ȳ)= ∑y/N= ? Standard Deviation= ?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section: Chapter Questions

Problem 59P

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Can you do the calculations in Excel file showing all the work?

You are a planner at a small distribution warehouse. Historically, the warehouse has targeted fulfilling 10 orders per hour for planning purposes. However, as the diversity of products has expanded, as well as the size of orders, this target has proven to be unreliable, as the orders are continually behind schedule and customers are complaining about late deliveries. Your supervisor has tasked you with determining a better target so that the warehouse may provide better delivery estimates to customers for their orders. Over the past week you gathered data for the number of orders fulfilled each day. This data is shown in the following table.

Day	Monday	Tuesday	Wednesday	Thursday	Friday
Orders	88	64	72	56	80

A. Assuming 8 hours of operations each day, what is the mean and standard deviation for orders fulfilled per hour? The following table may help with these calculations. N is the total number of observations (days in sample) and Ȳ is the mean orders per hour over the last week. Interpret the results. What could the new target be for the orders per hour based on these results?

Observation (Day)	Orders per hour (Y)	(Ȳ-Y)^2
1 (Monday)	11	4
2 (Tuesday)	8	1
3 (Wednesday)
4 (Thursday)
5 (Friday)
Total

Mean (Ȳ)= ∑y/N= ?

Standard Deviation= ?

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Thanks.

I have the below follow up question.

Although you found a new representative target for orders fulfilled per hour based on the mean over the last week, you feel that you can develop a better daily target by considering the average number of line items in each order. However, you first need to determine if there is a correlation between orders fulfilled per hour and line items per order. Use the following data and table to calculate the correlation coefficient and interpret the result.

Day
Line items
Obs.
1
2
3
4
5
Total
Monday
1056
Line items per order (X)
12
20
Correlation Coefficient
=
Wednesday
1008
Tuesday
1280
Orders per hour (Y)
11
8
X²
144
400
N (ΣΧΥ) - (Σ Χ)(ΣΥ)
[N Σ X2 – (Σ X)2][Ν ΣΥ2 – (ΣΥ)2]
Thursday
1008
y²
121
64
Friday
1200
XY
132
160

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