Given the following data on inputs and outputs at a work center, determine the cumulative deviation and the backlog for each time period. The beginning backlog is 7. (Negative amounts should be indicated by a minus sign.) Input Period 123456Planned200200180190190200Actual210200179195193194 Output Period 123456Planned200200180190190200Actual205194177195193200 123456InputCumulative Deviation OutputCumulative Deviation Backlog7

Answered: Given the following data on inputs and…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section4.8: Data Envelopment Analysis (dea)

Problem 43P

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Question

Given the following data on inputs and outputs at a work center, determine the cumulative deviation and the backlog for each time period. The beginning backlog is 7. (Negative amounts should be indicated by a minus sign.)

Input

	Period
	1	2	3	4	5	6
Planned	200	200	180	190	190	200
Actual	210	200	179	195	193	194

Output

	Period
	1	2	3	4	5	6
Planned	200	200	180	190	190	200
Actual	205	194	177	195	193	200

		1	2	3	4	5	6
Input	Cumulative Deviation
Output	Cumulative Deviation
Backlog	7

Expert Solution

Step 1

Calculate Deviation and cumulative deviation for both Input and Output.

Deviation is difference between Actual and Planned. For the primary period, deviation is calculated by subtracting 210 from 200. Thus, deviation is +10. Similarly, calculate for the remainder of the periods.

Cumulative deviation is addition useful to the previous deviation value. For the primary period, cumulative deviation is same value of the deviation. For the playing period , second deviation value is either added or subtracted to the primary period deviation value. Similarly, calculate for the remainder of the periods.

Input	1	2	3	4	5	6
Planned	200	200	180	190	190	200
Actual	210	200	179	195	193	194
Deviation	+10	0	-1	+5	+3	-6
Cum. Dev.	+10	+10	+9	+14	+17	+11

Output	1	2	3	4	5	6
Planned	200	200	180	190	190	200
Actual	205	194	177	195	193	200
Deviation	+5	-6	-3	+5	+3	0
Cum. Dev.	+5	-1	-4	+1	+4	+4

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