SimQuick with Excel and Software CD Package, 2E David Hartvigsen Solution Manuals

Type:

Solution Manual

Resource:

SimQuick with Excel and Software CD Package

Edition:

2

Author(s):

David Hartvigsen

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Typical overall mean cycle times in Line 1 Teller 2 Tellers 3 Tellers

17.13 1.67 0.25

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Time between arrivals Exp(2) Exp(1.8) Exp(1.6) Exp(1.4) Exp(1.2)

Typical overall mean cycle times in Line 0.72 0.94 1.52 2.27 3.74

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Work Station Counter 1 Entrance Customers

Buffer Line

Work Station Counter 2 Work Station Counter 3

Buffer Served Customers

Typical numbers for 3 checkout lanes Overall mean # of customers in line 6.00 Overall mean waiting time 6.22

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Typical numbers for 4 checkout lanes Overall mean # of customers in line 0.78 Overall mean waiting time 0.77

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Typical numbers for 3 checkout lanes, part d Overall mean # of customers in line 2.09 Overall mean waiting time 2.05

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# CS people 1 2 3 4 5

Overall mean waiting time

Service level

79.14 27.33 5.04 1.11 0.21

0.47 0.82 0.99 1 1

We recommend 4 CS people because this is the smallest number that achieves the objectives of under 2 minutes of waiting and a service level of .99, on average.

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Typical numbers Overall mean throughput 63.53 Overall mean cycle time (sum of 5 numbers) 13.93 =Results!D31+Results!D38+2+2.2+Results!D13 Overall mean service level 0.84

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Typical numbers Overall mean throughput 67.63 Overall mean cycle time (sum of 5 numbers) 10.12 =Results!D31+Results!D38+2+2.2+Results!D13 Overall mean service level 0.91

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Typical numbers Overall mean service level

# of tellers 1 2 3

0.7 0.98 1

Overall mean cycle time 21.03 3.42 0.52

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Typical numbers Overall mean service level

# of tellers 2 3

0.89 1

Overall mean cycle time 6.39 0.93

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Typical numbers for overall mean cycle time % to Sec. Line 2 10 15 20

2 Work Stations 0.67 1.85 5.42

3 Work Stations 0.06 0.22 0.76

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Typical numbers for 1 license clerk Overall mean cycle time for lic. plus reg.

31.53 =Results!D39+Results!D46+Results!D53+1+5+6 Overall mean cycle time waiting for lic.

13.11 Overall mean cycle time waiting for reg.

6.27

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Typical numbers Overall mean cycle time for lic. plus reg.

22.01 Overall mean cycle time waiting for lic.

0.76 Overall mean cycle time waiting for reg.

9.09

The overall mean cycle time waiting for lic. drops significantly due to the new clerk.

Customers who are getting both lic. and reg. are now moving more quickly into the Reg. Line and hence its cycle time increases.

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Typical numbers Part a Overall mean fraction time working

Overall mean cycle time

Part c

Desk Ambulatory X-ray Lab

0.2 0.29 0.18 0.83

0.3 0.45 0.29 0.95

Desk Line Ambulatory Line X-ray Line Lab Line

0.33 2.74 1 47.29

0.59 5.8 2.46 118.96

Part b Overall mean fraction time working

Desk Ambulatory X-ray Lab 1 Lab 2

0.2 0.32 0.19 0.57 0.35

Overall mean cycle time

Desk Line Ambulatory Line X-ray Line Lab Line

0.33 3.65 1.29 3.16

Part a: Clearly the Lab is the bo

Part b: The performance of the greatly improved.

Part c: The performance of the worse.

a: Clearly the Lab is the bottleneck.

b: The performance of the Lab on both statistics has been atly improved. c: The performance of the Lab on both statistics is much

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Typical numbers Overall mean cycle time in the Inside Line 10.02 Overall mean cycle time for the whole drive-through process 9.37 Inside service level 0.99 Outside service level 0.91 Fraction time working of Pay/Pickup 0.56

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Typical numbers Overall mean cycle time in the Inside Line 1.71 Overall mean cycle time for the whole drive-through process 18.66 Inside service level 1.00 Outside service level 0.76 Fraction time working of Pay/Pickup 0.45 Mean number in use of CT Worker (i.e., fraction time working at Pay/Pickup + Cashier 3) 0.90

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Typical numbers Overall mean waiting time (in Line plus mean of two Decision Points) 30% 13.08 35% 12.15 40% 11.56

=Results!$D$47+(Results!$D$59+Results!$D$64)/2

esults!$D$59+Results!$D$64)/2

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Typical numbers Input storage cap.:

94

Output service level:

1.00

Mean cycle time:

16.23

Storage cap. Service level 70 0.86 74 0.9 78 0.94 82 0.97 86 0.98 90 0.99 94 1

Mean cycle time 10.67 11.44 12.31 12.61 14.55 15.45 16.23

We recommend setting the storage capacity at 90 since this is the smallest capacity that achieves the desired service level.

Note: The capacity of Storage is linked to the cell C5 above. Hence to run this model, it suffices to set the number in C5 above, hit Run Simulations, and then read the Service level and Mean cycle time above. Then numbers can then be copied and pasted (use "Paste Special/Values") into the table above.

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Typical numbers Input storage cap.:

54

Output service level:

1.00

Mean cycle time:

10.14

Storage cap. Service level Mean cycle time 34 0.81 5.26 38 0.87 6.1 42 0.96 6.88 46 0.98 7.73 50 1 9.35 54 1 10.14

We recommend setting the storage capacity at 50 since this is the smallest capacity that achieves the desired service level.

Note: The capacity of Storage is linked to the cell C5 above.

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Inputs

Results

Order size:

75

ROP:

25

Ordering cost:

100

Holding cost:

0.5

Order size

ROP

Service level

Outputs: 35 45 55 65 75

25 25 25 25 25

0.97 0.94 0.97 0.96 0.98 0.97

Yes, the new reorder point achieves the desired se .9 for each ROP. The second scenario is recommended since it has total cost.

As the order size increases, the ordering cost decre the holding cost increases.

Note: The "# of output objects" for Delivery and the "Output group size" for Factory are linked to cell C5 above; the "Capacity" and "Initial # objects" of Reorder Point are linked to cell C7 above. Thus to run the various scenarios you only need to update the values in cells C5 and C7 above and then read the solution from Outputs.

Mean number of orders

Total mean inventory

4.30 8.65 6.80 6.00 5.00 4.30

order point achieves the desired sevice level of

enario is recommended since it has the lowest

e increases, the ordering cost decreases and

39.09 18.86 24.13 28.06 33.40 39.09

Total cost 1602.59 1430.65 1403.82 1441.67 1501.87 1602.59

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Typical numbers Order size

Inputs

ROP

Service level

Outputs:

Order size:

200

ROP:

60

Ordering cost:

300

Holding cost:

0.25

0.98 80 120 160 200

50 50 50 50

0.93 0.94 0.95 0.97

80 120 160 200

60 60 60 60

0.97 0.97 0.97 0.98

The second scenario is recommended since it has the lowest total cost.

Note: The "# of output objects" for Delivery and the "Output group size" for Factory are linked to C7 above.

The "Capacity" and "Initial # objects" of Reorder Point is linked to C9 above.

Mean number of orders

Total mean inventory

6.17

123.11

13.80 9.60 7.45 6.15

53.19 72.47 92.33 113.58

13.95 9.90 7.75 6.17

62.26 80.65 99.99 123.11

Total cost 6799.46999 6503.40607 6851.55716 7523.97079 0 7297.7774 7002.48108 7324.49432 8005.47837

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Typical numbers Order size

Inputs

ROP

Service level

Outputs:

Order size:

240

ROP:

20

Ordering cost:

500

Holding cost:

0.25

0.96 80 120 160 200 240

20 20 20 20 20

0.87 0.93 0.91 0.95 0.96

We do not recommend switching delivery companies since the lowest cost scenario in this case has higher cost than the lowest cost scenario in part a.

Mean number of orders

hing delivery companies since is case has higher cost than the

Total mean inventory

Total cost

5.03

125.99

8816.19

12.40 9.15 7.35 6.05 5.03

42.81 65.29 82.78 105.22 125.99

8340.73 7839.51 7813.91 8285.86 8816.19

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Typical numbers Inputs

WH order size Outputs/Calculations:

Order size placed200 by ware.

Warehouse ROP 50 Order size placed by 50 store Store ROP 10 Warehouse order150 cost Warehouse holding 0.1cost Store order cost 75 Store holding cost0.5

100 100 100 200 200 200

WH ROP St order size St ROP Total cost $4,169.76 50 50 50 50 50 50

40 45 50 40 45 50

10 10 10 10 10 10

$4,058.56 $3,966.11 $4,376.75 $3,993.84 $3,907.36 $4,169.76

We recommend the 5th scenario since it has the lowest total cost.

Note: There are various links between this worksheet and the worksheets for Buffers and Work Stations, in both directions. To run the model, just set the Inputs above for the scenario under consideration, hit Run Simulations, read the outputs above, and then copy and paste (use "Paste Special/Values) into the table.

Service level Mean no. of ord. by ware.

Total mean no. of ord. by stores

0.98

3.98

12.65

0.96 0.96 0.97 0.97 0.97 0.98

6.90 6.60 7.10 3.90 3.70 3.98

15.30 13.60 12.60 15.20 13.70 12.65

Total mean inv. at ware.

Total mean inv. at stores

131.23

59.14

65.59 54.95 87.66 118.57 106.34 131.23

47.37 52.20 59.29 49.89 54.18 59.14

Total mean inv. enroute to Store 1

Total mean inv. enroute to Store 2

5.45

5.10

5.34 5.14 5.21 5.23 5.26 5.45

4.87 4.92 5.14 4.88 4.98 5.10

Total mean inv. enroute to stores 10.55 10.21 10.06 10.35 10.11 10.24 10.55

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Inventory cost per day $1

Inputs:

Ordering cost $150

Outputs:

Order size Base stock level Backlog cycle time 2 6 1.02 1 1 1 2 2 2 2

4 5 6 3 4 5 6

4.794147193 1.412474784 0.416593837 116.5624865 8.629051119 4.740246388 1.020325146

Mean inv.

2.68 1.174083386 2.088093888 3.06236406 0.140765483 0.856924845 1.50052542 2.679908664

Note: The # of output objects for the Replen. Work Stations and the Output group sizes for the Del. Obj. Buffer are linked to cell B8 above. Also, the Initial # objects for the Inv. Buffer is linked to cell C8 above.

The first row of Outputs above are linked to the Results worksheet.

The worksheet is used by inputting the Order size and Base stock level in the first row, running the simulations from the Control Panel, and then copying and pasting the Outputs (paste special / values) from the first row into the table.

# orders Inv. Cost 29.88 160.79 58.4 60.02 60.44 19.36 29.72 28.94 29.88

70.44500315 125.2856333 183.7418436 8.445928967 51.41549068 90.03152519 160.7945199

Solution: The scenario with an or a base stock level of 5 is the lowe that achieves management's goa cycle time of under 8 time units.

Ord. Cost Total cost 4482.00 4642.79 8760 9003 9066 2904 4458 4341 4482

8830.445003 9128.285633 9249.741844 2912.445929 4509.415491 4431.031525 4642.79452

Solution: The scenario with an order size of 2 and a base stock level of 5 is the lowest cost policy hat achieves management's goal of a backlog cycle time of under 8 time units.

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Ordering cost Holding cost (per day per pair)

$50 $0.05

Inputs:

Outputs:

40

Order sizes 60

20 20 40 40 40

60 60 60 60 60

Service Target level # orders 120 120 0.90 11.97 100 100 100 100 120

100 120 100 120 120

0.87 0.93 0.87 0.94 0.90

12.00 12.00 11.90 12.00 11.97

Note: The first row of the Inputs are referenced by the three Deliv.

Work Stations and the Buffers Shelf and Pur. Obj. The Outputs contains references to the Results worksheet. To use this worksheet, enter each scenario into the first row of the Inputs, run the simulations, and copy and paste (paste special / values) the Outputs into the table below.

Mean inventory Order cost Holding cost Total cost 35.80 $598.33 $161.11 $759.44 31.40 44.74 31.04 44.17 35.80

nced by the three Deliv. ur. Obj. The Outputs eet. To use this st row of the Inputs, run e special / values) the

$600.00 $600.00 $595.00 $600.00 $598.33

$141.30 $201.31 $139.69 $198.76 $161.11

$741.30 $801.31 $734.69 $798.76 $759.44

Scenarios 2, 5, and 6 achieve the .9 service level goal. Of these, scenario 6 has the lowest cost.

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Typical numbers Overall mean inventory B1 B2 2000 2.4 5000 4.49 10000 6.17

# time units

Overall mean max. inventory B1 B2 2.32 6.6 2.56 10.9 4.8 15.17

It appears that inventory levels, when unconstrained by space, grow as the length of production runs increases.

6.83 8.2 13

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Typical numbers, original machine Throughput 314.97

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Typical numbers, new machine Throughput 404.63

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Part a:

20 + 55 + 2 + 20 + 30 = 127

Typical numbers for Part b: Mean duration:

133.81

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Part a:

30 + 7 + 2 + 2 + 7 +2 + 3 = 53

Typical numbers for Part b: Mean duration:

55.89