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					                                             10.1


Excersise 10-1: Harley Davidson

Harley Davidson has its engine assembly plant in Milwaukee and its motorcycle assembly
plant in Pennsylvania. Engines are transported between the two plants using trucks. Each
truck trip costs $1,000. The motorcycle plant assembles and sells 300 motorcycles each
day. Each engine costs $500 and Harley incurs a holding cost of 20 percent per year. How
many engines should Harley load onto each truck? What is the cycle inventory of engines at
Harley?

Input
Demand, R =                                              109,500 (assuming 365 operating days)
Fixed cost per order, S =                    $             1,000
Cost per engine, C =                         $               500
Holding cost, h =                                            20%

Output
EOQ =                                                      1,480
# of orders per year                                          74
Annual Order Cost                            $            73,993
Cycle inventory (units)                                      740
Cycle inventory (value)                                  369,966
Annual Holding Cost                          $            73,993
Total Inventory Cost                         $           147,986

Order Size Increment =                                          20

        Order                Annual                                   Total
        Size                Order Cost           Holding Cost          Cost
         300                 $365,000              $15,000           $380,000
         320                 $342,188              $16,000           $358,188
         340                 $322,059              $17,000           $339,059
         360                 $304,167              $18,000           $322,167
         380                 $288,158              $19,000           $307,158
         400                 $273,750              $20,000           $293,750
         420                 $260,714              $21,000           $281,714
         440                 $248,864              $22,000           $270,864
         460                 $238,043              $23,000           $261,043
         480                 $228,125              $24,000           $252,125
         500                 $219,000              $25,000           $244,000
         520                 $210,577              $26,000           $236,577
         540                 $202,778              $27,000           $229,778
         560                 $195,536              $28,000           $223,536
         580                 $188,793              $29,000           $217,793
         600                 $182,500              $30,000           $212,500
         620                 $176,613              $31,000           $207,613
         640                 $171,094              $32,000           $203,094
         660                 $165,909              $33,000           $198,909
         680                 $161,029              $34,000           $195,029
         700                 $156,429              $35,000           $191,429
         720                 $152,083              $36,000           $188,083
         740                 $147,973              $37,000           $184,973
         760                 $144,079              $38,000           $182,079




                                            Page 1
                   10.1


 780   $140,385            $39,000   $179,385
 800   $136,875            $40,000   $176,875
 820   $133,537            $41,000   $174,537
 840   $130,357            $42,000   $172,357
 860   $127,326            $43,000   $170,326
 880   $124,432            $44,000   $168,432
 900   $121,667            $45,000   $166,667
 920   $119,022            $46,000   $165,022
 940   $116,489            $47,000   $163,489
 960   $114,063            $48,000   $162,063
 980   $111,735            $49,000   $160,735
1000   $109,500            $50,000   $159,500
1020   $107,353            $51,000   $158,353
1040   $105,288            $52,000   $157,288
1060   $103,302            $53,000   $156,302
1080   $101,389            $54,000   $155,389
1100    $99,545            $55,000   $154,545
1120    $97,768            $56,000   $153,768
1140    $96,053            $57,000   $153,053
1160    $94,397            $58,000   $152,397
1180    $92,797            $59,000   $151,797
1200    $91,250            $60,000   $151,250
1220    $89,754            $61,000   $150,754
1240    $88,306            $62,000   $150,306
1260    $86,905            $63,000   $149,905
1280    $85,547            $64,000   $149,547
1300    $84,231            $65,000   $149,231
1320    $82,955            $66,000   $148,955
1340    $81,716            $67,000   $148,716
1360    $80,515            $68,000   $148,515
1380    $79,348            $69,000   $148,348
1400    $78,214            $70,000   $148,214
1420    $77,113            $71,000   $148,113
1440    $76,042            $72,000   $148,042
1460    $75,000            $73,000   $148,000
1480    $73,986            $74,000   $147,986
1500    $73,000            $75,000   $148,000
1520    $72,039            $76,000   $148,039
1540    $71,104            $77,000   $148,104
1560    $70,192            $78,000   $148,192
1580    $69,304            $79,000   $148,304
1600    $68,438            $80,000   $148,438
1620    $67,593            $81,000   $148,593
1640    $66,768            $82,000   $148,768
1660    $65,964            $83,000   $148,964
1680    $65,179            $84,000   $149,179
1700    $64,412            $85,000   $149,412
1720    $63,663            $86,000   $149,663
1740    $62,931            $87,000   $149,931
1760    $62,216            $88,000   $150,216
1780    $61,517            $89,000   $150,517
1800    $60,833            $90,000   $150,833




                  Page 2
                  10.1


1820   $60,165            $91,000   $151,165
1840   $59,511            $92,000   $151,511
1860   $58,871            $93,000   $151,871
1880   $58,245            $94,000   $152,245
1900   $57,632            $95,000   $152,632
1920   $57,031            $96,000   $153,031
1940   $56,443            $97,000   $153,443
1960   $55,867            $98,000   $153,867
1980   $55,303            $99,000   $154,303




                 Page 3
                             10.1




using trucks. Each

cent per year. How
entory of engines at



uming 365 operating days)




                            Page 4
Excersise 10-2: Harley Davidson

Harley has decided to implement Just In Time (JIT) at the motorcycle assembly plant. As
part of this initiative it has reduced the number of engines loaded on each truck to 100. If
each truck trip still costs $1,000, how does this decision impact annual costs at Harley?
What should the cost of each truck be if a load of 100 engines is to be optimal for Harley?



Part I

Inputs
Demand, R =                                                  109,500 (assuming 365 operating days)
Fixed cost per order, S =                      $               1,000
Cost per engine, C =                           $                 500
Holding cost, h =                                                20%
Order quantity                                                   100

Outputs
# of orders per year                                           1,095
Annual Order Cost                                          1,095,000
Cycle inventory (units)                                           50
Annual Holding Cost                            $               5,000
Total Inventory Cost                           $           1,100,000


Part II

Inputs
Demand, R =                                                  109,500 (assuming 365 operating days)
Fixed cost per order, S =                      $               1,000
Cost per engine, C =                           $                 500
Holding cost, h =                                                20%
EOQ                                                              100

Outputs
Fixed cost per order, S =                      $                 4.57

# of orders per year                                           1,095
Annual Order Cost                                              5,000
Cycle inventory (units)                                           50
Annual Holding Cost                            $               5,000
Total Inventory Cost                           $              10,000




CR - 4/27/2013 11:12 PM                            Page 5 cd6268fb-fee2-4091-9cfd-b4f4018d26ee.xls - 10.2
Excersise 11-1: Best Buy

Weekly demand for Motorola cell phones at a Best Buy store is normally distributed with a mean of 300
and a standard deviation of 200. Motorola takes two weeks to supply a Best Buy order. Best Buy is
targeting a cycle service level of 95 percent and monitors its inventory continuously. How much safety
inventory of cell phones should Best Buy carry? What should their reorder point be?




Inputs
Average demand per unit time R =                                                                    300
Lead time, L =                                                                                        2
SD of demand per unit time sR =                                                                     200
Target cycle service level                                                                         0.95

Distribution of demand during lead time
Mean demand during lead time R L =                                                                  600
SD of demand during lead time sL =                                                                  283

Output
Safety Inventory ss =                                                                               465
Reorder point R =                                                                                  1065

Reorder Point Increment =                                                                               10

Cycle Service Level & Inventory
Reorder                         Safety                                         Cycle Service
Point ROP                       Inventory ss                                    Level (CSL )
              600                                 0                               0.5000
              610                                10                               0.5141
              620                                20                               0.5282
              630                                30                               0.5422
              640                                40                               0.5562
              650                                50                               0.5702
              660                                60                               0.5840
              670                                70                               0.5977
              680                                80                               0.6114
              690                                90                               0.6248
              700                                100                              0.6382
              710                                110                              0.6513
              720                                120                              0.6643
              730                                130                              0.6771
              740                                140                              0.6897
              750                                150                              0.7021
              760                                160                              0.7142
              770                                170                              0.7261
              780                                180                              0.7377
              790                                190                              0.7491
              800                                200                              0.7602
              810                                210                              0.7711
              820                                220                              0.7817
              830                                230                              0.7919
              840                                240                              0.8019
              850                                250                              0.8116
              860                                260                              0.8210
              870                                270                              0.8301
              880                                280                              0.8389
              890                                290                              0.8474
              900                                300                              0.8556
              910                                310                              0.8635
              920                                320                              0.8711
              930                                330                              0.8783
              940                                340                              0.8853
              950                                350                              0.8920
              960                                360                              0.8985
              970                                370                              0.9046
              980                                380                              0.9104
              990                                390                              0.9160
             1000                                400                              0.9214
             1010                                410                              0.9264
             1020                                420                              0.9312
             1030                                430                              0.9358
             1040                                440                              0.9401
             1050                                450                              0.9442
             1060                                460                              0.9481
             1070                                470                              0.9517
             1080                                480                              0.9552
             1090                                490                              0.9584
             1100                                500                              0.9615
             1110                                510                              0.9643
             1120                                520                              0.9670
             1130                                530                              0.9695
             1140                                540                              0.9719
             1150                                550                              0.9741
             1160                                560                              0.9761
             1170                                570                              0.9781
             1180                                580                              0.9798
             1190                                590                              0.9815
             1200                                600                              0.9831
             1210                                610                              0.9845
             1220                                620                              0.9858
             1230                                630                              0.9870
             1240                                640                              0.9882
             1250                                650                              0.9892
             1260                                660                              0.9902




CR - 4/27/2013 11:12 PM                                                                        Page 6        cd6268fb-fee2-4091-9cfd-b4f4018d26ee.xls - 11.1
Excersise 11-2: Best Buy

Reconsider the Best Buy store in problem 1. The store manager has decided to follow a periodic review
policy to manage inventory of cell phones. They plan to order every three weeks. Given a desired cycle
service level of 95 percent, how much safety inventory should the store carry? What should their order
up to level be?….




Inputs
Average demand per unit time R =                                                                  300
Lead time, L =                                                                                      2
SD of demand per unit time sR =                                                                   200
Review Interval T =                                                                                 3
Target cycle service level                                                                       0.95

Distribution of demand during T + L
Mean demand during T+L, (T+L)R =                                                                1500
SD of demand during T+L, sT+L =                                                                  447

Outputs
Safety Inventory ss =                                                                             736
Order up to level OUL =                                                                          2236




CR - 4/27/2013 11:12 PM                                Page 7         cd6268fb-fee2-4091-9cfd-b4f4018d26ee.xls - 11.2
Excersise 11-3: Best Buy

Assume that the Best Buy store has a policy of ordering cell phones from Motorola in lots of 500.
Weekly demand for Motorola cell phones at the store is normally distributed with a mean of 300 and a
standard deviation of 200. Motorola takes two weeks to supply an order. If the store manager is
targeting a fill rate of 99 percent, what safety inventory should they carry? What should their reorder
point be?




Inputs
Average demand per unit time R =                                                      300
Lead time, L =                                                                         2
SD of demand per unit time sR =                                                       200
Lot size, Q=                                                                          500
Target fill rate                                                                      0.99

Distribution of demand during L
Mean demand during lead time RL =                                                     600
SD of demand during lead time sL =                                                    283

Intermediate Calculations
Required expected shortage per replenishment cycle =                                5.0000

Outputs
Safety Inventory ss =                                                                 485
Reorder Point                                                                        1085
Expected shortage per replenishment cycle ESC =                                     5.0000




CR - 4/27/2013 11:12 PM                           Page 8   cd6268fb-fee2-4091-9cfd-b4f4018d26ee.xls - 11.3
Excersise 11-4: Hewlett Packard

Weekly demand for Hewlett Packard printers at a Sam's Club store is normally distributed with a mean
of 250 and a standard deviation of 150. The store manager continuously monitors inventory and
currently orders a thousand printers each time the inventory drops to 600 printers. Hewlett Packard
currently takes two weeks to fill an order. How much safety inventory does the store carry? What cycle
service level does Sam's Club achieve as a result of this policy? What fill rate does the store achieve?




Inputs
Average demand per unit time R =                                                      250
Lead time, L =                                                                         2
SD of demand per unit time sR =                                                       150
Order quantity Q=                                                                    1000
Reorder Point                                                                         600

Distribution of demand during replenishment lead time
Mean demand during lead time RL =                                                     500
SD of demand during lead time sL =                                                    212

Outputs
Safety Inventory ss =                                                                 100
Cycle Service Level CSL =                                                             0.68
Expected shortage per replenishment cycle ESC =                                      43.86
Fill Rate fr =                                                                        0.96




CR - 4/27/2013 11:12 PM                                 Page 9           cd6268fb-fee2-4091-9cfd-b4f4018d26ee.xls - 11.4

				
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