Annual demand, D = 109500Unit cost per engine, C = 500Order cost per lot, S = 1000Holding cost per year as a fraction of unit cost, h = 0.2

Optimal order size, Q = √(2DS/hC)= 1480

Cycle inventory = Q/2= 740

Number of orders per year = D/Q= 73.98649

Annual ordering and holding cost = DS/Q + QhC/2= 147986.5

Average flow time = Q/2D= 0.006758 year

Desired lot size, Q = 100Annual demand, D = 109500Unit cost per engine, C = 500Holding cost per year as a fraction of unit cost, h = 0.2Order cost per lot, S = 1000

Annual ordering and holding cost = DS/Q + QhC/2= 1100000

Change in inventory cost = 952013.5

Desired order cost, S = hCQ^2/2D= 4.56621

Current StrategyA B C

Demand per year, D 240000 30000 10800Fixed cost / order, S 500 500 500Unit cost, C 5 4 5Holding cost, h 0.2 0.2 0.2Optimal order size, Q 15492 6124 3287Cycle inventory 7746 3062 1643.5Annual holding cost 7746 2449.6 1643.5Order frequency, n 15.49 4.90 3.29Annual ordering cost 7745.93 2449.38 1642.84Average flow time / year 0.03 0.10 0.15Annual cost 15491.93 4898.98 3286.34Total cost 23677.25

Product ordered and delivered jointlyA B C

Demand per year, D 240000 30000 10800Order frequency, n 14.01 14.01 14.01Optimal order size, Q 17130.38 2141.297 770.8669Cycle inventory 8565.188 1070.648 385.4335Annual holding cost 8565.188 856.5188 385.4335Annual ordering cost 9807.14 0.00 0.00Average flow time / year 0.04 0.04 0.04Annual cost 18372.33 856.52 385.43Total cost 19614.28

Combined fixed order cost, S = 700Optimal order frequency, n = 14.0102

Lot sizes and costs for ordering using heuristicsA B C

Demand per year, D 240000 30000 10800Order frequency, n 14.37 10.16 6.82Optimal order size, Q 16698.08 2951.831 1584.119Cycle inventory 8349.04 1475.916 792.0594Annual holding cost 8349.04 1180.733 792.0594Annual ordering cost 8623.75 1016.32 681.77Average flow time / year 0.03 0.05 0.07Annual cost 16972.79 2197.05 1473.83Total cost 20643.66

nA' = 15.49193nB' = 4.898979nC' = 3.286335nB'' = 10.95445nC'' = 7.348469mB = 1.414214mC = 2.108185n = 14.37291nA = 14.37291nB = 10.16318nC = 6.81767

Current StrategyA B C

Demand per month, D 20000 2500 900Fixed cost / order, S + s 500 500 500Unit cost, C 5 4 5Holding cost, h 0.01666667 0.0166667 0.0166667Optimal order size, Q 15492 6124 3287Cycle inventory 7746 3062 1643.5Annual holding cost 645.5 204.13333 136.95833Order frequency, n 1.29 0.41 0.27Annual ordering cost 645.49 204.11 136.90Average flow time / month 0.39 1.22 1.83Annual cost 1290.99 408.25 273.86Total cost / month 1973.10

Product ordered and delivered jointlyA B C

Demand per month, D 20000 2500 900Order frequency, n 1.17 1.17 1.17Optimal order size, Q 17130.38 2141.297 770.8669Cycle inventory 8565.188 1070.648 385.4335Annual holding cost 713.7657 71.37657 32.11945Annual ordering cost 817.26 0.00 0.00Average flow time / month 0.43 0.43 0.43Annual cost 1531.03 71.38 32.12Total cost / month 1634.52

Combined fixed order cost, S = 700Optimal order frequency, n = 1.167517

Lot sizes and costs for ordering using heuristicsA B C

Demand per month, D 20000 2500 900Order frequency, n 1.20 0.85 0.57Optimal order size, Q 16698.08 2951.831 1584.119Cycle inventory 8349.04 1475.916 792.0594Annual holding cost 695.7533 98.39438 66.00495Annual ordering cost 718.65 84.69 56.81Average flow time / month 0.42 0.59 0.88Annual cost 1414.40 183.09 122.82Total cost / month 1720.31

nA' = 1.290994nB' = 0.408248nC' = 0.273861nB'' = 0.912871nC'' = 0.612372mB = 1.414214mC = 2.108185n = 1.197743nA = 1.197743nB = 0.846932nC = 0.568139

Monthly demand, D = 20000Order cost per lot, S = 400Holding cost per month as a fraction of unit cost, h = 0.016667

Order Quantity Discount unit price0 1

20000 0.9840000 0.96

q0 = 0q1 = 20000q2 = 40000C0 = 1C1 = 0.98C2 = 0.96Q0 = 30983.87Q1 = 31298.43Q2 = 31622.78

We ignore I = 0 and 1, because Q0>q0 and q1Q2 = 40000

Total annual cost = 19720

Average demand per week, D = 300= 200

Average lead time for replenishment, L = 2 weeksDesired cycle service level = 0.95

Average demand during lead time, DL = 600Standard deviation of demand during lead time, σL = √LσD

= 282.8427

Safety inventory, ss = 465.2349Reorder point, ROP = ss + DL

= 1065.2351065.235 Directly

Standard deviation of weekly demand, σD

Average demand per week, D = 300= 200

Average lead time for replenishment, L = 2 weeksDesired cycle service level = 0.95Review interval, T = 3 weeks

Mean demand during T + L periods, DT+L = (T+L)D= 1500

Standard deviation of demand during lead time, σL+T = √(T+L)σD= 447.2136

Safety inventory, ss = 735.6009

Order upto Level, OUL = DT+L + ss= 2235.601

Standard deviation of weekly demand, σD

CSL = 0.95L = 8 weeksIndependent ss in different countries

Country Mean Demand, D σL ss ROPFrance 3000 2000 5656.9 9304.7 33304.7

Germany 4000 2200 6222.5 10235.2 42235.2Spain 2000 1400 3959.8 6513.3 22513.3Italy 2500 1600 4525.5 7443.8 27443.8

Portugal 1000 800 2262.7 3721.9 11721.9UK 4000 2400 6788.2 11165.6 43165.6

Total 48384.4 180384.4

ss in TaiwanCountry Mean Demand, D σL ss ROPFrance 3000 2000 5656.9 9304.7 33304.7

Germany 4000 2200 6222.5 10235.2 42235.2Spain 2000 1400 3959.8 6513.3 22513.3Italy 2500 1600 4525.5 7443.8 27443.8

Portugal 1000 800 2262.7 3721.9 11721.9UK 4000 2400 6788.2 11165.6 43165.6

16500 4445.22215417857 12573.0 20680.7 152680.7

Standard deviation,σD

Standard deviation,σD

Demand, DA = 250= 100

Revenue from segment A, pA = 10Revenue from segment B, pB = 5Total capacity per day = 1000

Capacity to be reserved for segment A = 250

Standard deviation, σA

= 60000= 20000

Bulk contract cost, cB = 0.1Spot contract cost, cs = 0.13Total capacity = 200000Optimal value of p = (cS-cB)/cS

= 0.230769

Optimal amount to be purchased using the spot contract, Q = 45273.68

Mean for spot market, µStandard deviation for spot market, σ

Quantity at the beginning of the season, Q = 5000Costs per unit, C = 40First month d1 = 2000-10p1Second month d2 = 2000-20p2Third month d3 = 2000-30p3

Max p1(20000-10p1) + p2(20000-20p2) + p3(20000-30p3)subjected to

Fixed price for entire seasonPeriod Price Demand Revenue

1 50.0 1500 750002 50.0 1000 500003 50.0 500 25000

Total 3000 150000

Dynamic pricingPeriod Price Demand Revenue

1 100 1000 1000002 50 1000 500003 33.33333 1000 33333.33

Total 3000 183333.3

Optimal quantityPeriod Price Demand Revenue Profit

1 120 800 96000 640002 120 800 96000 640003 120.00 800 96000 64000

Total 2400 288000 192000

(20000-10p1) + (20000-20p2) + (20000-30p3) ≤ 5000(20000-10p1), (20000-20p2), (20000-30p3) ≥ 0