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Inventory Management: Cycle Inventory-II

第五單元： Inventory Management: Cycle Inventory-II. Inventory Management: Cycle Inventory-II. 郭瑞祥教授. 【 本著作除另有註明外，採取 創用 CC 「姓名標示－非商業性－相同方式分享」台灣 3.0 版 授權釋出 】. 1. Lessons From Aggregation. Aggregation allows firm to lower lot size without increasing cost.

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Inventory Management: Cycle Inventory-II

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  1. 第五單元：Inventory Management: Cycle Inventory-II Inventory Management: Cycle Inventory-II 郭瑞祥教授 【本著作除另有註明外，採取創用CC「姓名標示－非商業性－相同方式分享」台灣3.0版授權釋出】 1

  2. Lessons From Aggregation • Aggregation allows firm to lower lot size without increasing cost • Complete aggregation is effective if product specific fixed cost is a small fraction of joint fixed cost • Tailored aggregation is effective if product specific fixed cost is a large fraction of joint fixed cost 2

  3. Holding Cycle Inventory for Economies of Scale • Fixed costs associated with lots • Quantity discounts • Trade Promotions 3

  4. Total Material Cost Average Cost per Unit C0 C1 C2 Quantity Purchased Order Quantity q1 q2 q3 q1 q2 q3 Quantity Discounts • Lot size based • Volume based • Based on the quantity ordered in a single lot • All units • Marginal unit • Based on total quantity purchased over a given period • How should buyer react? How does this decision affect the supply chain in terms of lot sizes, cycle inventory, and flow time?  What are appropriate discounting schemes that suppliers should offer? 4

  5. 2 DS = Qi hCi Evaluate EOQ for All Unit Quantity Discounts • Evaluate EOQ for price in range qi to qi+1 , • Case 1:If qiQi < qi+1 , evaluate cost of ordering Qi • Case 2:If Qi < qi, evaluate cost of ordering qi • Case 3:If Qiqi+1 , evaluate cost of ordering qi+1 • Choose the lot size that minimizes the total cost over all price ranges. Qi D = + + TCi S hCi DCi 2 Qi qi D = + + TCi S hCi DCi 2 qi qi+1 D = + + TCi S hCi DCi+1 qi+1 2 5

  6. Marginal Unit Quantity Discounts Marginal Cost per Unit Total Material Cost C0 C1 C2 Quantity Purchased Order Quantity q1 q2 q3 q1 q2 q3 If an order of size q is placed, the first q1-q0 units are priced at C0, the next q2-q1 are priced at C1, and so on. 6

  7. Optimal lot size Evaluate EOQ for Marginal Unit Discounts • Evaluate EOQ for each marginal price Ci (or lot size between qi and qi+1) • Let Vi be the cost of order qi units. Define V0 = 0 and • Vi=C0(q1-q0)+C1(q2-q1)+‧‧‧+Ci-1(qi-qi-1) • Consider an order size Q in the range qi to qi+1 • Total annual cost = ( D/Q )S (Annual order cost) • +[Vi+(Q-qi)Ci] h/2 (Annual holding cost) • + ( D/Q ) [Vi+(Q-qi)Ci](Annual material cost) 2D(S+Vi-qiCi) Qi= hCi 7

  8. 2D(S+Vi-qiCi) Qi= hCi ì ü D h D D h D = + + + + TC Min S V V , S V V í ý + + 1 1 i i i i i q 2 q q 2 q î þ + + 1 1 i i i i D h D = +[ Vi+(Qi-qi)Ci] + [ Vi+(Qi-qi)Ci] TCi S 2 Qi Qi Evaluate EOQ for Marginal Unit Discounts • Evaluate EOQ for each marginal price Ci, • Evaluate EOQ for each marginal price Ci • Case 1 :If qiQi < qi+1 , calculate cost of ordering Qi • Case 2 and 3 : If Qi < qi or Qi > qi+1 , the lot size in this range • is either qi or qi+1 depending on which has the • lower total cost • Choose the lot size that minimizes the total cost over all price ranges. 8

  9. The Comparison between All Unit and Marginal Unit Quantity Discounts • The order quantity of all unit quantity discounts is less than the order quantity of marginal unit quantity discounts. • The marginal unit quantity discounts will further enlarge the cycle inventory and average flow time. 9

  10. Why Quantity Discounts? • Quantity discounts are valuable only if they result in: • Improved coordination in the supply chain • Extraction of surplus through price discrimination • Coordination: max total profits of suppliers and retailers • Coordination in the supply chain • Use price discrimination to max supplier’s profits • Quantity discounts for commodity products (in the perfect competition market, price is fixed) • Quantity discounts for products for which the firm has market power (in the oligopoly market, the determined price can influence demand) >Two-part tariffs >Volume discounts 10

  11. 120,000 6,324 = x + x x = x x TC 100 0.2 3 $3,795 2 120,000 100 120,000 6,324 = x + x x = 6,324 2 TC 250 0.2 2 $6,009 = = * 6,324 2 Q 6,324 x 0.2 3 Coordination for Commodity Products • Assume the following data. • Retailer: D =120,000/year , SR=$100 , hR=0.2 , CR=$3 • Suplier: SS =$250 , hS =0.2 , CS =$2 • Retailer cost • Supplier’s cost is based on retailer’s optimal order size. • Supply chain total cost = 3,795+6,009=$9,804 11

  12. $3,795 $6,009 Suppler's TC=100x + x0.2x3 =$4,059 120,000 120,000 9,165 9,165 Suppler's TC=250x + x0.2x2 =$5,106 9,165 9,165 2 2 Coordination for Commodity Products • Consider a coordinated order size=9,165. (Increased by $264) (decreased by $903) • Supply chain total cost=4,059+5,106 =$9,165(decreased by $639) • Coordination through all unit quantity discounts. • $3 for lots below 9,165 • $2.9978 for lots of 9,165 or higher • Increase in retailer’s holding cost and order cost can be compensated • by the reduction in material cost. 120,000(3-2.9978)=$264 • Decrease in supplier’s cost = supply chain savings = 903–264=$639 (can be further shared between two parties) 12

  13. Coordination for Commodity Products • Since the price is determined by the market, supplier can use lot- size based quantity discounts to achieve coordination in supply chain and decrease supply chain cost. • Lot size-based quantity discounts will increase cycle inventory. • In theory, if supplier reduces its setup or order cost, the discount it offers will change and the cycle inventory is expected to decrease. • In practice, the cycle inventory does not decrease in the supply chain because in most firms, marketing and sales department design quantity discounts independent of operations department who works on reducing the order cost. 13

  14. Quantity Discounts When Firm has Market Power • No inventory related costs. • Assume the following data • Demand curve = 360,000-60,000p (p is retailer’s sale price) • CS = $2 (cost of supplier). • Need to determine CR (Suppler’s charge on retailer) and p. p CR CS =$2 Supplier Retailer Demand =360,000-60,000p 14

  15. Maximize individual profits and make pricing decision independently Demand = 360,000-60,000(5)=60,000 Profit for retailer = (5-4)(60,000)=$60,000 Profit for supplier = (4-2)(60,000)=$120,000 Profit for supply chain = 60,000+120,000=$180,000 CR CR (ProfitR) ¶ Þ p=3+ = 0 2 2 ¶p =(CR-2)[360,000-60,000( 3+ )] (ProfitS) ¶ Þ = CR=4; p=5 0 ¶CR p CR CS =$2 Supplier Retailer Demand =360,000-60,000p Scenario 1: No Coordination =(p-CR) ProfitR (360,000-60,000p) ProfitS= (CR-2) (360,000-60,000p) 15

  16. Variation Fix Quantity Discounts When Firm has Market Power • No inventory related costs. • Assume the following data • Demand curve = 360,000-60,000p (p is retailer’s sale price) • CS = $2 (cost of supplier). • Need to determine CR (Suppler’s charge on retailer) and p. p CR CS =$2 Supplier Retailer Demand =360,000-60,000p 16

  17. (Profit) ¶ = 0 ¶p Maximize Supply Chain Profits • Profit for supply chain • Demand = 360,000-60,000(4)=120,000 • Profit for supple chain = (4-2)(120,000)=$240,000 > $180,000 =(p-Cs) (360,000-60,000p) =(p-2) (360,000-60,000p) Þ p=4 Microsoft。 Microsoft。 Microsoft。 How to increase the total profit through coordination ? 17

  18. Scenario 2: Coordination through Two-Part Tariff -I • Supplier charges his entire profit as an up-front franchise fee. • Supplier sells to the retailer at production cost (CS). • Proof:Assume demand function = a-bp (a, b are constants) Then retailer’s profit = (p-cR)(a-bp)-F (F: franchise fee) The supply chain’s profit = (p-cS)(a-bp) Maximize both profits will obtain 18

  19. Scenario 2: Coordination through Two-Part Tariff-II • Supplier charges his entire profit as an up-front franchise fee. • Supplier sells to the retailer at production cost (CS). • Proof:Assume demand function = a-bp (a, b are constants) Then retailer’s profit = (p-cR)(a-bp)-F (F: franchise fee) The supply chain’s profit = (p-cS)(a-bp) Maximize both profits will obtain 19

  20. P = + = + CR CS a a 2b 2b 2 2 Scenario 2: Coordination through Two-Part Tariff-III • Supplier charges his entire profit as an up-front franchise fee. • Supplier sells to the retailer at production cost (CS). • Proof:Assume demand function = a-bp (a, b are constants) Then retailer’s profit = (p-cR)(a-bp)-F (F: franchise fee) The supply chain’s profit = (p-cS)(a-bp) Maximize both profits will obtain \ CR=CS In our example, CR =CS =2 , p =4, demand=120,000 Assume a franchise fee of 180,000 Retailer’s profit =(4-2)(120,000)-180,000=$60,000 (same as before) Supplier’s profit = F = $180,000 Supply chain’s profit = 60,000+180,000=$240,000 20

  21. Scenario 3: Coordination through Volume- based Quantity Discounts • The two-part tariff is really a volume-based quantity discounts. • Supplier offers the volume discounts at the break point of optimal demand. • Supplier offers the discount price so that the retailer will have a profit  the profit of no coordination and no discount. In our example, design the volume discounts CR =$4 (for volume < 120,000) CR =$3.5 (for volume  120,000) To sell 120,000, the retailer sets price at p = 4.(from the demand function) Retailer’s profit =(4-3.5)(120,000)=$60,000 (same as before) Supplier’s profit = (3.5-2)(120,000) = $180,000 Supply chain’s profit = 60,000+180,000=$240,000 21

  22. Lessons From Discounting Schemes • Lot size-based discounts increase lot size and cycle inventory in the supply chain. • Lot size-based discounts are justified to achieve coordination for commodity products. • Volume-based discounts with some fixed cost passed on to retailer are more effective in general • Volume-based discounts are better using rolling horizon to avoid the “hockey stick phenomenon”. 22

  23. (Profit) ¶ = 0 ¶CR Price Discrimination to Max Supplier Profits • Price discrimination is the practice which a firm charges differential prices to maximize profits. • Price discrimination is also a volume-based discount scheme. • Consider an example • Demand curve (supplier sells to retailer)=200,000-50,000CR • CS =2 • Profit of supplier = (CR-2)(200,000-50,000CR) • What is the optimal “ fixed ” price CR to maximize profit ? Þ CR=$3 Demand=200,000-50,000(3)=50,000 Profit=(3-2)(50,000)=$50,000 23

  24. Demand Curve and Demand at Price of $3 • The fixed price of $3 does not maximize profits for the supplier. • The profit is only the shaded area in the following figure. • The supplier could obtain the entire area under the demand curve above his marginal cost of $2 (the triangle within the solid lines) by pricing each unit differently. Price p=4 p=3 Marginal cost = $2 p=2 200,000 Demand 50,000 100,000 24

  25. Price Price 50,000 p=4 p=4 p=3 p=3 Marginal cost = $2 Marginal cost = $2 p=2 p=2 50,000 200,000 200,000 Demand Demand 50,000 50,000 100,000 100,000 An Equivalent Two-Part Tariff to Price Discrimination • The entire triangle under the demand curve (above the marginal cost of $2) = franchise fee = 1/2(4-2)(100,000)=$100,000 • The selling price to retailer: CR =CS =2. • Demand = 200,000-50,000(2)=100,000 • Profit of supplier = F = $100,000 25

  26. Price 50,000 p=4 p=3 Marginal cost = $2 p=2 50,000 200,000 Demand 50,000 100,000 Demand Curve and Demand at Price of $3 • The fixed price of $3 does not maximize profits for the supplier. • The profit is only the shaded area in the following figure. • The supplier could obtain the entire area under the demand curve above his marginal cost of $2 (the triangle within the solid lines) by pricing each unit differently. 26

  27. Holding Cycle Inventory for Economies of Scale • Fixed costs associated with lots • Quantity discounts • Trade Promotions 27

  28. Trade Promotion • Goals: • Induce retailers to spur sales • Shift inventory from manufacture to retailer and the customer • Defend a brand against competition • Retailer options: • Pass through some or all of the promotion to customers to spur sales • Pass through very little of the promotion to customers but purchase in greater quantity to exploit temporary reduction in price (forward buying) 28

  29. Inventory Profile for Forward Buying I(t) Qd:lot size ordered at the discount price Q*:EOQ at normal price Qd Q* Q* Q* Q* Q* t 29

  30. I(t) Qd:lot size ordered at the discount price Q*:EOQ at normal price Qd Q* Q* Q* Q* Q* t Forward Buying Decisions • Goal: • Assumptions: • Identify Qd that maximizes the reduction in total cost (material cost + order cost + holding cost) • Discount will only be offered once. • Order quantity Qd is a multiple of Q*. • The retailer takes no action to influence the demand. 30

  31. Q* = 2DS hC I(t) Qd:lot size ordered at the discount price Q*:EOQ at normal price Qd Q* Q* Q* Q* Q* t Decision on Q*d • Assume the following data • Normal order quantity = EOQ = • The discount = $d. • The discounted material cost = $(C-d ) • Now estimate the total cost of ordering Qd in the discount period • TC(Qd) = material cost + order cost + inventory cost =(C-d)Qd + S + Qd/2 (C-d)h [ Qd/D ] =(C-d)Qd + S + (Qd/D)2 (C-d)h / 2D Note: Discount period =Qd/D 31

  32. 2DS +hC/2 hC 2DS hC +(D/ )S =CD+ 2hCDS =Qd/D [CD+ 2hCDS ] ¶F(Qd) CQ* dD Þ =0 Qd= + ¶Qd [C-d]h C-d Decision on Q*d • Now estimate the total cost of ordering Q* in the discount period Annual TC(Q*) = material cost + order cost + inventory cost =CD Discount period TC (Q*) = Qd/D [Annual TC(Q*) ] • Define the cost reduction in the discount period • F(Qd) = TC(Qd) – Discount period TC(Q*) • Forward buy = Qd – Q* 32

  33. 2DS +hC/2 hC 2DS hC +(D/ )S =CD+ 2hCDS =Qd/D [CD+ 2hCDS ] ¶F(Qd) CQ* dD Þ =0 Qd= + ¶Qd [C-d]h C-d Decision on Q*d • Now estimate the total cost of ordering Q* in the discount period Annual TC(Q*) = material cost + order cost + inventory cost =CD Discount period TC (Q*) = Qd/D [Annual TC(Q*) ] • Define the cost reduction in the discount period • F(Qd) = TC(Qd) – Discount period TC(Q*) • Forward buy = Qd – Q* 33

  34. 2DS +hC/2 hC 2DS hC +(D/ )S =CD+ 2hCDS =Qd/D [CD+ 2hCDS ] ¶F(Qd) CQ* dD Þ =0 Qd= + ¶Qd [C-d]h C-d Decision on Q*d • Now estimate the total cost of ordering Q* in the discount period Annual TC(Q*) = material cost + order cost + inventory cost =CD Discount period TC (Q*) = Qd/D [Annual TC(Q*) ] • Define the cost reduction in the discount period • F(Qd) = TC(Qd) – Discount period TC(Q*) • Forward buy = Qd – Q* 34

  35. 0.15X120,000 3(6,324) + [3-0.15][0.2] 3-0.15 dD CD* Qd = + = [C-d]h C-d Example Assume the following data without promotion. • D =120,000/year , C =$3 , h =0.2 , S =$100 • then →Q* = 6,324 • Cycle inventory = Q*/2 = 3,162 • Average flow time = Q*/2D = 0.02635(year) = 0.3162 (month). • Forward buy = 38,236 – 6,324 =31,912 • Trade promotions lead to a significant increase in lot size and cycle inventory because of forward buying by the retailer. • Trade promotions generally result in reduced supply chain profits unless the trade promotions reduce demand fluctuations. • Assume a promotion is offered (d =$0.15) =38,236 Cycle inventory = Qd/2 = 19,118 Average flow time = Qd/2D = 0.1593(year) = 1.9118 (month). 35

  36. CR a + P = 2b 2 p CR a d d ¢ + - = - p = p 2 2b 2 2 Promotion Pass through to Customers • Assume demand function = a-bp (a, b are constants) • Then retailer’s profit = [p-CR][a-bp] • Maximizing retailer’s profits will obtain • If a discount d is offered, the new C¢R=CR-d • Then the new • Retailer’s optimal response to a discount is to pass only 50% of the discount to the customers. 36

  37. Example-I • Demand curve at retailer: 300,000 – 60,000p • Normal supplier price, CR = $3.00 • Promotion discount = $0.15 • Retailer only passes through half the promotion discount • Optimal retail price = $4.00 • Customer demand = 60,000 37

  38. Example-II • Demand curve at retailer: 300,000 – 60,000p • Normal supplier price, CR = $3.00 • Promotion discount = $0.15 • Retailer only passes through half the promotion discount • Optimal retail price = $4.00 • Customer demand = 60,000 38

  39. Example-III • Demand curve at retailer: 300,000 – 60,000p • Normal supplier price, CR = $3.00 • Promotion discount = $0.15 • Retailer only passes through half the promotion discount • Optimal retail price = $4.00 • Customer demand = 60,000 • Optimal retail price = $3.925 • Customer demand = 64,500 • Demand increases by only 7.5% • Cycle inventory increases significantly 39

  40. Goal is to discourage forward buying in the supply chain Trade Promotions Counter measures • EDLP • Scan based promotions • Customer coupons Wikipedia Microsoft。 Microsoft。 40

  41. Levers to Reduce Lot Sizes Without Hurting Costs Cycle Inventory Reduction • Reduce transfer and production lot sizes • Aggregate fixed cost across multiple products, supply points, or delivery points. • Are quantity discounts consistent with manufacturing and logistics operations? • Volume discounts on rolling horizon • Two-part tariff • Are trade promotions essential? • EDLP • Base on sell-thru rather than sell-in 41

  42. 版權聲明 42

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