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Managing Economies of Scale in the Supply Chain: Cycle Inventory

Managing Economies of Scale in the Supply Chain: Cycle Inventory. Fall, 2014 Supply Chain Management: Strategy, Planning, and Operation Chapter 10 Byung-Hyun Ha. Contents. Introduction Economies of scale to exploit fixed costs Economies of scale to exploit quantity discount

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Managing Economies of Scale in the Supply Chain: Cycle Inventory

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  1. Managing Economies of Scale in the Supply Chain: Cycle Inventory Fall, 2014 Supply Chain Management:Strategy, Planning, and Operation Chapter 10 Byung-Hyun Ha

  2. Contents • Introduction • Economies of scale to exploit fixed costs • Economies of scale to exploit quantity discount • Short-term discounting: trade promotions • Managing multiechelon cycle inventory

  3. Introduction • Cycle inventory • Notation • D: demand per unit time • Q: quantity in a lot or batch size (order quantity) • Cycle inventory management (basic) • Determining optimal order quantity Q*that minimizes total inventory cost, with demand D given inventory level time

  4. Introduction • Basic analysis of cycle • Average inventory level (cycle inventory) = Q/2 • Average flow time = Q/2D  Little’s law: (arrival rate) = (avg. number in system)/(avg. flow time) • Example • D = 2 units/day, Q = 8 units • Average inventory level • (7 + 5 + 3 + 1)/4 = 4 = Q/2 • Average flow time • (0.25 + 0.75 + 1.25 + 1.75 + 2.25 + 2.75 + 3.25 + 3.75)/8 = 2 = Q/2D

  5. Introduction • Costs that influence total cost by order quantity • C: (unit) material cost ($/unit) • Average price paid per unit purchased  Quantity discount • H: holding cost ($/unit/year) • Cost of carrying one unit in inventory for a specific period of time • Cost of capital, obsolescence, handling, occupancy, etc. • H = hC  Related to average flow time • S: ordering cost ($/order) • Cost incurred per order • Assuming fixed cost regardless of order quantity • Cost of buyer time, transportation, receiving, etc.  10.2 Estimating cycle inventory-related costs in practice • SKIP!

  6. Introduction • Assumptions • Constant (stable) demand, fixed lead time, infinite time horizon • Cycle optimality regarding total cost • Order arrival at zero inventory level is optimal. • Identical order quantities are optimal. ? ?

  7. Introduction • Determining optimal order quantity Q* • Economy of scale vs. diseconomy of scale, or • Tradeoff between total fixed cost and total variable cost Q1 D ? Q2 D

  8. Economies of Scale to Exploit Fixed Costs • Lot sizing for a single product • Economic order quantity (EOQ) • Economic production quantity (EPQ) • Production lot sizing • Lot sizing for multiple products • Aggregating multiple products in a single order • Lot sizing with multiple products or customers

  9. Economic Order Quantity (EOQ) • Assumptions • Same price regardless of order quantity • Input • D: demand per unit time, C: unit material cost • S: ordering cost, H = hC: holding cost • Decision • Q: order quantity • D/Q: average number of orders per unit time • Q/D: order interval • Q/2: average inventory level • Total inventory cost per unit time (TC) TO: total order cost TH: total holding cost TM: total material cost

  10. Economic Order Quantity (EOQ) • Total cost by order quantity Q • Optimal order quantity Q* that minimizes total cost • Opt. order frequency • Avg. flow time TC Q Q*

  11. Economic Order Quantity (EOQ) • Robustness around optimal order quantity (KEY POINT) • Using order quantity Q' = Q* instead of Q* TC' = 1.25TC* TC*  0.5 1 2

  12. Economic Order Quantity (EOQ) • Robustness regarding input parameters • Mistake by indentifying ordering cost S' = S instead of real S • Misleading to TC' = 1.061TC* TC*  Robustness?  0.5 1 2

  13. Economic Order Quantity (EOQ) • Sensitivity regarding demand (KEY POINT) • Demand change from D to D1 = kD • Opt. order frequency • Avg. flow time

  14. Economic Order Quantity (EOQ) • Effect of reducing order quantity • Using order quantity Q' = Q* instead of Q* (revisited) • Reducing flow time by reducing ordering cost (KEY POINT) • Efforts on reducing S to S1 = S • Hoping Q1* = kQ* • How much should S be reduced? (What is ?)   = k2 (ordering cost must be reduced by a factor of k2)

  15. Economic Production Quantity (EPQ) • Production of lot instead of ordering • P: production per unit time • Total cost by production lot size Q • Optimal production quantity Q*  When P goes to infinite, Q* goes to EOQ. Q x D (P – D) Q/P Q/D – Q/P = Q(1/D – 1/P) 1/(D/Q) = Q/D

  16. Aggregating Products in a Single Order • Multiple products • m products • D: demand of each product • S: ordering cost regardless of aggregation level • All the other parameters across products are the same. • All-separate ordering • All-aggregate ordering  Impractical supposition (for analysis purpose)

  17. Lot Sizing with Multiple Products • Multiple products with different parameters • m products • Di, Ci, hi: demand, price, holding cost fraction of product i • S: ordering cost each time an order is placed • Independent of the variety of products • si: additional ordering cost incurred if product i is included in order • Ordering each products independently? • Ordering all products jointly • Decision • n: number of orders placed per unit time • Qi = Di /n: order quantity of item i • Total cost and optimal number of orders

  18. Lot Sizing with Multiple Products • Example 10-3 and 10-4 • Input • Common transportation cost, S = $4,000 • Holding cost fraction, h = 0.2 • Ordering each products independently • ITC* = $155,140 • Ordering jointly • n* = 9.75 • JTC* = $136,528

  19. Lot Sizing with Multiple Products • How does joint ordering work? • Reducing fixed cost by enjoying robustness around optimal order quantity • Is joint ordering is always good? • No! • Then, possible other approaches? • Partially joint • NP-hard problem (i.e., difficult)  Number of all possible ways • http://en.wikipedia.org/wiki/Bell_number • A heuristic algorithm • Subsection: “Lots are ordered and delivered jointly for a selected subset of the products” • SKIP!

  20. Exploiting Quantity Discount • Total cost with quantity discount • Types of quantity discount • Lot size-based • All unit quantity discount • Marginal unit quantity discount • Volume-based • Decision making we consider • Optimal response of a retailer • Coordination of supply chain TO: total ordering cost TH: total holding cost TM: total material cost

  21. All Unit Quantity Discount • Pricing schedule • Quantity break points: q0, q1, ..., qr , qr+1 • where q0 = 0 and qr+1 =  • Unit cost Ci when qi Q qi+1, for i=0,...,r • where C0  C1    Cr  It is possible that qiCi  (qi + 1)Ci averagecostper unit C0 C1 C2 ... Cr ... ... q0 q1 q2 q3 qr

  22. All Unit Quantity Discount • Solution procedure 1. Evaluate the optimal lot size for each Ci. 2. Determine lot size that minimizes the overall cost by the total cost of the following cases for each i. • Case 1: qi Qi*  qi+1 , Case 2: Qi*  qi, Case 3: qi+1 Qi*

  23. All Unit Quantity Discount • Example 10-7 • r = 2, D = 120,000/year • S = $100/lot, h = 0.2 • Q* = 10,000

  24. All Unit Quantity Discount • Example 10-7 (cont’d) • Sensitivity analysis • Optimal order quantity Q* with regard to ordering cost

  25. Marginal Unit Quantity Discount • Pricing schedule • Quantity break points: q0, q1, ..., qr , qr+1 • where q0 = 0 and qr+1 =  • Marginal unit cost Ci when qi Q qi+1, for i=0,...,r • where C0  C1    Cr • Price of qi units • Vi = C0(q1 – q0) + C1(q2 – q1) + ... + Ci–1(qi – qi–1) • Ordering Q units • Suppose qiQ  qi+1 . marginalcostper unit C0 C1 C2 ... Cr ... ... q0 q1 q2 q3 qr

  26. Marginal Unit Quantity Discount • Example 10-8 • r = 2, D = 120,000/year • S = $100/lot, h = 0.2 • Q* = 16,961

  27. Marginal Unit Quantity Discount • Example 10-8 (cont’d) • Sensitivity analysis • Optimal order quantity Q* with regard to ordering cost  Higher inventory level (longer average flow time)

  28. Why Quantity Discount? 1. Improve coordination to increase total supply chain profit • Each stage’s independent decision making for its own profit • Hard to maximize supply chain profit (i.e., hard to coordinate) • How can a manufacturer control a myopic retailer? • Quantity discounts for commodity products • Quantity discounts for products for which firm has market power 2. Extraction of surplus through price discrimination • Revenue management (Ch. 15)  Other factors such as marketing that motivates sellers • Munson and Rosenblatt (1998) Manufacturer (supplier) Retailer customers supply chain

  29. Coordination for Total Supply Chain Profit • Quantity discounts for commodity products • Assumptions • Fixed price and stable demand  fixed total revenue  Max. profit  min. total cost • Example case • Two stages with a manufacture (supplier) and a retailer Manufacturer (supplier) Retailer customers SS = 250 hS = 0.2 CS = 2 SR = 100 hR = 0.2 CR = 3 D = 120,000

  30. Coordination for Total Supply Chain Profit • Quantity discounts for commodity products (cont’d) • (a) No discount • Retailer’s (local) optimal order quantity ( supply chain’s decision) • Q(a) = (2120,000100/0.23)1/2 = 6,325 • Total cost (without material cost) • TC0(a) = TCS(a) + TCR(a) = $6,008 + $3,795 = $9,803 • () Minimum total cost, TC*, regarding supply chain (coordination) • Q* = 9,165 • TC0* = TCS* + TCR* = $5,106 + $4,059 = $9,165 • Dilemma? • Manufacturer saving by $902, but retailer cost increase by $264 • How to coordinate (decision maker is the retailer)?

  31. Coordination for Total Supply Chain Profit • Quantity discounts for commodity products (cont’d) • (b) Lot size-based quantity discount offering by manufacturer • Price schedule of CR • q1 = 9,165, C0 = $3, C1 = $2.9978 • Retailer’s (local) optimal order quantity (considering material cost) • Q(b) = 9,165 • Total cost (without material cost) • TC0(b) = TCS(b) + TCR(b) = $5,106 + $4,057 = $9,163 • Savings (compared to no discount) • Manufacturer: $902 • Retailer: $264 (material cost) – $262 (inventory cost) = $2 • KEY POINT • For commodity products for which price is set by the market, manufacturers with large fixed cost per lot can use lot size-based quantity discounts to maximize total supply chain profit. • Lot size-based discount, however, increase cycle inventory in the supply chain.

  32. Coordination for Total Supply Chain Profit • Quantity discounts for commodity products (cont’d) • (c) Other approach: setup cost reduction by manufacturer • Retailer’s (local) optimal order quantity • Q(c) = Q(a) = 6,325 • Total cost (without material cost): no need to discount! • TC0(c) = TCS(c) + TCR(c) = $3,162 + $3,795 = $6,957  Same with optimal supply chain cost when material cost is considered  Expanding scope of strategic fit • Operations and marketing departments should be cooperate! Manufacturer (supplier) Retailer customers S'S = 100 hS = 0.2 CS = 2 SR = 100 hR = 0.2 CR = 3 D = 120,000

  33. Coordination for Total Supply Chain Profit • Quantity discounts for products with market power • Assumption • Manufacturer’s cost, CS = $2 • Customer demand depending on price, p, set by retailer • D = 360,000 – 60,000p  Profit depends on price. D = 360,000 – 60,000p Manufacturer (supplier) Retailer customers CS = 2 CR = ? p = ?

  34. Coordination for Total Supply Chain Profit • Quantity discounts for products with market power (cont’d) • (a) No coordination (deciding independently) • Manufacturer’s decision on CR • Expected retailer’s profit, ProfR • ProfR = (p – CR)(360 – 60p) • Retailer’s optimal price setting (behavior) when CR is given • p = 3 + 0.5CR • Demand by p (supplier’s order quantity) • D = 360 – 60p = 180 – 30CR • Expected manufacturer’s profit, ProfS • ProfS = (CR – CS)(180 – 30CR)  CR(a) that maximizes ProfS (manufacturer’s decision) • CR(a) = $4 • Retailer’s decision on p(a) with given CR(a) • p(a) = $5 (D(a) = 360,000 – 60,000p(a) = 60,000) • Supply chain profit, Prof0(a) • Prof0(a) = ProfS(a) + ProfR(a) = $120,000 + $60,000 = $180,000

  35. Coordination for Total Supply Chain Profit • Quantity discounts for products with market power (cont’d) • () Coordinating supply chain • Optimal supply chain profit, Prof0* • Prof0 = (p – CS)(360 – 60p) • p* = $4 • D* = 120,000 • Prof0* = $240,000  Double marginalization problem (local optimization) • But how to coordinate? • i.e., ProfS* = ?, ProfR* = ?

  36. Coordination for Total Supply Chain Profit • Quantity discounts for products with market power (cont’d) • Two pricing schemes that can be used by manufacturer • (b) Two-part tariff • Up-front fee $180,000 (fixed) + material cost $2/unit (variable) • Retailer’s decision • ProfR = (p – CR)(360 – 60p) – 180,000 • p(b) = 3 + 0.5CR = $4 • Prof0(b) = Prof S(b) + ProfR(b) = $180,000 + $60,000 = $240,000  Retailer’s side: larger volume  more discount • (c) Volume-based quantity discount • Pricing schedule of CR • q1 = 120,000, C0 = $4, C1 = $3.5 • p(c) = $4 • Prof0(c) = ProfS(c) + ProfR(c) = $180,000 + $60,000 = $240,000

  37. Coordination for Total Supply Chain Profit • Quantity discounts for products with market power (cont’d) • KEY POINT • For products for which the firm has market power, two-part tariffs or volume-based quantity discounts can be used to achieve coordination in the supply chain and maximizing supply chain profits. • For those products, lot size-based discounts cannot coordinate the supply chain even in the presence of inventory cost. • In such a setting, either a two-part tariff or a volume-based quantity discount, with the supplier passing on some of its fixed cost to the retailer, is needed for the supply chain to be coordinated and maximize profits. • Lot size-based vs. volume-based discount • Lot size-based: raising inventory level  suitable for supplier’s high setup cost  Hockey stick phenomenon & rolling horizon-based discount

  38. Short-term Discounting: Trade Promotion • Trade promotion by manufacturers • Induce retailers to use price discount, displays, or advertising to spur sales. • Shift inventory from manufactures to retailers and customers. • Defend a brand against competition. • Retailer’s reaction? • 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 during the promotion period to exploit the temporary reduction in price. • Forward buy  demand variability increase  inventory & flow time increase  supply chain profit decrease

  39. Short-term Discounting: Trade Promotion • Analysis • Determining order quantity with discount Qd • Unit cost discounted by d (C' = C – d) • Assumptions • Discount is offered only once. • Customer demand remains unchanged. • Retailer takes no action to influence customer demand. Qd Q* Qd/D 1 – Qd/D

  40. Short-term Discounting: Trade Promotion • Analysis (cont’d) • Optimal order quantity without discount Q* = (2DS/hC)1/2 • Optimal total cost without discount TC* = CD + (2DShC)1/2 • Total cost with Qd • Example 10-9 • C = $3  Q* = 6,324 • d = $0.15  Qd* = 38,236 (forward buy: 31,912  500%) • KEY POINT • Trade promotions lead to a significant increase in lot size and cycle inventory, which results in reduced supply chain profits unless the trade promotion reduces demand fluctuation.

  41. Short-term Discounting: Trade Promotion • Retailer’s action of passing discount to customers • Example 10-10 • Assumptions • Customer demand: D = 300,000 – 60,000p • Normal price: CR = $3 • Ignoring all inventory-related cost • Analysis • Retailer’s profit, ProfR • ProfR = (p – CR)(300 – 60p) • Retailer’s optimal price setting with regard to CR • p = 2.5 + 0.5CR • (a) No discount: CR = $3 • p(a) = $4, D(a) = 60,000 • (b) Discount: C'R = $2.85 • p(b) = $3.925, D(b) = 64,500 p(a) – p(b) = 0.075 < 0.15 = CR – C'R

  42. Short-term Discounting: Trade Promotion • Retailers’ response to short-term discount • Insignificant efforts on trade promotion, but • High forward buying • Not only by retailers but also by end customers • Loss to total revenue because most inventory could be provided with discounted price • KEY POINT • Trade promotions often lead to increase of cycle inventory in supply chain without a significant increase in customer demand.

  43. Short-term Discounting: Trade Promotion • Some implications • Motivation for every day low price (EDLP) • Suitable to • high elasticity goods with high holding cost • e.g., paper goods • strong brands than weaker brand (Blattberg & Neslin, 1990) • Competitive reasons  Sometimes bad consequence for all competitors • Discount by not sell-in but sell-through • Scanner-based promotion

  44. Managing Multiechelon Cycle Inventory • Configuration • Multiple stages and many players at each stage • General policy -- synchronization • Integer multiple order frequency or order interval • Cross-docking • (Skip!)

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