SCM 404 Exam 2 - Nicholson

What is the difference between a "lot-size discount" and a "volume discount"?

2 Types of Quantity Discounts 1. Lot-size discount • Pricing schedule is based on the quantity ordered in a single lot • We will focus more on this, to be consistent with EOQ 2. Volume-based discount • Pricing schedule is based on the total quantity purchased during a given time period

With the EOQ formula, you can calculate:

• # of times to order per year =(D/Q) • How frequently you will order = 52/[D/Q] - If we are dealing with weeks per year • Cycle inventory amount = Q/2 • Materials Cost = (C)(D) • Holding Cost=(Q/2)hC • Order Cost = DS/Q • Total cost = M + O + H • Average flow time = Q/2D - Avg time that product is in inventory - Avg time between receipt and sale

Relationship PFR & OFR

• As we aggregate more, it is harder to achieve a higher levels of product availability • Product is least aggregated • Order is more aggregated - Multiple products included, all must be met • For an order with 10 products, all must be available for the order to be filled - So, OFR usually < PFR

*? If a retailer carries no SI at all (SI=0), why will they not stock out during every period between when an order is placed and when it is received?

*ask prof.

How is it possible to have a very high order fill rate and a very low cycle service level?

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How is it possible to have a very high product fill rate and a very low order fill rate?

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If all of the replenishment cycles had these two orders and they were filled in exactly this way, what would the CSL be for this distributor?

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What is the order fill rate?

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What would be the overall product fill rate across both Orders?

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What would be the product fill rate for Order 1 and for Order 2?

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Why does demand uncertainty (forecast error) imply a need to hold safety inventory?

All forecasts wrong, so demand in a given period can commonly be more than the forecasted value

What are the trade-offs that a buyer needs to consider to determine if it is appropriate to take advantage of a "lot-based" discount offered by a supplier?

All-unit Quantity Discounts • The pricing schedule has specific break points, but the buyer pays one price for all units purchased • There is one average unit cost (C) for the order, but it varies with how large the order is Is Discount Good for You? • That is, does the discount lower overall costs? • Lower materials cost (C) • Lower order cost - If order larger Q, D/Q means fewer orders • Larger Q means that cycle inventory (Q/2)will be larger - Larger holding cost

What are two types of "lot-based" discounts that a supplier might offer a buyer?

All-unit quantity discounts • Buy a larger amount, pay a lower average price for all units • Every unit costs the same Marginal unit quantity discounts • Buy a larger amount, additional amounts purchased cost progressively less • First units cost more than later units

What are the more detailed components of these costs categories?

Average Cost per Unit • Usually straight forward, but some volume discounts can be complex Simple Example: Jeans - Cost per unit for < 500 is $20/pair - Cost per unit for 500+ is $18/pair • Called the Material Cost Fixed Ordering Cost • Buyer time to place an order - (But not applicable if buyer is not fully occupied) • Transportation costs - Costs don't vary with size of order • Receiving costs - Reviewing and processing order upon receipt - Purchase order matching, updating inventory records, inspecting stock before placement Holding Costs • Cost of capital - Basically, the value of money you have tied up in inventory that you could be doing something more productive with - Largest component for products that do not become obsolete quickly - Based on Weighted Average Cost of Capital (WACC) • Obsolescence or spoilage cost - Loss in value or quantity over time - Lg. for perishable products & those w/ short life cycles • Handling costs - Receiving and storage costs that vary with quantity • Occupancy costs - Additional costs for storage space if the quantity of cycle inventory is increased • Holding Costs - Are often expressed as a faction of the average unit cost (materials cost) - "Holding costs are 25% of the materials cost" - Or, as an equation - Holding = (0.25)(Materials Cost) • H = hC

If the order quantity is Q, what is the amount of cycle inventory that a retailer would hold, and why is this the amount?

Average Inventory • Average inventory for this pattern (sawtooth) is always ½ of the order amount • In this case, 500 = ½ order amount of 1,000 • If we call the order amount Q • Average inventory = Q/2 • Average inventory is also Cycle Inventory - The average amount held between receipts of product to meet customer needs • Cycle Inventory = Q/2

*? What is the importance of a Z-statistic for determining the CSL?

CSL Probabilities • To standardize, calculate a "Z-statistic" Z = (Actual Value - Mean) / s.d. = (ROP-DL) / sD,L

What is the definition of component commonality, and why is it important for inventory management?

Component Commonality • Most supply chains hold significant inventory in the form of components - Sometimes, "raw materials" Examples: • PC (Mac!) have hundreds of components - Keyboards, motherboards, modems, etc. • Aircraft (Airbus A3XX series) • Automobiles - Engines, frames, etc. "Automobile platform" • An automobile platform is a shared set of common design, engineering,and production efforts, as well as major components over a number of outwardly distinct models Benefits of Commonality • Reduce the costs associated with the development of products - Using a smaller number of "platforms" • Allows companies to create distinct models from similar components • Facilitates "postponement"

*? What is the impact on the total amount of SI held when there are multiple outlets?

Consider Two Options 1) Each outlet orders and stores its own inventory to achieve a given CSL 2) All inventories are held at a centralized facility that serves all 4 outlets -This is what we mean by "aggregation" option 1 holds more SI

What are the two basic replenishment policies discussed in class? What is constant for each, and what varies?

Continuous Review: • Track inventory continuously • Re-order Q when amount in inventory< certain amount • That amount is Reorder Point (ROP) • Order = Q (constant) • Timing for order varies Periodic Review: • Check inventory at regular intervals - Like "Every 3 weeks" • Order the amount required to get to a specified amount • Order = Desired-Actual • Order = Q (varies) • Timing for order is constant

Two Replenishment Policies

Continuous Review: • Track inventory continuously • Reorder Q when amount in inventory < certain amount • That amount is Reorder Point (ROP) • Order = Q (constant) • Timing for order varies - We have been assumingthis sort of policy to calculate SI... But there is another kind of policy Periodic Review: • Check inventory at regular intervals - Like "Every 3 weeks" • Order the amount required to get to a specified amount • Order = Desired-Actual • Order = Q (varies) • Timing for order is constant

What are the types of costs associated with holding inventory?

Cycle Inventory Costs • Cost per unit purchased ($/unit) - May be constant or include volume discounts - Often, buying a larger amount at one time lowers the average cost • Fixed ordering cost ($/order) - For each order, the cost is the same - Administrative, trucking, labor cost to receive • Holding Cost ($/unit/time) - Cost of carrying inventory for a given time

The Easier Way to E[L]...

E[L] = -SI[1-F(SI/sD,L)] +sD,Lf(SI/sD,L)] • PFR = (Q-L)/Q = (Q-E[L])/Q

If you are provided information under a continuous review replenishment policy about the ROP, the DL and the sD,L, how can you determine the CSL?

For a given ROP, find area under curve to the right of it to get probability that DL > ROP. CSL = 100 - that probability CSL Probabilities: • Can be calculated in Excel with the formula: • CSL = NORMDIST(ROP,DL,sD,L,1) • Where you specify the values of ROP, DL, and sD,L in other cells of the worksheet • Or, you can look up in a table of probabilities what the area to right is and subtract from 1 - But you need to "standardize" the values

Total costs, graphically

How to Calculate Q? • Slope at the lowest cost is zero - A derivative gives the value of the slope • A derivative of the Total Cost function set equal to 0 gives the Q that minimizes TC

How can a relatively small lot-based price discount result in much larger inventory holdings in a supply chain?

Impact of Discount • A relatively small % quantity discount of $0.04/unit (about 1%) resulted in • About a 1% reduction in costs, but... • A 57% increase in cycle inventory • A 55% increase in holding costs - Slightly less than 57% because of the smaller value of C, because H = hC • Volume discounts will often increase the amount of inventory held in the SC!

How does inventory management affect demand fulfillment, in general terms?

Inventory Management - Affects orders placed, inventory held, order fulfillment and delivery delay Inventory Benefit & Cost • Inventories allow for customer needs to be met, but cost money • Inventory costs include: - Materials Cost + Order Cost + Holding Costs - $/unit + $/order + $/unit/time

For what period of time does the OUL need to cover demand for a product? How is this different than the amount of demand that the ROP needs to cover under a continuous review replenishment policy?

Inventory To Cover Demand • OUL needs to cover the amount of demand during the period T+L weeks • This is clear for the first order in the graph, but also true for subsequent ones

What is the definition of safety inventory (SI)?

Inventory held to satisfy demand that exceeds the amount forecasted for a given period

What is the implication of a variable L for the amount of SI that a firm (supply chain) would need to hold? Is the effect likely to be large or small, and why?

Key Points • A reduction in lead time uncertainty can dramatically reduce the amount of SI without lowering product availability - Involves incentives to suppliers? • More certain lead times allow increased product availability for a given amount of SI - One reason to "qualify" suppliers—are they reliable about delivery times? - SI holdings are large when lead times are variable (SI is more than 10 times larger than when lead time is constant) Bottom line: Here, the additional variation in L results in a large increase in safety inventory compared to a constant L. (One motivation to have reliable, timely suppliers. Certifying suppliers is part of procurement/sourcing.)

What factors affect how much SI a firm (supply chain) would want to hold?

Level of Safety Inventory depends on three things: • Uncertainty of demand (IDU again) • Uncertainty of supply (ex. lead times) • Desired level of product availability

How does aggregating orders for multiple products typically affect the EOQ and the total costs, and why?

Not surprisingly, joint ordering lowers costs. Why? -Lowers ordering costs, but also lowers holding costs, because It changes Q, Q/2 and the ordering frequency. -Fixed order costs are now spread across multiple products. Aggregating Orders • Lowers costs • Get similar savings by spreading fixed transportation costs across multiple suppliers • In practice, American companies importing from Asia have built hubs that all suppliers deliver to • This spreads the fixed transportation cost component of the order • The best aggregation strategy can vary with product specific order costs and demands

What is the interpretation of the Expected Lost Sales value, and why is it important to calculating the Product Fill Rate when demand is variable?

PFR for CRP • PFR = Sales/Q • PFR = (Demand - Lost Sales )/Q • PFR = (Q-LS)/Q • So, we need to know the value of Lost Sales is to calculate the PFR • Based on statistics, this is the sum of the possible values of lost sales times their probabilities • If we have n possible values of lost sales,L, and p is the probability of L, then: E[L] = L1 × p1 +L2 × p2 +... +Ln × pn = åLi × pi Lost sales value =Sales-ROP

What are the basic differences between a continuous review replenishment policy and a periodic review replenishment policy?

Periodic Review • Does not require continuous monitoring of inventory - As continuous review does • Costs of monitoring with automated and online systems have gone down, but still some companies use this approach Under Periodic Review, the timing is the same,but the quantity ordered varies based on demand Under Continuous Review, the order amount Q is always the same, but the timing varies based on demand & Low point of inventories varies with demand

What are the definitions of the Review Interval (RI) and Order-up-to Level (OUL) under a periodic review replenishment policy?

Periodic Review Notation • Review Interval (T) - Time between reviews of inventory - Also, the time between orders • Order-up-to Level (OUL) - Desired level ("Re-stocking Level") - OUL = Current inventory + Order amount • Order amount will vary, based on amount of current inventory at review time

Compare to Continuous Review

Periodic Review: SI = 47.5 SI = (Z)√(T+L)(sD) - Difference is the increased variability of demand because T+L is longer than L - sD,L < sD,T+L Continuous Review: SI = 26 SI = (Z)√(L)(sD) Role for IT in IM: • IT systems that allow for continuous monitoring allow use of continuous replenishment - Lower SI compared to periodic -REI Monitors inventory at DCs and stores simultaneously

What is the definition of postponement, and why is it important for inventory management?

Postponement • Ability of a supply chain to delay product differentiation or customization until closer to the time the product is sold Examples: • Final mixing of paint at retail store from components - Paint base and color • High-end home furnishings - Hand-painted wallpaper completed after order • Make, stock and use common components - For the "push phase" (pre-order) • Differentiate after the product is ordered - For the "pull phase" (post-order) • (Postponement and component commonality often are linked)

How would you express in the words the meaning of the CSL for a periodic review replenishment policy?

Probability of Not Stocking Out • Is the probability that demand during L+T ≤ OUL • This is the CSL for periodic review • What is the probability of not stocking out? • The approach is similar to what we used for the continuous review policy CSL = area under this curve up to the OUL, for a normal distribution with mean DL+T and sD,L+T

What is the difference in the amount of SI that needs to be held under continuous and periodic review replenishment policies, and why does this difference exist? (That is, which policy is typically better, and why?)

SI Formulas, Periodic Review • DT+L = D(T+L) • sD,T+L = √(T+L) (sD) • SI = (Z)(sD,T+L) - Z chosen for a CSL • OUL = DT+L + SI • Average Q = (D)(T) - Average demand per week times time between orders - SI is larger under periodic review compared to continuous review

What is the impact of SI on total inventory holdings and inventory management costs?

Safety Inventory • Increases average inventory held • Total inventory is cycle inventory + safety inventory • In this case, Q/2 + Safety • Obviously, increases inventory costs • But, can increase sales and margin

What is the trade-off between ordering and handling costs when determining how frequently to order in a replenishment cycle?

There is a Trade-Off • Between ordering and handling costs • And we want to figure out the lowest value of these combined costs • Given a level of demand - Given the same materials costs Can We Find the Best Order Quantity? • Yes! How? • Using the Economic Order Quantity Formula • The order quantity and frequency that minimizes the inventory costs

How can a supplier provide incentives to a buyer to order the quantity Q that minimizes total supply chain costs?

Total Supply Chain Costs • TSCC = Retailer Order + Holding Costs + Manufacturer Order + Holding Costs - Here we ignore the material cost to the retailer,because this is received as revenue by the manufacturer Combined SC EOQ • But to minimize the costs to the entire supply chain, we would need to account for both the retailer and manufacturer costs, given that Q is the same for the manufacturer and the retailer • For this, we can modify the EOQ formula to include both - And see why this could give the manufacturer an incentive to reduce the unit cost for larger orders Does This Lower SC Costs? • Compare the values with the retailer's optimal EOQ and the SC optimal EOQ

Postponement and SI

What is the likely impact of postponement on SI? • Without postponement, product differentiation occurs early in the SC - Most inventories are disaggregated, less "flexible" • With postponement, more inventory is carried as components - More flexible, aggregated • Postponement and CC allow aggregation • Intuition suggests CC & P allow for smaller SI! Key Points • Component commonality and postponement an reduce the amount of SI required to achieve a given CSL • These can be combined with joint ordering to reduce costs

Why is it important to account for variable lead times in determining how much SI to hold?

When Supply Is Uncertain • We need to re-visit the sD,L • Now, it needs to include the supply uncertainty also • Intuitively, we would hold more safety inventory Modifying sD,L • Previously: sD,L = (√L)(sD) - This included lead time, but as a constant • Now: sD,L = √(L*sD^2 +D^2*sL^2) - D^2*σL^2 is the new component of this that accounts for the variable lead time

What is the impact of centralizing SI to serve multiple outlets on the total quantity of SI held?

With 1 Centralized Facility • Demand is the sum of the demands at K=4 outlets (D1+D2+D3+D4) - Remember, each outlet can vary - But D and sD is same for each outlet • If we assume that the demands at each outlet are not correlated, • sD,L,K = (√L)(√K)(sD) • SI = (Z)(sD,L,K) Aggregation Benefits • Reduces the amount of safety inventory needed • Reduces total inventory held • Reduces flow time

How would the amount of that incentive be calculated?

[from jeans example Class_15 pg 45] • Manufacturer could offer the retailer a quantity discount so that Q=9,165 is optimal for the retailer • How? The difference in cost to the retailer with a Q=9,165 is $4,059-$3,795 = $264 • If manufacturer offers a quantity discount based on this will cause Q=9,165 • $264/120,000 is about 0.2 cents per unit • Cost to retailer would be $2.997799/unit

*? How can you use the Z-statistic, the the DL and the sD,L to determine the CSL?

can use these to find ROP & CSL

Which is often the largest component of inventory management costs?

cost of capital?

EOQ Notation & Cost Components

• C = Unit cost ($/unit) • D = Annual demand, units • Q = Quantity per order (units/order) • h = Holding cost (proportion of C) • S = Fixed order cost ($/order) • Orders per year = D/Q Materials Cost = (C)(D) Annual Ordering Cost = (S)(D/Q) - Cost per order times orders per year Annual Holding Cost = (Q/2)(h)(C) - Average (cycle) inventories time unit holding costs (h, the proportion, times C) Total Costs = MC + OC + HC = TC = (C)(D) + (S)(D/Q) + (Q/2)(h)(C)

What is the basic definition of the CSL, expressed in terms of a probability of a stockout?

• CSL is the probability of a not stocking out during the replenishment cycle - (Over many replenishment cycles) • A stockout occurs if demand during the lead time L is > the ROP - That is, a stockout occurs if sum of demands during L > ROP • CSL = Prob that demand during L ≤ ROP

Are there any reasons why a firm (supply chain) might not want to centralize inventories?

• Can increase response time to customer order - Here we assumed instantaneous transport from DC to outlet - Next day (direct) delivery requires multiple outlets • Can increase transportation cost - For customers or for product - Did not consider this at all here One Last Point • We assumed that demand at the outlets was not correlated • This is a main reason why the aggregation works to lower safety inventories • If demand is perfectly correlated (same value at each outlet each time), then there is no value to aggregating - We would need to hold the same safety inventories as for 4 individual outlets

What are the different types of inventory (which describe both the form of the inventory and its purpose)?

• Cycle Inventory is held to satisfy customer demand between receipts of shipments from suppliers - Cars on an an auto dealer's lot - Arises due to cost savings in production, transportation or purchasing goods in larger lots, but also customer responsiveness • Safety Inventory is held to in case demand exceeds the expected (forecasted) amount - Toys during the holiday season - Too much safety inventory is costly, too little is "not responsive" to customers • Seasonal inventory is held to meet predictable seasonal changes in demand - Seasonal needs may exceed production capacity so, make now and store - Or costs of changing capacity are large

What are some of the differences in the management of dependent versus independent demand inventories, push versus pull inventories and system-wide versus individual facility inventories?

• For dependent versus independent demand - Independent requires a forecast • Push versus pull - Pull uses customer orders, holds less inventory, uses short-term forecasts - Push holds inventory in anticipation of orders, uses longer-term forecasts • System versus individual facility - System makes IM decisions across multiple nodes in a logistics system

What are some of the key questions for inventory management?

• How much and when to order? • Where should inventory be held? • What specific items should be available at specific locations? - IM needs to balance service and cost

Types of Inventory II

• In-Transit or Work-in-Progress Inventory - Cars on an assembly line - Goods being transported to a customer or to the buyer • Anticipatory inventory is held when the SC believes an "unusual" event will negatively affect its source of supply - Milk before snowstorms or hurricanes • Maintenance, Repair and Operations inventory (MRO) • Supplies consumed during production that do not become part of the finished good - Repair components, office supplies, cleaning supplies, furniture, etc. • Often, not managed like other types of inventory - APICS Magazine, January 2013

What is the trade-off involved in deciding how much SI to hold?

• Increased product availability means more sales and margin - Fewer stockouts and lost sales • Larger inventory means larger holding costs - Especially for industries with high IDU - Or short product life cycles (end up with low-valued inventory) Best Strategy... • Companies that provide better product availability with lower levels of safety inventory will out perform others - Measured by average flow time (Q/2D)

How would you describe the trade-off between responsiveness and efficiency for inventory management?

• Is a part of competitive strategy - Which customer needs the SC will meet • The form, location and quantity of inventory affect the efficiency and the responsiveness of the SC - Efficiency = low cost - Responsive = meets customer needs

Why are inventories important to manage correctly (for both manufacturers and retailers)?

• Is an important component of demand fulfillment • Inventories are often the largest asset category for manufacturers and retailers • Inventories affect financial performance through costs and revenues - Delivery delays influence customer satisfaction and future sales

What are some of the reasons why companies (supply chains) hold inventory?

• It's a mismatch between supply & demand! - Between production and sales • Economies of scale in production - For steel production, long and large production runs are much lower cost - So, make a lot in a run and store it • Increase the demand that can be satisfied by having the product available to a buyer - "Push process" that anticipates demand - Make the SC more "responsive" • Economies of scale in sourcing - Volume discounts from suppliers may make it attractive to purchase in bigger lots (orders) • Seasonality of production - Many commodities (food) are produced during a single growing season, and must be stored to ensure availability at other times - Demand can be seasonal also (Turkeys at thanksgiving)

Receiving Costs

• More products in a single order means more variety • Some costs are not fixed, but vary with the number of products • Must update inventory records for more items per shipment (truckload) • Physically placing inventory is more costly • Must account for these - Before we assumed they were fixed • Advanced Shipping Notices (ASN) are files with exact records of truck content sent by the supplier - Reduces receiving cost, increases accuracy, allows shipper to know the "fill rate" and can be used for billing • RFID (Radio Frequency Identification) can also be used to reduce receiving costs

What is one reason that a supplier might offer a buyer a "lot-based discount"?

• One reason: the order and inventory costs that manufacturers incur in order to supply retailers can be lower with quantity discounts • This can apply to commodity products, where the price is set by the market

Key Points Class_23

• Periodic replenishment evaluates inventory at a review interval, then ordersan amount to bring inventory to a OUL • The value of SI and OUL can be calculated with methods similar to those for continuous replenishment • Periodic replenishment results in larger safety inventory than continuous replenishment, due to a longer time for which demand must be covered from SI

Why is it that PFR, OFR and CSL can be thought of as probabilities? *? What does that allow us to do to calculate them?

• Product Fill Rate - Probability that product demand is satisfied from product in inventory • Order Fill Rate - Probability that orders are filled from product in inventory • Cycle Service Level - Probability that replenishment cycles end with all demand being met

What are the basic measures of product availability? How do they differ?

• Product Fill Rate - Proportion of product demand is satisfied from product in inventory • Order Fill Rate - Proportion of orders that are filled from product in inventory • Cycle Service Level - Fraction of replenishment cyclesthat end with all demand being met

Why is product availability (in general) a component of inventory management?

• Product availability is the fraction of demand (%) that can be served on time from product held in inventory - % of total sales (some measures, % of orders) - "On time" depends on the usual (or promised) delivery delay • A benefit of holding larger inventories is increasing product availability, which is one component of responsiveness

Product Fill Rate (PFR)

• Proportion of demand satisfied frominventory • Calculate based on demand, not time Example: • Customers ordered 100,000 units • Only had available to sell 95,000 units • PFR = 95,000/(100,000) = 0.95 = 95%

Order Fill Rate (OFR)

• Proportion of orders satisfied from inventory • Calculate based on orders, not time • All products in an order must be filled Example: • 2 million total orders placed • 1.5 million orders filled completely from inventory • OFR = 1.5/2 = 0.75 = 75%

Cycle Service Level (CSL)

• Proportion of replenishment cycles satisfied from inventory - All orders for all products • Do I run out of inventory between receipt of orders? - If so, then I have not satisfied demand from inventory during that replenishment cycle • Calculate based on cycles, not time Example: • 10 replenishment cycles - 100 weeks for jeans if order every 10 weeks • Ran out of inventory between receipt of orders 5 times - Recall the example from last time using the random number generator! • CSL = 5/10 = 0.5 = 50%

Key Points Class_15

• Quantity discounts are common in SC • QD change the EOQ, increasing holding costs and cycle inventory - Often by an % amount much larger than thechange size of the discount • QD can arise because they minimize overall SC costs - One SC member has an incentive to offer discounts to another

Why CC and Postponement?

• Reduces relevant demand uncertainty - Aggregated demand for components is more predictable than for individual (final) products - Shortens the forecast horizon for the final products (more accurate forecast) - Some products more like make-to-order, rather than make-to-stock • Economies of scale in production of components and product design

What are some of the basic strategies that supply chain managers could use to reduce the amount of SI they hold? Why would these strategies reduce SI, and what are some of the challenges to implementing them?

• Safety inventory = (Z)(sD,L) • Reduce CSL (lower Z) would reduce SI - But product availability will be lower • If we want to maintain product availability (like CSL=95%) what can we do? • Two options: 1) Shorten lead time (L) 2) Reduce uncertainty (sD,L) Shorten L: Impacts on SI • Recall that sD,L = (√L)(sD) • So, if we reduce L, we reduce sD,L • Example: • Reduce L from 16 weeks to 4 weeks • sD,16 = (√16)(sD) = 4sD • sD,4 = (√4)(sD) = 2sD • So, we can cut sD,L in half if we do this • This would also cut safety inventory in half - Because SI = (Z)(sD,L) Reduce σD: Impacts on SI • Recall that σD,L = (√L)(σD) • So, if we reduce σD, we reduce sD,L • Example: • Reduce σD from 9.1 to 6.0 • σD,4 = (√4)(9.1) = 18.2 • σD',4 = (√4)(6.0) = 12.0 • So, we can cut sD,L by 1/3 • This would also cut safety inventory by 1/3 Why Not Shorten L, Reduce σ? • Shortening L usually requires effort on the part of the supplier, but saves $ for the buyer - Need to share the benefits with supplier • Reducing σ requires better forecasting so that the demand can be predicted more accurately - Can be difficult to do (as we mentioned) - Focus on customer demand data - Use CPFR

How would you use the 4-step process to determine if it is appropriate take advantage of a "lot based" discount offered by a supplier?

• Step 1: Calculate the EOQ at each cost • Step 2: Select the best order quantity Q for each cost by comparing to price schedule - If the Qi you calculated is within the volume range for that cost, Q*i is just that quantity - If the Qi you calculated is greater than maximum volume for that cost, it can be dropped from consideration - If the Qi you calculated is less than the minimum volume for that cost, Q*i is the minimum volume required for that cost • Step 3: Calculate the total cost for ordering the Q from Step 2 - Using the formula: TCi = (D/Qi)S + (Qi/2)hCi + DCi • Step 4: Choose the Q with the lowest total cost

A key decision for inventory management is what quantity to order (as a part of the replenishment cycle, most typically for a retailer ordering from a manufacturer). How is this order quantity determined to minimize costs, and what are some of the simplifying assumptions that are required in the most basic case?

• The Economic Order Quantity indicates how frequently to order and what size the order will be to minimize inventory costs • There is a trade-off between more frequent, smaller orders and larger, less frequent orders • Why? More frequent orders mean smaller holding costs, but higher ordering costs Assumptions for EOQ • Continuous, constant, known demand • Constant, known replenishment or lead time • All demand satisfied (- No stockouts) • Constant materials cost (- No volume discounts) • No in-transit or WIP inventory • Only one item in inventory (- No interactions) • No capital constraints • Infinite planning horizon

Why does the inventory profile for constant demand display a "sawtooth" pattern? How is this pattern different if demand is not constant (see 3/15/13, for example)?

• The lot or batch size is the quantity that is purchased (ordered) or produced at a time Inventory Profile Assumptions • Here, we assume constant, known demand - No need to forecast it, we know exactly! Not realistic.. • Retailer places the same quantity order every 10 weeks - Never any variation in quantity or order - Again, not realistic (but we have to start somewhere!)

How do we measure demand uncertainty for the purposes of calculating SI?

• This looks at how randomthe "random component" is - We can't predict the exact value, but we assume we can determine some basic characteristics • Forecasting is about the "systematic component", so this is similar to assessing the "forecast error" Notation: • D = Average demand per period - NOT the annual demand now • L = lead time, periods - Time between when an order is placed and when it is received (assume known, constant) • σD = standard deviation of demand - Or forecast error - Per period (like week or quarter) - We usually estimate σ because it is not known • Formula is: sD = sqrt((Dt - D)^2) • We can interpret this as a measure of variation in demand, or how large is the forecast error (D-F, similar to F-D) • sD = Similar to square root of MSE!

How can we calculate the ROP required to achieve a certain CSL under a continuous review replenishment policy?

• Use the Normal distribution tables in reverse • Find the probability in the table • Determine the Z-statistic • Convert the Z-statistic to an ROP value

Relationship PFR & CSL

• Usually CSL < PFR • Even if have a stockout during the replenishment cycle, it is likely that a much higher proportion of the demand was met from inventory

Why is it important to calculate the mean and the standard deviation of demand DURING THE LEAD TIME, rather than just for a given week, when determining SI?

• We need to know the variation during the lead time - How much might demand vary during the time between when we order and when we receive the shipment? • This is the important factor for safety inventory D and σ During Lead Time • If we assume that demand in each period is not related to demand in a previous period -Demand is "not correlated" over time,It is "independent" • If demand is not correlated over time • Then the expected (average) demand during the lead time is: • DL = D*L (that is, D times L) • The standard deviation during L is: • σD,L = √L*σD (square root of L times σD) - Where we will measure σD with sD - So, really sD,L = √L*SD Coefficient of Variation • Ratio of sD/D • Measures variation in demand relative to demand • Allows comparisons across products

What are some of the "key questions" about the "best" level of SI?

• What is the appropriate level of product availability? • How much safety inventory is needed to achieve that level of product availability? • What actions will improve product availability with lower safety inventory?

Key Points Class_16

• When demand is not certain, supply chains hold safety inventory - To meet unexpected demand, but extra cost • Appropriate safety inventory depends on demand uncertainty - Also supply uncertainty and desired availability • Expected D, sD and cv are important measures of variation in demand - Which is similar to forecast error

What is the difference between the F(SI/sD,L) and the f(SI/sD,L) in the formula for expected lost sales? How would you find a value for the f(SI/sD,L)?

• Where F is the cumulative normal distribution we've used before • f is the standard normal distribution (not cumulative) • And the F( ) and f( ) mean you look up the values of these for the value SI/sD,L Where is f(SI/sD,L) Value From? • This is the normal distribution "density function" not the "cumulative distribution" • A table http://myhandbook.info/table_normal_density.html • Your calculator http://pages.central.edu/emp/lintont/classes/fall99/Intro_Stat/tinormal.html • A website http://www.danielsoper.com/statcalc3/calc.aspx?id=56 • Excel, using the function - NORMDIST(SI/sD,L,0,1,0)