Lecture 3: Inventory Management Flashcards Preview

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Flashcards in Lecture 3: Inventory Management Deck (34):

Define inventory.

“The stocks or items used to support production (raw materials and work-­in-­process items), supporting activities (maintenance, repair, and operating supplies), and customer service (finished goods and spare parts).”

- APICS (Association for Operations Management) Dictionary


Sketch the inventory/service tradeoff curve. What is the limitation of this?

See diagram:

  • Inventory on the y-axis, service on the x-axis
  • Non-linear trade-off between high inventory and good service
  • An oversimplification  - also need to consider location/mix/quality of inventory

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Describe three types of inventory (by time).

  1. Raw materials - materials to which the manufacturer has not yet added value
  2. Work-in-Progress (WIP) - materials to which the manufacturer has added some value, but still has more to add
  3. Finished Goods (FG) - goods ready for shipment to customers, with no more value to be added
    • Also considers service parts (for maintenance and repair)
    • Could be held in distribution centres


Describe four types of inventory (by function)

  1. Cycle stock - an active component that depletes over time, and is replenished cyclically
  2. Safety stock - surplus held to protect against fluctuations of supply, demand and production
  3. Pipeline stock - stock created by the time spent to move and produce inventory (Little's Law), used to reduce lead times
  4. Anticipation stock - stock held to smooth output rates by stockpiling during the slack season, or overbuying before a price increase or capacity shortage


What is the significance of inventory on a macro level?

  • Total investments by firms in inventory in the US is ~10% of GNP
  • Current US inventory levels (11/2016) = $1.8 trillion
    • 33% held by retailers
    • 33% held by wholesalers
    • 34% held by manufacturers
    • (Spiked at the end of 2008)
  • Enormous potential for efficiency increase by controlling inventories


Give an example of a firm who has recently made inventory reduction efforts

Wal Mart

  • Sales of over $300 billion, operates more than 6,000 stores
    • 3,500 in the US and > 2,500 in 15 other countries
  • Employs more than 1.3 million people
  • Has over 10,000 stock-­keeping units (SKUs) at each store
  • Manages 60 million individual stocking locations and at least 0.25 million line-­item orders per day
  • Became the world’s largest retailer in large part because of its excellent management of inventory

Announced an effort to reduce inventory costs by $6 billion (20% of its yearly total) in 2006

  • This reflects its strategy of cutting costs and improving margins
  • Suppliers took notice: WalMart accounts for 10-30% of many suppliers’ sales
  • The inventory correction also affects shippers, with estimates of a $300 - $400 million reduction in freight revenue



Give 6 arguments for inventory

  1. Need pipeline inventory - Little’s Law:
    1. A minimum inventory is needed to run the factory
  2. Buffer against uncertainty
  3. To meet fluctuations in market demand (seasonality, promotions, etc.)
    • Production throughput (quality, machine breakdown, etc.) 
    • Supply of components
  4. Exploitation of price fluctuations
    • Raw materials: cocoa, coffee, etc.
  5. Smoothing or levelling of production
    • A small variation can be buffered through final goods inventory
  6. Enables the achievement of economies of scale


Describe one method of protection against cost fluctuations, other than holding inventory

  • Option pricing - paying suppliers a deposit to reserve capacity, i.e. time and quantity
  • Making upfront payments helps suppliers manage their own risk
  • Example: Southwest Airlines protected themselves during oil price fluctuations using fixed variable costs -> didn't have to increase prices


List 5 hidden costs of holding inventory.

  1. Longer lead times

    • Time spent adding value is typically only 2-5% of the total time spent in the job shop

  2. Reduced responsiveness

  3. Underlying problems are hidden, rather than being exposed and solved (rock-boat analogy)

  4. Quality problems are not identified immediately

  5. No incentive for improvement of the process



Outline the additional costs associated with holding inventory. Give an estimate of the total cost of this, and explain whether this is usually accurate.

  1. Cost of capital: value*i
    • Where i = interest rate per unit time
  2. Opportunity cost
    • ​​How much would the capital earn otherwise?
  3. Depreciation of goods
  4. Stock obsolescence and deterioration
  5. Quality defects due to handling
  6. Labour and handling
  7. Warehousing, rent and energy
  8. Insurance and overheads to admin labour, space, etc.

Overall costs:

  • Typical estimate 20-­30% of value per annum
  • In practice, often quality, depreciation, and opportunity cost are not considered

-> estimates almost always too conservative


Why is inventory reduction alone not a suitable technique?

  • Rock-boat analogy
  • Problems such as damage, supply issues, defects, shortages and equipment breakdowns are hidden by an inventory buffer
  • Reducing inventory exposes these unresolved issues


State Little's Law, defining each of the key terms. What kind of system is this based on?

John D.C. Little’s Theorem (or Little's Law) gives a simple relation between inventory, production rate and lead-­time:

I = r * T


  • I = the number of items or inventory in a system [units]
    • This determines the minimum pipeline stock (for the whole system)
  • r = the production rate at which items arrive/leave [units/period]
  • T = the throughput lead-­time (time spent in the system [periods]

Applies to all types of systems

  • All based on average, steady-­state values.


Give two metrics that can be used to measure inventory performance

Days of Inventory (DOI)

  • The number of periods an organisation can satisfy demand using its current inventory

DOI = Quantity of Inventory [units] / Average Demand [units/day]

Stock Turns

  • The number of times an organisation replaces its stocks during a period (usually measured annually)
  • Often used as a key measure for operational and cost efficiency

Stock Turns =  GOGS in Period [£] / Avg. Inventory Valuation [£]


What are typical values for stock turns? Outline the significance of stock turns wrt holding cost.

Stock turns value:

  • Typically 5 - 20, world class lean manufacturers achieve 40+
  • Varies between industries: 
    • Bakery products very high (median 23)
    • AV equipment and electric components very low (3.9 and 4.9 respectively)

Lower stock turns means each item is stored for longer before being sold -> higher holding cost

  • A realistic stock holding cost is 22-40% of value per year
    • This includes handling, cost of quality, obsolescence and warehousing


What is ABC analysis? What implications does this for re-ordering stock?

Inventory control models are part-­specific, so the attention given to a part depends on cost impact

ABC Classification (H Ford Dickie, 1951)

  • Compares the number of parts and the Usage Value
    • Usage Value = Unit Value * Volume (per period|)
  • Parts held in inventory should depend on this:
    • A - 20% of parts = 80% of usage value
    • B - 30% of parts = 15% of usage value
    • C - 50% of parts = 5% of usage value

(exact percentages differ from one author to another)

  • Relates Pareto’s Law of Analysis, the “80-­20 Rule”
    • 20% of inventory held should contribute 80% of usage value
    • Vilfredo Pareto (1848-­1923), study of income in Italy in 1897

Relates to stock re-ordering and control:

  • A - order what is needed, when it is needed (MRP/JIT)
    • Watch closely, minimise stock, aim for flow
    • (Cars - track each individual item)
  • B - continuous review
    • Review ordering policy from time to time, observe
    • (transmissions - count the number on hand)
  • C - automate replenishment, use ROP as a trigger
    • (fuses - buy a box or two and make sure there's always a box on the shelf)


List the four basic approaches to ordering, giving examples of methods used in each

  1. Fixed Order Quantity Models
    • ​​Economic Order Quantity (EOQ)
    • Re-Order Point (ROP)
  2. Fixed Time Period Models
    • ​Fixed Period Ordering
    • Lot-for-Lot (LfL) ordering, aka Order-Up-To (OUT)
    • Period Order Quantity (POQ)
  3. Variable Order Quantity and Ordering Interval
    • ​Least Unit Cost (LUC)
    • Least Total Cost (LTC)
    • Past-Period Balancing (PPB)
  4. Material Requirements Planning (MRP)
    • ​​Calculating time-phased requirements


Sketch the sawtooth inventory cycle, indicating the ROP and LT. What is the limitation of this model. 

Limitation: requires everything to be known and predictable

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Describe a Fixed Order Quantity inventory management system, outlining which types of items this is used and why. Give advantages, disadvantages and an example.

A system where the order quantity remains constant but the time between orders varies

  • Example: always ordering a dozen eggs when there are only 2 left in the basket


  1. Average inventory is lower -> preferred for more expdensive items
  2. Quicker response to stockouts


  1. More expensive to maintain, due to inventory record-keeping costs


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Describe the processes of two-bin and three-bin re-ordering

2-bin reordering:

  • Bin 1 -> items being used
  • Bin 2 -> Reorder level + safety inventory
    • i.e. reorder when bin 1 is empty

3-bin reordering:

  • Addition of a third bin makes it clear when demand is exceeding expectations, i.e. if the second bin empties before replenishment


Illustrate, using a sketch,  the trade off associated with choosing an order size? 

  • Using a large order size (ordering infrequently) -> large inventory -> large holding ost
  • Using a small order size (ordering frequently) -> large fixed cost of ordering
    • Clerical / labour cost of processing an order
    • Fixed costs imposed by supplier
    • Inspection and return of poor quality products
    • Transport costs
    • Handling costs
    • Labour cost of organising transportation

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What is the Economic Order Quantity?

The order quantity that minimises the total cost per period


Give the formula for the total inventory cost per period, defining each of the terms

T(Q) = 0.5Q·CH+ (D/Q)C0 [+ DC+ SS·CH]

total cost per period =

avg inventory level * holding cost per item per period

+ orders per period * (fixed) cost of placing one order

+ demand rate per period * cost per item (i.e. variable cost)

+ safety stock level * holding cost per item per period


NB these last two terms have no effect on the EOQ

  • They are independent of Q


How can the total cost formula be used to find the EOQ? Give 2 methods.

  1. Differentiate wrt Q and set = 0 to find turning points
    • Differentiate again to check point is a minimum
  2. Marginal Cost analysis
    • At minima, the MC of ordering both one more and one less unit is negative


Give the formula for the minimum reorder point needed to ensure inventory is replenished before a stockout occurs. 

R = dL + SS

  • R = reorder point
  • d = average demand per time period (constant)
    • ​E.g. d = D/working days in the year
  • L = number of time periods between placing order and delivery (e.g. number of days)
  • SS = safety stock


How is EOQ calculated when there are incremental discounts?

When there are incremental, i.e. wholesale, discounts:

  1. Replace Cv with the average unit cost CAVG = C(Q)/Q
  2. Calculate the EOQ for each price interval
  3. For each interval, find the feasible value Qj* that minimises T(Qj)
    • I.e. max[EOQj, minimum order for that price]
  4. Select the minimum T(Qj) over j=0, ... ,n
    • Call this T*(Qj)
  5. Q* is the value of Qj* corresponding to T*(Qj)



When is Economic Production Quantity used instead of EOQ? With the aid of a graph, give the total cost T(Q) for this case.

Used when a firm is producing the batch themselves, rather than ordering it from an external supplier. Mostly the same as the EOQ, but:

  1. Cost of ordering C0 → cost of set up Cs
    • Clerical/labour cost of setting up a machine
    • Loss of production while the set up takes place
    • Return of poor quality products after set up
  2. The batch does not arrive instantaneously
    • It builds up at production rate P

Assuming a constant production rate P > D for each batch, this gives the graph shown

  • Starting with the EOQ formula:
    • Replace C0 with Cs
    • Replace CH with CH(1 - D/P)
      • Average stock is now 0.5Q·(1-D/P)
      • [time to reach peak t' = P/Q]
      • [Imax = (P-D)t' = Q(1-D/P)]


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Explain, with the aid of a graph, the meaning of Fixed Time Period ordering. Give the advantages and disadvantages.

A system where the time period between orders remains constant, but the order quantity varies.

  • Example: refillng the petrol tank of a delivery truck at the end of each day.
  • Every T time periods, the system replenishes to S
    • Can add another variable s, so system only replenishes if stock is below s


  • Reduced chance of stockouts
  • Useful when purchasing multiple items from one vendor, to save on ordering cost



  • Larger average inventory → higher holding cost

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What is lot-for-lot ordering?

  • A form of FTP ordering
    • Also called pass-­on-­orders, or order-­up-­to model (OUT)

  • Customer orders are passed on to the supplier as they come in, without interference

    • Only order from the supplier what is demanded by the customer

  • No fixed order quantity, but fixed time intervals (each period)

  • Optimal solution for inventory cost, but ordering cost may be high


What is Period Order Quantity (POQ) ordering?

EOQ logic, modified so that we order to cover demand for a whole number of periods, while still minimising cost - ordering interval is computed, rather than ordering quantity

  1. Calculate the EOQ for a given period
  2. Calculate the average time between orders = EOQ/D
  3. This is the Economic Cycle Time


List 4 benefits of the EOP and EPQ models.

  1. Robust - relatively insensitive to errors in estimating D, CH, CO/CS
  2. Tends to inflate batch/ order sizes
  3. Can be adapted to different situations and types of inventory
  4. • Empirically, EOQ/EPQ models are <12% away from optimum


List 10 issues with the EOQ and EPQ models.

Rigid Assumptions:

  1. Demand is constant and steady, and continues indefinitely
  2. (EOQ) whole replenishment lot arrives at same time
  3. Replenishment lead-­time known
  4. Order size is not constrained by supplier, no min/max restrictions
  5. Holding cost per item per period is constant
  6. Cost of ordering/setup is constant
  7. Item is independent of others - benefits from joint reviews are ignored
  8. Doesn’t encourage reduction of fixed ordering/setup costs

Problem Cost Accuracy:

  1. Issues determining how much set-­up or placing an order costs
  2. Holding costs may not be fully known
    • Often calculated at interest level (cost of capital)


Describe Variable Order Quantity  and Variable Ordering Interval methods, giving three examples.

Methods that allow both lot size & ordering interval to vary from batch to batch - demand doesn't have to be constant

  • Still assume demand is known, even if it is not constant
  • Seek to cover demand for a whole number of periods
  • As in EOQ, the objective is to minimise the sum of setup and inventory costs

3 possible methods:

LUC -­ Least Unit Cost (a heuristic)

  1. Consider seeking to cover demand for next n= 1,2,3... periods
  2. Find cost/unit for each value of n (incl. holding cost)

  3. Stop just before this starts to rise, and restart calculation from there.

  4. Assume holding costs are only incurred when items are held over from one period to the next

NB this is an open system - looks at one cycle at a time, rather than all of the possible interactions between different cycles

  • Looks myopically at what it needs to do right now

LTC -­ Least Total Cost

  • Consider seeking to cover demand for next n=1,2,3... periods (as LUC)
  • Choose n to most closely balance set-­up and inventory cost for this batch (average cost per period for the batch is minimised)

PPB -­ Part-­Period Balancing

  • Basic version as LTC
  • Advanced versions include “look-­ahead / look-­back’ facility to see if simple modifications to schedule reduce total costs