Lecture 3: Inventory Management

Question 1

Draw the inventory/service trade off curve

Answer 1

• Lots of inventory does not necessarily mean a really good service. Depends on where inventory is located. If company has a good understanding of customers/market then it can produce the inventory when required.

Question 2

What are the different types of inventory through raw materials to finished goods?

Answer 2

• Raw Materials
  
  • Materials to which the manufacturer has not yet added value.
• Work-in-progress or Work-in-process (WIP)
  
  • Materials to which the manufacturer has added some value but still has more to add
• Finished Goods (FGI)
  
  • Goods ready for shipment to the customers, with no more value to be added
  • Also consider service parts (maintenance and repair)

Question 3

What are the types of stock by function?

Answer 3

• Cycle Stock
  
  • Active component that depletes over time, and is replenished cyclically. or example, suppose a baker makes three types of bread, each of which is equally popular with its customers. Because of the nature of the mixing and baking process, only one kind of bread can be produced at any time. The baker would have to produce each type of bread in batches. The batches must be large enough to satisfy the demand for each kind of bread between the times when each batch is ready for sale. So even when demand is steady and predictable, there will always be some inventory to compensate for the intermittent supply of each type of bread.
• Safety Stock
  
  • Surplus held to protect against fluctuations of demand, production and supply.
  • This minimum level of inventory is there to cover against the possibility that demand will be greater than expected during the time taken to deliver the goods. This is buffer, or safety inventory. It can also compensate for the uncertainties in the process of the supply of goods into the store, perhaps because of the unreliability of certain suppliers or transport firms.
• Pipeline Stock
  
  • Stock created by the time spent to move and produce inventory. There is lead time of production, e.g takes a week to produce stock then need stock already sitting ready to be ordered to make up for lead time.
  • Pipeline inventory exists because material cannot be transported instantaneously between the point of supply and the point of demand. If a retail store orders a consignment of items from one of its suppliers, the supplier will allocate the stock to the retail store in its own warehouse, pack it, load it onto its truck, transport it to its destination, and unload it into the retailer’s inventory. From the time that stock is allocated (and therefore it is unavailable to any other customer) to the time it becomes available for the retail store, it is pipeline inventory.
• Anticipation Stock
  
  • Stock held to smooth output rates by stockpiling during the slack season or overbuy before a price increase or capacity shortage
  • Rather than trying to make the product (such as chocolate) only when it was needed, it was produced throughout the year ahead of demand and put into inventory until it was needed.
  • Anticipation inventory is most commonly used when demand fluctuations are large but relatively predictable. It might also be used when supply variations are significant, such as in the canning or freezing of seasonal foods.
• De-coupling inventory
  
  • ​Each of these areas can be scheduled to work relatively independently in order to maximize the local utilization and efficiency of the equipment and staff. As a result, each batch of work-in-progress inventory joins a queue, awaiting its turn in the schedule for the next processing stage.

Question 4

What is the US inventory level and what does it show?

Answer 4

US inventory level (11/2016): $1.8 Trillion

33% held by retailers

33% held by wholesalers

34% held by manufacturers

Enormous potential for efficiency increase by controlling inventories

Question 5

What are arguments for Inventory?

Answer 5

• Little’s Law (see later) implies: There is a minimum inventory needed to run the factory
• Buffer against uncertainty
• Market demand (seasonality, promotions, etc.)
  
  • Production throughput (quality, machine breakdown, etc.)
  • Supply of components
• Exploitation of price fluctuations
  
  • Raw materials: cocoa, coffee, etc.
• Smoothing or levelling of production
  
  • Small variation can be buffered through final goods inventory
• Enables the achievement of economies of scale - can only be achieved by producing large batches.

Question 6

What are arguments against inventory?

Answer 6

• Cost involved:
  
  • Cost of capital: value*i, i = interest rate per unit time
  • Opportunity cost: How much would the capital earn otherwise?
  • Depreciation of goods
  • Stock obsolescence and deterioration
  • Quality defects due to handling
  • Labour and handling
  • Warehousing, rent and energy
  • Insurance and overhead to admin labour, space, etc.
• Overall costs:
  
  • Typical estimate is 20-30% of value per annum
  • In practice, often quality, depreciation, and opportunity cost are not considered
  • Key issue: estimates almost always too conservative!

Question 7

What are the hidden costs of inventory?

Answer 7

• Longer lead times - Producing batch B while batch A has been ordered
• Reduced responsiveness - due to longer lead times
• Underlying problems are hidden rather than being exposed and solved
• Quality problems are not identified immediately
• No incentive for improvement of the process

Question 8

Explain Little’s Law

Answer 8

Question 9

Question 10

What are two equations used to measure inventory performance?

Answer 10

• Typical stock turns: 5 to 20, world-class lean manufacturers achieve >40

Question 11

Explain the link between Stock Turns and Holding Cost.

Answer 11

• Suppose stock turnover is 5 times per year
• Thus, each item sits in the warehouse for about 1/5 of a year
• 22-40% represent realistic stock holding cost, including handling, cost of quality, obsolescence and warehousing
• The cost of holding inventory is hence approximately: 1/5 * (22 to 40%) = 4.5% to 8% of sales value
• Stock turns is often used as key measure for operational and cost efficiency

Question 12

Explain the ABC system and the Pareto Rule.

Answer 12

Inventory Priorities

• In any inventory some items will be more important to the organization than others. Some might have a very high usage rate, so if they ran out many customers would be disappointed. Other items might be of particularly high value, so excessively high inventory levels would be particularly expensive.
• One way of discriminating between different stock is usage value (their usage rate multiplied by their individual value). Items with a particularly high usage value are deemed to warrant the most careful control.
• Generally, a relatively small proportion of the total range of items contained in an inventory will account for a large proportion of the total usage value. This phenomenon is known as the Pareto law (after the person who described it), sometimes referred to as the 80/20 rule. It is called this because, typically, 80 per cent of an operation’s sales are accounted for by only 20 per cent of all stocked item types.
  
  • Class A items are those 20 per cent or so of high-usage-value items which account for around 80 per cent of the total usage value. Watch closely, minimise stock, aim for flow.
  • Class B items are those of medium usage value, usually the next 30 per cent of items which often account for around 10 per cent of the total usage value. Review ordering policy from time to time, observe.
  • Class C items are those low-usage-value items which, although comprising around 50 per cent of the total types of items stocked, probably only account for around 10 per cent of the total usage value of the operation. Automate replenishment, use reorder point as a trigger.

Question 13

Although annual usage and value are the two criteria (ABC) most commonly used to determine a stock classification system. What other criteria might also contribute towards the (higher) classification of an item?

Answer 13

Consequence of stock-out - High priority might be given to those items which would seriously delay or disrupt other operations, or the customers, if they were not in stock.

Uncertainty of supply - Some items, although of low value, might warrant more attention if their supply is erratic or uncertain.

High obsolescence or deterioration risk. - Items which could lose their value through obsolescence or deterioration might need extra attention and monitoring.

Question 14

What are the four basic approaches to ordering?

Answer 14

• Fixed Order Quantity Models
  
  • Economic Order Quantity (EOQ)
  • Re-Order Point (ROP)
• Fixed Time Period Models
  
  • Fixed Period Ordering
  • Lot-for-Lot (LfL) ordering aka Order-Up-To (OUT)
• Period Order Quantity (POQ)
  
  • Variable Order Quantity and Ordering Interval Least Unit Cost (LUC)
  • Least Total Cost (LTC)
  • Part-Period Balancing (PPB)
• Material Requirements Planning (MRP)
  
  • Calculates time-phased requirements

Question 15

Draw the saw tooth inventory cycle.

Answer 15

Question 16

Explain reorder point and safety stock with an inventory profile.

Answer 16

Question 17

Explain the point of EOQ formula, by illustrating two re-order different approaches to re-ordering stock. (This is all under a fixed quantity order model)

Answer 17

• Plan A, represented by the unbroken line, involves ordering in quantities of 400 at a time. Demand in this case is running at 1,000 units per year. Plan B, represented by the dotted line, uses smaller but more frequent replenishment orders. This time only 100 are ordered at a time, with orders being placed four times as often. However, the average inventory for plan B is one-quarter of that for plan A.
• EPQ is about finding the balance between using a large order size (i.e., ordering infrequently), and using a small order size (i.e., ordering frequently).

Question 18

Explain Fixed Order Quantity. (Give adv/disadv etc)

Answer 18

• A system where the order quantity remains constant but the time between orders varies
• Preferred for important or expensive items because average inventory is lower
• Provides a quicker response to stockouts
• Is more expensive to maintain due to inventory record-keeping costs
• Example: Always purchasing a dozen eggs when there are only two eggs left in the refrigerator.
• The virtue of this approach is that, although the timing of orders may be irregular (depending on the variation in demand rate), the order size (Q) is constant and can be set at the optimum economic order quantity. Such continual checking on inventory levels can be time-consuming, especially when there are many stock withdrawals compared with the average level of stock, but in an environment where all inventory records are computerized, this should not be a problem unless the records are inaccurate.

Question 19

Explain two bin and three-bin re-ordering.

Answer 19

Question 20

What are the issues of ordering frequently?

Answer 20

Ordering frequently,we suffer a large fixed cost of ordering.

• Clerical / labour cost of processing an order
• Any fixed costs imposed by supplier
• Inspection and return of poor quality products
• Transport costs
• Handling costs
• Labour cost of organising transportation

Question 21

Explain the total cost formula and illustrate it on a graph.

Answer 21

Question 22

Derive EOQ.

Answer 22

Question 23

Explain why EPQ estimations do not need to be very accurate.

Answer 23

• Examination of the graphical representation of the total cost curve shows that, although there is a single value of Q which minimizes total costs, any relatively small deviation from the EOQ will not increase total costs significantly.
• Put another way, small errors in estimating either holding costs or order costs will not result in a significant deviation from the EOQ.
• This is a particularly convenient phenomenon because, in practice, both holding and order costs are not easy to estimate accurately.

Question 24

Write the EPQ equation.

Answer 24

Question 25

What is the equation that gives the reorder point?

Answer 25

Question 26

Answer 26

Yes, though here it makes no difference to the optimal Q, so we often ignore the terms DC_v and SS*C_h.

(If you apply these to the total cost graph, everything just moves up vertically.)

Question 27

Explain EOQ with incremental discounts.

and explain how to find the lowest total cost.

Answer 27

• The total cost is now not solely dependent on EOQ, because of the discount rates of holding inventory.
• Purchase is also included because its not a fixed price meaning it affects different graphs in different ways. (doesnt simply scale everything up)
• https://www.youtube.com/watch?v=smMhdlojqiY - Explains how to find best Q*.

Question 28

What if we are producing the batch ourselves, rather than ordering it in from an external supplier?

What are the logistical differences?

Answer 28

Most of the issues are the same as they were when we were ordering the batch in.

The differences are:

(1) The cost of ordering becomes the cost of setup

• Clerical / labour cost of setting up a machine
• Loss of production while set-up takes place
• Return of poor quality products after start-up

(2) The batch does not now arrive instantaneously
* The optimum batch size is known as the Economic Production Quantity (EPQ) (Aka Economic Batch Size)

Example

• A typical example of this is where an internal order is placed for a batch of parts to be produced on a machine.
• The machine will start to produce the parts and ship them in a more or less continuous stream into inventory, but at the same time demand is continuing to remove parts from the inventory.
• Provided the rate at which parts are being made and put into the inventory (P) is higher than the rate at which demand is depleting the inventory (D), then the size of the inventory will increase.

Question 29

Draw the inventory profile for gradual replacement of inventory.

Answer 29

Question 30

Give the EPQ equation

Answer 30

• Derivation found on page 380 of the 3P4 book.

Question 31

Explain Fixed Time Period Ordering.

Answer 31

• A system where the time period between orders remains constant but the order quantity varies
• Has larger average inventory to prevent stockouts
• Useful when purchasing multiple items from one vendor to save on costs
• Example: Always refilling the petrol tank of a delivery truck at the end of each day.

Question 32

Fixed Time Period Ordering: Explain “Lot-for-Lot” ordering.

Answer 32

• Also called pass-on-orders, or order-up-to model (OUT)
• Simply passes on customer orders 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 an issue?

Question 33

Explain Period Order Quantity.

Answer 33

EOQ logic, modified so that we order to cover demand for a whole number of periods, while still minimising cost

Example:

• Say D = 200 units per year and EOQ = 58 units, with “period” equal to one month
• EOQ/D = 58 units / 200 units = 0.29 years between orders
• 0.29 years = 3.48 months, so order every 3 months to cover expected demand in the next 3 months

Same logic as EOQ, except that ordering interval is computed, but NOT ordering quantity

Also known as “Economic Time Cycle”

Question 34

What are the assumptions made in EOQ and EPQ.

Answer 34

Rigid Assumptions

• Demand is constant and steady, and continues indefinitely
• EOQ assumes whole replenishment lot arrives at same time
• Replenishment lead-time is known
• Order size is not constrained by supplier, no min/max restrictions
• Holding cost per item per period is a constant
• Cost of ordering/setup is a constant
• Item is independent of others; benefits from joint reviews are ignored
• Doesn’t encourage us to decrease fixed ordering/setup costs

Question 35

What are some criticisms of EOQ models?

Answer 35

• The assumption of steady demand (or even demand which conforms to some known probability distribution) is untrue for a wide range of the operation’s inventory problems. For example, a bookseller might be very happy to adopt an EOQ-type ordering policy for some of its most regular and stable products such as dictionaries and popular reference books. However, the demand patterns for many other books could be highly erratic, dependent on critics’ reviews and word-of-mouth recommendations.
• Perhaps the most fundamental criticism of the EOQ approach again comes from the Japanese-inspired ‘lean’ and JIT philosophies.
  
  • The EOQ tries to optimize order decisions.
  • EOQ is essentially a reactive approach. Some critics would argue that it fails to ask the right question. Rather than asking the EOQ question of ‘What is the optimum order quantity?’, operations managers should really be asking, ‘How can I change the operation in some way so as to reduce the overall level of inventory I need to hold?’
  • The EOQ approach may be a reasonable description of stock-holding costs but should not necessarily be taken as a strict prescription over what decisions to take. For example, many organizations have made considerable efforts to reduce the effective cost of placing an order.
  • Often they have done this by working to reduce changeover times on machines. This means that less time is taken changing over from one product to the other, and therefore less operating capacity is lost, which in turn reduces the cost of the changeover. Under these circumstances, the order cost curve in the EOQ formula reduces and, in turn, reduces the effective economic order quantity.
• Many organizations (such as supermarkets and wholesalers) make most of their revenue and profits simply by holding and supplying inventory. Because their main investment is in the inventory it is critical that they make a good return on this capital, by ensuring that it has the highest possible ‘stock turn’ (defined later in this chapter) and/or gross profit margin. Alternatively, they may also be concerned to maximize the use of space by seeking to maximize the profit earned per square metre. The EOQ model does not address these objectives. Similarly for products that deteriorate or go out of fashion, the EOQ model can result in excess inventory of slower-moving items. In fact, the EOQ model is rarely used in such organizations, and there is more likely to be a system of periodic review (described later) for regular ordering of replenishment inventory.
• Other questions surround some of the assumptions made concerning the nature of stockrelated costs. For example, placing an order with a supplier as part of a regular and multi-item order might be relatively inexpensive, whereas asking for a special one-off delivery of an item could prove far more costly. Similarly with stock-holding costs – although many companies make a standard percentage charge on the purchase price of stock items, this might not be appropriate over a wide range of stock-holding levels. The marginal costs of increasing stockholding levels might be merely the cost of the working capital involved. On the other hand, it might necessitate the construction or lease of a whole new stock-holding facility such as a warehouse. Operations managers using an EOQ-type approach must check that the decisions implied by the use of the formulae do not exceed the boundaries within which the cost assumptions apply.

Question 36

Why are all the assumptions made for the EPQ model not a major issue?

Answer 36

• In order to keep EOQ-type models relatively straightforward, it was necessary to make assumptions. These concerned such things as the stability of demand, the existence of a fixed and identifiable ordering cost, that the cost of stock holding can be expressed by a linear function, shortage costs which were identifiable, and so on. While these assumptions are rarely strictly true, most of them can approximate to reality. Furthermore, the shape of the total cost curve has a relatively flat optimum point which means that small errors will not significantly affect the total cost of a near-optimum order quantity.

Question 37

Explain Variable Order Quantity and Ordering Interval.

Answer 37

Methods that allow lot size & ordering interval to vary from batch to batch

• We still assume that demand is known, even if it is not constant
• Seek to cover demand for a whole number of periods
• As in EOQ, objective of minimising the sum of setup and inventory cost

Three Types:

• LUC - Least Unit Cost
• 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, but advanced versions include “look-ahead / look-back’ facility to see if simple modifications to schedule reduce total costs.

Question 38

How does LUC (Variable Order Quantity and Ordering Interval: Least Unit Cost) work?

Answer 38

Basic idea: Consider seeking to cover demand for next 1,2,3… periods. Find cost/unit for each case. Stop just before this starts to rise. Restart calculation from there.

Assume we suffer holding cost on only items held over from one period to the next.

Question 39

For a firm producing batches, the set-up cost is £100, inventory holding cost = £1 / period / item.

Calculate the LUC.

Answer 39

Question 40

Discuss the need for, and problems associated with inventory in manufacturing systems. Give at least three examples each.

Answer 40

Inventory will always exist due to differences in the timing/rate of supply and demand.If the supply of any item occurred exactly when it was demanded, the item would never be stored. Input process and output process is the simplified view of manufacturing, however, between these two stages involve many steps that lead to WIP’s or raw material and its rare for all these steps to be in complete sink. The different types of inventory can be rounded down to: buffer inventory, cycle inventory, de-coupling inventory, anticipation inventory and pipeline inventory.

Safety Inventory is designed to be buffer for unexpected fluctuations in supply and demand. A retail operation can never forecast their demand accuractely, and so will always order more than their expected demand requires. It can also compensate for the uncertainties in the process of the supply of goods into the store, perhaps because of the unreliability of certain suppliers or transport firms.

Buying Inventory during certain seasons may be cheaper than others.

Cycle inventory is occurs when a process can only supply the demand for one good at a time. For example, a car manufacturer may produce 3 different types of cars, but can only produce one type of model per batch. The manufacturer will produce the batches so that they compensate for the demand that occurs when they are producing a different model. This requires a lot of inventory but does reduce setup costs.

De-coupling inventory is work in progress inventory that ques between departments that compromise of similar operations. This allows for each operation to be set at the maximum processing speed.

Anticipation inventory is used to used to compensate for differences in the timing of supply and demand. Rather than trying to make the product it is pro-duced throughout the year ahead of demand and put into inventory until it was needed.

Pipeline inventory occurs because inventory needs to be transported. From the retail placed order to the delivery it is pipeline inventory, this include allocation of the material in the warehouse and delivery/travel of the product.

However, keeping inventory has a range of disadvantages. Inventories are an inactive asset of the company and such capital could have been used to reducing payables or productive fixed assets.

Inventory also requires storage costs such as leasing space or maintaining the correct conditions for the material. This problem also ties in with the issue of inventory deterioration or damage. This is especially an issue with large inventory orders where firms may hold damaged inventory for extended periods of time without realising. Inventory can also become obselete, such issues can found in the fashion industry where clothes manufacturers may have clothes that are useless because they have gone out fashion.

Tracking and counting inventory can be an issue for manufacturers who store it all onsite. Issues such as insurance costs need to be considered and if the inventories are hazadrous to store, more investment is needed for the safe handling of these components and more regulation is needed.

In conclusion, there are many reasons to have inventory and despite the added costs of holding and handling the inventory, it is imperative that firms are able to deliver their products/services when ordered in order to maintain their competitive advantage, in this sense inventory is unavoidable. However, the need for inventory can be reflection that manufacturing firms need to improve their internal processes and apply lean principles rather than compensating with inventory.