inventory management1 slides 2 inventory management global supply chain management

Inventory Management 1

Slides 2

Inventory Management

Global Supply Chain Management

Inventory Management Slide 2

Agenda

Inventory Management Intro Economic Lot Size Model Continuous Review Policy Service level optimization Risk Pooling / Centralization


Inventory Management (IM)

We will introduce here the basics…. Later, course cases GM, Meditech, Reebok

present a diagnosis of a typical problem: low service levels & too high inventory levels. This is actually an Oxymoron…..

Solutions: co-ordination within or across, better forecasts, reduction of lead time, use Pull, Push-Pull boundaries, postponement.


IM implies Order (or Production) Management

Key Question: what, when and how much to order (or: to produce – assume order)

Simple models and principles can provide valuable guidance

At start not like continuous replenishment policy (case of Tesco): we order, the order arrives before we need to order again. Later: orders are underway when we order.


Why do we keep Inventory? Logical: incentives for orders or arriving

shipments that are larger (and hence less frequent) compared to leaving sales based on demand: think of a grocery retailer

Uncertainty in supply levels, in lead times To address uncertainty in demand in combination

with long lead times– demand may be hard to forecast, demand may

suddenly go up, with high “unsatisfied demand” costs we rather keep some stock, especially if it takes a long time to replenish.

Risks associated with inventories– Shorter lifecycles, more competing products


Typical Inventory Policy Factors Expectations about customer demand Expectations about lead time Length of the planning horizon (e.g. seasonal ?) Costs:

– Fixed (order) costs, consisting of fixed costs in• Materials and components, storage, admin costs,

production costs, transportation costs,Assume that variable costs are covered with sales

– Inventory holding costs and associated costs• Taxes and Insurance costs, Maintenance costs• Obsolescence costs and Loss of Opportunity costs

Service level (availability) requirements


Economic Lot Size Model

FIGURE 2-3: Inventory level as a function of time

Assumptions- Constant demand rate of D items per unit of time- Q items per order: Order quantities are always the same- Lead Time = 0 : Time between placement of an order and its receipt is assumed to be zero.- Planning horizon is long, infinite (for that product)


Other Assumptions

K fixed setup cost: Every time the warehouse places an order, a fixed setup cost of K is incurred

h inventory carrying cost: A holding cost of h is incurred per unit held in inventory per unit of time

Requested is Q* or EOQ, the Economic Order Quantity


EOQ: Minimizing Total Costs

FIGURE 2-4: Economic lot size model: total cost per unit of time as a function of the order quantity


Deriving EOQ Whatever Q is, at the start of cycle time T we

order Q units The average inventory during a cycle is: Q/2,

see diagram Per T this means a total holding cost of: T * h

* Q/2 For every cycle T we also incur a fixed order

cost: K So the average total cost per cycle:

K + T * h *Q/2 Average total cost per unit of time: K/T +

h * Q/2

Total demand during a cycle is Q = D * T, so T = Q/D

Average total cost per unit of time: K * D/Q + h * Q/2

This sum of the Order Cost per of unit time and Holding Cost per unit of time can be shown in a Diagram…..


Where is the minimum ? Function f(Q) = K*D/Q +

h*Q/2 Gives f ’(Q) = -1*K*D/Q^2 + h/2 This being 0, implies that the

optimal order quantity is

Example: K = 2000$, D = 180 units per day and h = 0.5$ per unit per day

What is Q*? How often will we order?

h

KDQ

2*


Sensitivity Analysis

b 0.5 0.8 0.9 1.0 1.1 1.2 1.5 2.0

Cost Increase 25% 2.5% 0.5% 0% 0.4% 1.6% 8.9% 25%

Total costs relatively insensitive to order quantities

Actual order quantity: Q Q is a multiple b of the optimal order quantity Q*. For a given b, the quantity ordered is Q = bQ*

Nevertheless: it makes a difference


What if the Manufacturer (or Retailer) has an Initial Inventory?

Trying to use the existing inventory to meet the demand has….– Advantage: no need to pay production (order) cost– Disadvantage: it may be impossible to meet demand

Producing/ordering on the other hand has….– Advantage: more likely to meet demand– Disadvantage: implies a production (order) cost,

which is relatively high a as we will produce (order) a smaller quantity


Multiple Order OpportunitiesSuppose: demand is uncertain & lead times existQuestion: when and how much to order each time? to balance annual inventory holding costs and

annual fixed order costs to satisfy demand occurring during lead time to protect against uncertainty in demandMajor strategies Continuous review policy

– inventory is continuously reviewed (computerized inventory system) and an order is placed when the inventory reaches a particular level, the reorder point

Periodic review policy (less relevant today)


Continuous Review Policy An entity faces demand according to a normal distribution,

the mean demand is AVG and its standard deviation STD. Every time the entity places an order to its supplier (or

decides to manufacture), the entity pays a fixed cost K (plus an amount proportional to the quantity).

Inventory holding cost h is charged per item per unit time. Inventory level is continuously reviewed, and if an order is

placed, the order arrives after the (constant) lead time L. If customer demand occurs when there is no inventory on

hand (i.e. when the entity is stocked out), the order is lost. The entity specifies a required service level α. This implies

that the probability of stocking out during L out is 1 – α.


(Q,R) policy – whenever inventory level falls to a reorder level (point) R, place an order for Q units (optimal order quantity)

What is the optimal value of R?– What is the safety stock level?– What is the demand during the lead time ?

What is the optimal value of Q? The expected time between orders TBO? How many inventory turns per unit of time?

Continuous Review Policy

Time

inve

nto

ry

TBO1 TBO2 TBO3

L L L

R

Orderreceived

Q

Orderplaced

Orderplaced

Orderreceived

Inventory + PipelineInventory + Pipeline

Q

Orderplaced

Q

Orderreceived

Orderreceived

Inventory development over time


Continuous Review Policy

Expected demand during lead time L x AVG Required safety stock

Reorder level R=

Order quantity

Expected time between orders = Q / AVG

LSTDz

LSTDzAVGL

h

AVGKQ

2


Relation between Service Level α and Safety Factor z

Service Level

90%

91%

92%

93%

94%

95%

96%

97%

98%

99%

99.9%

Z - value 1.29 1.34 1.41 1.48 1.56 1.65 1.75 1.88 2.05 2.33 3.08

z is chosen from statistical tables to ensure that the probability of stock-outsduring lead time is exactly 1 - α


Inventory Level Over Time

LSTDz Inventory level before receiving an order =

Inventory level after receiving an order =

Average Inventory (AvInv) =

LSTDzQ

LSTDzQ 2

FIGURE 2-9: Inventory level as a function of time in a (Q,R) policy

Inventory Turn = AVG / AvInv


Continuous Review Policy Example: calculate (Q,R)

A distributor of TV sets that orders from a manufacturer and sells to retailers

Fixed ordering cost = $4,500 Cost of a TV set to the distributor = $250 Annual inventory holding cost = 18% of product

cost (so 18% of $260) Lead time = 2 weeks Expected service level = 97% AVG = 49 per week. STD = √50 per week (variance is 50)


Optimal inventory policy assumes a specific service level target.

What is the appropriate level of service? – May be determined by the downstream customer

• The customer may require its supplier (the entity), to maintain a specific service level

• The supplier will use that target to manage its own inventory

– The Supplier (the Entity) may have the flexibility to choose the appropriate level of service

Service Level Optimization



FIGURE 2-11: Service level versus inventory level as a function of lead time


Trade-Offs Everything else being equal:

– the higher the service level, the higher the inventory level and vice versa (see graph),

– the lower the inventory level, the higher the impact of a unit of inventory on service level and hence on expected profit (form of curves),

– for the same inventory level, the longer the lead time to the facility, the lower the service level provided by the facility (dotted curve).


Defining a Retail Strategy Given a target overall service level across

all products Determine the service level for each SKU

so as to maximize expected profit Everything else being equal, service level

will be higher for products with:– high profit margin– high volume– low variability– short lead time



FIGURE 2-12: Service level optimization by SKU (Example)

Note that the size of the circles is an indication of the profitability


A target service level of 97% across all products combined typically leads to a: – Service level > 99% for products with high

profit margin, high volume, low variability. – Service level < 95% for products with low

profit margin, low volume and high variability.

Profit Optimization


Risk Pooling (based on location) Demand variability is reduced if one

aggregates demand across locations. More likely that high demand from one

customer will be offset by low demand from another customer.

Reduction in variability allows a decrease in safety stock and therefore reduces average inventory.

Other RP factors are time and product

inventory management1 slides 2 inventory management global supply chain management

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