AGRI FOOD

Supply chain: chain of companies that interact to transform raw materials into
finished product and services and deliver them to the final customer
It includes movement of products from suppliers to manufacturers to distributors, but
also includes movement of information, funds, products in both directions.
Supplier, manufacturer (which considers the property of the product like freshness),
distributor, retailer (like Cortilla), customer
Example: supplier of aluminium foils for Coca Cola
Not all the stages need to be present in all supply chains, this can be intentionally
done to have competition (strategy) with supply chain configurations of other
companies. For example Dell for personal computers that have low cost customization
(skip retailer) to give customer the possibility to design their own computer.
https://www.britannica.com/money/retailing
Retailing is the selling of goods and services to consumer end users. Retailing is seen as a
contrast to wholesaling, which typically involves selling in mass quantities at lower prices.
Retailers frequently buy in bulk from wholesalers, then repackage merchandise for individual
sale.

Main directions: supplier … customer

- Product -> (from suppliers to customer)
- Information <- (about the customer order)
- Finances <- (the customer pays the suppliers)

Many supply chains are networks where each stage receives product from several
suppliers and sends output to several customers. It is possible to divide the network in
supply side and echelons (scaglioni) for distribution

Raw material-tier2-tier1-assembly plant (core operations)-dealers-customers

Immagine slide 4 pacco 1
example FritoLay, RioMare, the SC for this products are made of several suppliers, but
example RioMare has the highest power on the others-

Supply chain and supply networks: STRUCTURAL VIEW

Immagine slide 7
Upstream: composed by the tier (livelli) suppliers
Focal company: company with highest influence
Downstream: levels in distribution network
To the final market

The network structure is reached because of relevance (relevance of different

performance dimensions of companies, what was important in that decade) and time
(which decade)

1960s: main goal: volume, high production for high request

Demand>capacity
most suitable model is integrated factory because of high control on the production
in terms of time and quality. High control is needed because of the high investment
(risk) and high scale (max production). This was the main goal for western economies
in 1960s like automotive companies.
Example: Ford taking care of all the stages of the production (production of the parts +
assembling)

1970/1980s: outsourcing and offshoring; main goals: cost and quality

Demand<capacity
Less cost for more quality, that’s why outsourcing is used, because every process
step is given to a company specialised in that. Outsourcing is a way to low the cost
production (by outsourcing in low-cost countries like Poland) and so a way to beat
competitors.
more competition and more companies, the cost becomes important.
Example Toyota: better quality and convenient price, invests in quality making cost a
dominating competitive factor.

2000s: main goals: service and quality (different variety of products ex: colour of
the cars, flexibility in satisfying the customer, quickness)
Network of enterprises (network configuration)
As production becomes increasingly disaggregated, corporations are called on to be
more accountable for the practices of their suppliers.

Last years: sustainability (companies need to preserve resources to protect

production)
demand> capacity
Circular economy business models to face the issue of the capacity of the planet

There have been developments in adapting production facilities to satisfy the requests
of the customer, for example by opening facilities in different locations
like Mc Donalds french fries in India: MC Donalds opened new production facilities in
India and witnessed high demand because of MC success, the solution was to start
cultivating potatoes near new Mc Donalds to adapt production facilities to the
customer demand.

Different trends led to the establishment of SCM (supply chain management):

In the upstream: at the beginning
- Outsourcing
- Off-shoring (delocalizzazione)
In the downstream: later
- Explosion and volatility in customer requirements (they change quickly)
- New products and process technologies
- Request for faster processes
- Internationalization and market globalization

Supply chain management: the management of upstream and downstream

relationships with suppliers and customers to deliver superior customer value at less
cost to the supply chain as whole.

The management of a network of relationships within a firm and between

interdependent organizations and business units consisting of material suppliers,
purchasing (acquisto), production facilities, logistics and related systems that facilitate
the forward and reverse flow of materials, services, finances and information from the
original producer to final customer with the benefits of adding value, maximizing
profitability through efficiences, and achieving customer satisfaction.
So, being efficient and satisfy the customer reducing the cost; satisfy the customer
means deliver the product quickly, having high quality with less cost.

DECISION PHASES IN SCM

What differentiates:
- Frequency of decision making
- Time frame in which the decisions made have an impact (time horizon)

1. Supply chain strategy or design: how to structure the supply chain over the
next several years
2. Supply chain planning: decisions over the next quarter of year
3. Supply chain operations: daily or weekly operational decisions

1. Supply chain strategy or design: how to structure the supply chain over the
next several years
Decisions have an impact for several years and need 5-10-15 years to be taken
Decisions about the structure of the supply chain and what processes each stage will
perform
Strategic supply chain decisions:
- Locations and capacities of facilities (where, how big, which type of production
plant I place here?)
- Products to be made or stored at various locations
- Modes of transportation
- Information systems
Supply chain design must support strategic objectives
Supply chain design decisions are long-term and expensive to reverse, need to
consider market uncertainty

2. Supply chain planning: from a quarter of year to a year

Definition of a set of policies that govern short-term operations
Fixed by the supply configuration from previous phase
Starts with a forecast of demand in the coming year
Planning decisions:
- Which markets will be supplied from which locations
- Planned buildup of inventories (aumento previsto delle scorte)
- Subcontracting (subappalto), backup locations
(Il subappalto è un contratto derivato dall’originario contratto di appalto, con il quale l’appaltatore
affida ad un terzo l’esecuzione dell’opera o del servizio, a lui direttamente ordinata dal
committente.)
- Inventory policies (norme)
- Timing and size of market promotions
Must consider in planning decisions demand uncertainty, exchange rates,
competition over the time horizon

3. Supply chain operations: daily or weekly operational decisions

- Time horizon in weekly or daily
- Decisions regarding individual customer orders
- Supply chain configuration is fixed, and operating policies are determined
- Goal is to implement the operating policies as effectively as possible
 - Allocate orders to inventory or production, set order due dates, generate pick
lists at a warehouse, allocate an order to a particular shipment, set delivery
schedules, place replenishment orders
- Much less uncertainty (short time horizon)

PROCESS VIEWS OF A SUPPLY CHAIN

Push/Pull View: processes in a supply chain are divided into two categories
depending on whether they are executed in response to a customer order (pull) or in
anticipation of a customer order (push) (forecast, taking decisions without knowing the
customer order)
Cycle View: processes in a supply chain are divided into a series of cycles, each
performed at the interfaces between two successive supply chain stages

Supply chain processes fall into one of the two categories depending on the
timing of their execution relative to customer demand:
pull: execution is initiated in response to a customer order (reactive)
push: execution is initiated in anticipation of customer orders, based on speculated
(or forecasted), rather than actual, demand

push/ pull boundary (or CODP customer order decoupling point) separates push
processes from pull processes

example Benetton produces white sweaters (push process) and paints them (pull)
after the customer order is received at the CODP, when the pull process starts.

different strategy to respond to the demand: where to put the customer order
decoupling point CDOP

lead time: from the customer order to the end of the delivery

purchase to order PTO: purchasing the raw material when is needed, based on
order (fully pulled) example tomato sauce for pizza
make to order MTO: production starts when the order arrives, by companies that
have stock of raw materials example Dominoe’s pizza has in stock raw materials and
the production of pizza starts when the order arrives (all the production is pull but raw
materials)
assemble to order ATO: only the final assembling is pull, for example the
automotive industry waits the order to assemble the car
make to stock MTS: delivery to stock (fully pushed), final delivery without receiving
the order (when you see the product you buy it. Made to create stock, for example
supermarkets or door to door sailors or catering service (it forecasts a number of food
needed by the number of participants).

The ways to respond to a demand changes based on the time of the day (peak time
(punta)) and during not busy time of the day)
For example,
Mc Donalds is a combination of MTO/ATO and MTS/just in time
At Mc Donalds, during peak time, a customer orders one hamburger, the server takes
one from the rack and assembles new burgers when the number of hamburgers gets
low under a certain threshold (soglia).
MTS-requirements based: a catering service operating in a push mode, produces the
ingredients and assembles the hamburger before the customer order on the basis of a
forecast.
MTS-just in time: when one hamburger is consumed, the kitchen receives the order to
replenish one
MTO/ATO: During non-peak times or for specific type of products orders are handled
MTO/ATO, so the hamburgers are assembled/cooked after the customer order (pull
process).

subsystem Peak time Not busy time of the day

Bun toasting Push (MTS) Pull (MTO)
Gluten free bun toasting Pull (MTO) Pull (MTO)
Meat cooking Push (MTS) Pull (MTO)
French fries frying Push (MTS) Push (MTS)
French fries packing Pull (MTO) Pull (MTO)
Final assembling Before push, now mostly Pull
Pull

who’s better for:

push has higher saturation, use entirely the production capacity
pull is more flexible
MTS MTO/ATO (more flexible)
service time to answer V
the customer order (lower
time to answer)

inventory costs V stocking finished

products is expensive
Flexibility (possibility to V more options to
customize) customize (Benetton)
saturation of V better a bit of capacity
production resources to adapt the product to
the customer order

Cycle view of supply chain processes:

There are 6 SUB-PROCESSES IN EACH CYCLE:
- Supplier stage markets product
- Buyer stage places order
- Supplier stage receives the order
- Supplier stage supplies the order
- Buyer stage receives supply
- Buyer returns reverse flows to supplier or third party
Example of buying a book:
- Customer
Customer order cycle: connects the customer with the retailer, the book is selected
by the customer that pays to buy it
- Retailer (rivenditore)
Replenishment cycle: connects the retailer with the distributor (need to replenish
the sold book), triggered by the retailer’s need to fill the empty shelf space with
another copy of this book
- Distributor (magazzino, rivenditore ripartitore es concessionario grande)
Manufacturing cycle: connects the distributor to the manufacturer, as the demand
for the book is realized and distributors empty their warehouses, they signal the
manufacturer to print another million copies to fill their empty warehouses
- Manufacturer (produttore)
Procurement cycle: connects the manufacturer to the supplier, the manufacturer
requires raw material inputs of paper, ink…. To begin the assembly process for another
batch of the book.
- Supplier (fornitore)

THE SCOR MODEL

SCOR Supply Chain Operations Reference model was developed by the Supply-Chain-
Council (SCC), an independent, no profit association whose members belong to
companies and organizations involved in the implementation of systems and
advanced techniques of supply chain management.
The SCOR model allows to describe in detail SCM macro-processes that aim to
satisfy customer demands.
Plan: develop a course of action that best meets sourcing, production and delivery
requirements (acquisition of needed resources to match demand and to steer
(orientare) the execution processes)
Execution process:
- Source: procure goods and services to meet planned or actual demand.
(Possibility to return products, components to suppliers)
- Make: transform a product to a finished state to meet planned or actual
demand. (Possibility to return products, post-delivery customer support)
- Deliver: provide products to meet demand, including order management,
transportation and distribution

The Orchestrate Supply Chain process describes the activities associated with the
integration and enablement of supply chain strategies.
The Order process describes the activities associated with the customer purchase of
products and services, including attributes such as payment methods, pricing,
fulfillment status, and any other order data.

The 3 main processes of SCOR model can be classified according to complexity

and uncertainty through the main drivers.

COMPLEXITY OF A DECISIONAL PROCESS FOR A SC MANAGER: extimated by:

- Number of decisions
- Number of linkages among decisions
- Number of constraints
MAIN DRIVERS OF COMPLEXITY FOR EVERY PROCESS (3):
Source:
- Numbers of suppliers
- Number of items/product categories for the procurement team
- Geographic dispersion of the supply network
 - Degree of customization asked to the supplier
Make:
- Product architecture and length and width of the BILL OF MATERIALS (BOM, it is
representative of the parts that compose the product, structured in more levels)
(example of Mc Donald’s BOM). The wider and the longer is the BOM, the more
the manufacturing process is complex. BMW is to show the BOM of a car with
the list of suppliers to show that the complexity depends also on the industrial
context.
- Variety of technological processes
- Degree of customization asked from the customer (increases complexity of
manufacturing process)
Deliver:
- Number of customers (points of destination)
- Number of echelons (related to levels) of the distribution network
- Geographic dispersion of the point of destination
- Customer heterogeneity (B2B business to business, 1 business sells products to
another business, like orto di Jack sells vegetables to restaurants; B2C business
to consumer, orto di Jack sells vegetables directly to consumer)
Example of BOM:
McDonalds
Levels:
0 Mc
1 Hamburger french fries
2 meat, bun, sauce potatoes, oil, packaging, salt
3 bun: water, flower …

KEY FACTORS FOR SUPPLY CHAIN PLAN

Internal uncertainty depends on:
- Machines
- Manpower
- Materials
External uncertainty depends on relationships with:
- Customers
- suppliers
MAIN DRIVERS OF UNCERTAINTY FOR EVERY PROCESS:
Source:
- quality of the supply (its correctness can be controlled, but there will always be
a part of uncertainty)
- lead time and impact of delays (its correctness can be controlled, but there will
always be a part of uncertainty)
- flexibility of the suppliers (limited mix and quantity of products that can be
produced, that depends also on the dimensions of the supplier)
Make:
- plants and machineries (breakdowns (guasti), idle (inattività) time (also for
tests), defect rate)
- workforce (productivity factors)
- materials (quality and avaiability)
Deliver:
- demand uncertainty
- delivery lead time uncertainty (incertezza nel tempo di consegna)
complexity: cose difficili da gestire, che necessitano di più passaggi ecc (about the
product complexity)
instability: quanto la struttura della SC funziona in modo continuo (about source,
make)
uncertainty: cose che prevedi ma che rischi di sbagliare (about the demand for a
product, about deliver)

matrix uncertainty-complexity
complexity
uncertain low High
ty
High Fashion/toys Telecom, aerospace
simple BOM, simple making Complex BOM, high complexity
processes with slightly low variety (many parts) and many
so low complexity, but high innovations which means having
uncertainty which varies quickly inner instability/ uncertainty in
demand
low Mineral water, cement Cars/ household appliances
Water: consolidated sourcing Complex BOM, but durable
process, low dispersion, often local products that have lower demand
sourcing, simple making process uncertainty
and BOM, just supply, filling and
packaging. Main suppliers for
water and packaging.

High turns: good management of stocks, to reduce and consume stocks, which are a
cost

FISHER MODEL differentiates products in functional and innovative and allows to

recognize the right supply chain strategy for the product based on its features (like
variety, contribution margin etc). It is a way to delineate a product profile, there is a
mixture of features (prevalence approach). Distinction based on demand uncertainty.

2 types of product: functional and innovative, which request a different supply chain
strategy.
Functional product: bread, beans
- stable and predictable demand
- long life cycle
innovative product: alpro milk, ice cream, HiPro yogurt
- unpredictable demand
- short life cycle
Functional: answers basic needs, high competition
Innovative: buy instinctively, demand uncertain, difficult to predict, bounded to
fashion or technological content (companies ben and jerry for ice cream tastes)

life cycle: time from which the product has been launched on the market to when is
retired from the market

Supply chain performs two distinct types of functions:

- physical function: includes converting raw materials into parts, components
and eventually finished goods, and transporting them from one point to the next
in the supply chain. Focus for functional product.
 - market mediation function: ensuring that the variety of products reaching
the marketplace matches what consumers want to buy. Focus for innovative
product.
Tabella slide 7 pacco 2 for the features for functional and innovative products
Features:
- product lifecycle
- Unitary contribution margin: unitary profit associated to the product.
p−c
ucm %= p: price, c: initial cost
c
- Product variety
- Forecast error: prediction error of the demand, related to demand uncertainty
- Stock out rate: there is a customer order but the company is not able to
answer it
- end of season markdowns: at the end of the lifecycle the product is
discounted (different from promotion), example: Starbucks cinnamon
Frappuccino limited product lifecycle (Dec-Jan), in January, they sell it under
discount due to the fact that its lifecycle is over (different from promotions).
- Required lead time for make to order

Different products require different supply chain strategies:

functional: physically efficient supply chain, reducing logistic costs while satisfying a
predictable demand, reducing stocks, internal lead time should be respected, quality
of the suppliers, products designed to maximise performance while minimizing costs
innovative: market responsive supply chain, reactive to unpredictable demand, build
flexibility, excessive production capacity and through stocks, quality of the suppliers,
speed, flexibility, ability to innovate, common modules customized at the end example
Frappuccino with different flavours by Starbucks.

Supply chain Physically efficient Market responsive

Primary purpose Lowest possible cost Respond quickly
Manufacturing High utilization Deploy excess capacity
focus
Inventory strategy Generate high turns, Deploy significant buffer or
minimizing average stock safety stocks
Lead time focus Shorten if no cost increase Invest to decrease
(minimize it)
Supplier selection Low price and quality Speed, flexibility, quality, and
in order to have it, the
company needs to have a
spear capacity, which means
have the capacity to stock a
product if needed if the
production is slightly in excess
Product design Minimize cost, high Modular design: simplify
performance product structure by dividing
the production in simple
modules; for example Dell
applies modular design so that
when the order arrives it is
quick to reassemble the
modules
postponement
Different options for market responsive supply chain to cope with demand uncertainty:
- Avoid uncertainty: by cutting lead time and investing in flexibility (MTO)
- Reduce uncertainty by finding sources of new data/leveraging on shared
components
- Hedge against uncertainty, with inventories or excess capacity

Strategic fit: supply chain and the company have aligned goals (not having it could
cause problems, negative impact on profitability)

DEFINE A SUPPLY CHAIN STRATEGY video

Video: define a supply chain strategy
Aim: ensure strategic fit of the supply with demand
Example: ice cream company
Competitive strategy of the company: customize, variety strategy
Supply chain management: cost reduction ->trouble
- Product life cicle: from phase in to phase out (in the market, out of the
market)
Functional long
Innovative short
- Low unitary margin: business relies on high volume, low cost of the supply
chain
Functional low
Innovative high
- Variety
Funct low
Innovative high
- Forecast error
Difficult to forecast the demand for innovative products
Funct low
Innovative high
- Stockout rate average: customer wont find what he’s searching for
High in innovative, low in functional
- End of season markdown: promotion at the end of the lifecycle of the product
Functionale is 0, innovative is high(might be considered obsolete on the next
season)
- Lead time for products “made to order”:
short for innovative (made to be reactive), long for functional products
hybrid situations

HAU LEE MODELS

Considers uncertainty by different sources in addiction to demand, considering
sourcing and manufacturing.
It defines supply process according to its instability:
supply process:
- Sourcing of components and raw materials from suppliers
- Manufacturing process
- Production technologies
Sourcing process between a juice made of tropical fruits and a soft drink is different
- Quantity and quality needed of tropical fruits are highly uncertain
- Global distances of tropical fruits, possible damage of transport
 - Supply market are complex of the tropical
Distinction according to supply process instability in 2 types of processes:
Stable processes:
- mature processes and technology,
- established supply system (more supply sources)
- automation
- quality controlled easily
- medium long term supply contracts
Evolving processes (unstable):
- technology and production processes evolve fast,
- narrow and unstable supply system.
- Production processes with continuous changes and adjustments,
- variable productivity
- innovation in the products
- spot supply contracts

Matrix: suggests to a company ways to cope with uncertainty, to reduce uncertainty

4 types of supply chains:
Lean efficient supply chains: low demand uncertainty, low processes instability
Strategic object: cost reduction (low logistic costs), economies of scale (speed up the
production and reduce stocks); like grocery and oil&gas, coca cola
Risk hedging: stable demand, unstable supply process
Strategic object: reduction of the risk on upstreams, sharing the risk to garantee
continuity, like fruits and veg; supply process is not stable, requires hedging to protect
against intability
Ex tropical fruit juice
Responsive: stable processes, uncertain demand
Strategic object: request speed, responsiveness, avoid uncertainty by producing
“make to order” (activate the production after an order); they can build flexibility by
creating stability on the process. like fashion, alpro
Example of Seven Eleven in Japan as a Responsive SC
Agile: unstable processes, uncertain demand
Strategic object: responsive supply chain, requires flexibility, also to face some
turbulence in the supply system. For products new in the market, so with few data to
predict the demand, maybe related to trends or with not so clear demand pattern; like
hi-tech (more likely), goji berries
If founded in food is because there is an issue related to a mismatch between SC
strategy and the demand.
example Juice fruit bio case, the company is operating in an unpredictable unstable
business context. Large orders with low lead time required, short company history, so
high forecast error, whose management in the launch of new products (recipe,
packaging and timing) is in the hands of mass market retailers, making the demand
uncertain for JFB. The supply process is also unstable because of the supply of fresh
fruit which makes the SC vulnerable and the ‘framework agreements’ with suppliers
are done by JFB to cope with the uncertainty in the upstream.
Possible actions for JFB to reduce demand and supply uncertainty:
- avoid by responding to actual orders (MTO): unfeasible, because the delivery
lead time required is much lower than the internal production lead time
- reduce uncertainty by sourcing of data: visibility on customer demand (Vedere
la domanda del cliente) enables JFB to reduce uncertainty related to sales
promotion and better plan production and distribution.
- Hedge: increasing stocks is not possible given high perishability of the product,
but can be possible double sourcing agreements, only valuable in supply
process.
Demand Uncertainty reduction strategies:
 - Avoid uncertainty: Cutting in time and investing in flexibility, through make to
order
- Reduce uncertainty: invest in visibility and collect data
- Hedge against uncertainty: redundant inventories and suppliers, excess
capacity, increase stocks, hedging (copertura) for example double sourcing
agreements

Fisher and Hau Lee models help recognising the right supply chain strategy reflecting
a specific uncertainty landscape. In reality a company strategy is hybrid between more
than one model.

Other factors that make the food SC challenging to be managed (in addiction
to complexity and uncertainty):
- Even in the same industry, there are products with different features (producer-
focused/ consumer-driven)
- legislation and food conservation / safety standards
- sustainability challenges
- consumers’ choices vary around the world

producer-focused food products: commodities

commodity: raw material or other standardized goods, easily stackable and storable
over time, suitable for a wide and easy sale
without qualitative differences and replaceable

regulation: impact on global trade, standards to whom the food product need to
adhere, like WTO (world trade organization) and Codex Alimentarius, food code, born
with harmonization purpose, developed by FAO, a commission who defined standards
for food products. Also EFSA (European food safety assessment), for food intoxication.

Wide set of challenges: safety, sustainability, food waste, food insecurity, food
preferences that vary around the world (developed economies tend to use more ready
to cook/eat food, so ultra processed food) (while developing economies have grain
based diets, most impactive food production with environmental impact)

Another industrial classification for food products

Classification can be based on the different industrial steps carried out for the
transformation from fresh raw material to food product.
3 groups according to the extent and purpose of the processing used in the
production:
- minimal processed food: minimal modifications to extend duration, enable
storage and reduce effort/time in the preparation. (pasteurized milk)
- Processed culinary ingredients: extract substances from food products enabling
manufacturing of highly storable ingredients used in the culinary elaboration of
dishes/meals. (oil)
- Ultra processed food: extract substances from food products, subsequent
assembling (usually with additives), enabling the manufacture of long shelf-life,
ultra-palatable, ready-to-consume products. (bread, cookies)

KEY ACTORS IN A GENERIC EXTENDED AGRI-FOOD SUPPLY CHAIN: complexity

Wholesalers are the intermediaries between input providers, food producers and food
processors, which receive technologies (robot), packaging (time + refrigeration),
logistic and services (vet) from other providers. From food processors the food goes to
distributors and retailers or restaurants.

ALSO: there might be public and third sector organizations like charity, which interact
with the public (ex. Green deal), so affect the supply chain (charity, help to farmers).
And Trade Associations like Confagricoltura, which keeps contacts with farmers.

ONE MAIN ISSUE FOR FOOD SUPPLY CHAIN PLANNING

For some food products, orders are ‘one shot’, meaning with a limited time window of
demand but also in which the product is sellable.
Twofold point of view:
- If materials are purchased with wrong quantities, either is not possible to
produce all the requested products or there are excessive stocks in the
warehouse
- If shops are supplied with wrong quantities, there can be missing or unsold
items in the ‘chain’
An example of these ‘one shot’ products are newspapers, whose order and demand
last 1 day.
Problem similar to the newsvendor boy in which the decision to take regards how
many newspapers to buy to be distributed in a limited time window. The decision
needs to be taken before an actual demand. Missing products represent lost sales (lost
margin), products in excess are to be sold under-price (lost/negative margin) or even
destroyed (product cost lost). In food you can apply this Newsvendor model with how
much bread to bake for today’s sales, or how much vegetables to bring to the farmers’
market.
THE NEWSVENDOR MODEL: usable also for food and fashion
Hp: demand is uniform for all the newspapers (p=0.01 for one newspaper) and Cu and
Co fixed
Cost of coverage (Co): or cost of overproduction, means stocking more units than
the demand. The newsvendor buys a newspaper for 0.8 euro, if he has newspapers
remaining unsold, he loses 0.8 euro (simplified model)
Cost of underage (Cu): or cost of underproduction, means not having enough units
to satisfy the demand. The newsvendor buys a newspaper for 0.8 euro and sells it for
1 euro, so if he does not have newspapers to sell when a customer requests one, he
loses 0.20 euro of profits for every unit of unmet demand (simplified model) (lost
profit)
slide 49/50 pack 1
Expected contribution:
Cu: profit (0.2)
Co: loss (0.8)
P: probability of the demand to be less than the order
expected cumulative profit= (1− p )∗Cu−p∗Co=expected addictional margin

2 ways to find the max number of newspapers to buy:

1) Probabilistic breakeven analysis
Stop when the expected additional margin (expected contribution) values 0, it
is not convenient to buy the next newspaper, because there is no contribution over
this choice, if you reach 0 at 21st newspaper (in this case p=0.21), stop at 20.
2) Compute Total expected profit (cumulative function) = sum of all the
unitary expected additional margins
And look for the maximum of this cumulative function.
The value of Q, Optimal Service Level (OSL, p*) or ‘critical fractile’, corresponds
to the max of expected profit (cumulative) function, the p value which corresponds to
the OSL is the number of newspapers which allows the best result in terms of profit
Basically, you put to zero this expression:
(1− p) Cu− pCo=0
And you get:
Cu 0.2
OSL= p∗¿ = =0.2
Co+Cu 0.2+ 0.8

The maximum of the expected cumulative profit function is reached with the optimal
number of units Q to buy, the value that should not be overcome in order not to have
losses.
The quantity is obtained by:

Q∗¿ 1+OSL∗99=19.8=20 units

Q∗¿ 1+OSL∗(number of newspaper−1)

(the newsvendor buys at least one newspaper)

(tot newspaper available=100, uniform distribution Hp)

I could have different expressions for Cu and Co, that can change maybe during the
time window
REMOVE HYPOTESIS ON THE DEMAND: demand is not uniform but can be expressed by
a normal distribution for example (you express the tot number of newspaper available
as a distribution).