Inventory Management in Dairy Systems

Week 6 - ANSCI 4940 - Spring 2026

Miel Hostens

Inventory Management in Dairy Systems

Why Inventory Calculations Matter

  • Inventory is the constraint layer under everything else.
  • If a herd inventory snapshot is wrong → future decisions will all be wrong.
  • Today:
    • Build the mental model
    • Understand the math
    • Lab on CDREC flow

Learning Outcomes

By the end you can:

  • Distinguish state vs flow
  • Define risk vs rate
  • Compute and interpret key herd dynamics metrics
  • Avoid synonym traps
  • Use DC305 to extract numerators/denominators for CDREC strategy

Two herds, same cow count, different future

  • Herd A and Herd B both have 1,000 cows today
  • One shrinks, one grows
  • The difference is flows

flowchart LR
Births --> Heifers --> Cows
Cows -->|Cull/Sell| Exit
Cows -->|Death| Exit

Vocabulary

  • Statics: snapshot at a moment
    • “what exists”
  • Dynamics: movement over time
    • “where it is going”

DC305

Choose the “as‑of” date intentionally

Set date in cowfile to “today”

SETDAY\*

Set date to last event entry date

SETDAY\E

Set date to most recent test date

SETDAY\T

Set date to selected date

SETDAY\mm/dd/yy

Why date matters

  • “Last 365 days” depends on file date
  • If the backup date is wrong → your rates are wrong

Definitions

Risk vs Rate (the core confusion)

Most bad inventory math comes from mixing:

  • Probabilities and
  • Time‑based rates

Risk (probability)

  • Fraction experiencing event over specified period
  • Unitless
  • Must specify time window

Example - Culling Risk

Definition

Probability that a cow is culled during a specified time period.

\[ Risk = \frac{\text{Number of cows culled during period}}{\text{Number of cows at risk at start}} \]

  • Unit: none (0–1)
  • Time period must be defined
  • Bounded by 1

Better example - Annual Culling Risk

Suppose:

  • 100 cows at start of year
  • 20 cows culled during the year

\[ Risk = 20/100 = 0.20 \]

👉 20% probability of being culled during that year

This is a probability over one year.

Rate

  • Events per unit time (per cow‑time)
  • Units: 1/time
  • Supports unequal follow‑up

Incidence Rate

Definition

Speed at which culling events occur.

\[ Rate = \frac{\text{Number of cullings}}{\text{Total cow-time at risk}} \]

  • Unit: 1 / time (e.g., per cow-year)
  • Uses animal-time
  • No upper bound

Cow-year — definition

A cow-year is animal-time at risk:

  • 1 cow-year = one cow present and at risk for 1 year
  • More generally: sum the time each cow is “in the population at risk,” expressed in years.

This is the recommended denominator logic for herd turnover: exits / animal time at risk.

Cow-year — formula

\[ \text{Cow-years} = \sum_{i=1}^{n} \frac{\text{days cow } i \text{ is at risk during period}}{365} \]

Key idea: time belongs in the denominator when you report a rate.

Example: counting cow-years

  • Cow A present all year: (365/365 = 1.00) cow-year
  • Cow B present 180 days: (180/365 = 0.49) cow-year
  • Cow C present 90 days: (90/365 = 0.25) cow-year

Total exposure = (1.00 + 0.49 + 0.25 = 1.74) cow-years

Herd-level approximation

For a 12-month window, if herd size is fairly stable:

\[ \text{Cow-years} \approx \text{Average number of cows present during the year} \times \text{1 year} \]

This is why many “annual” turnover metrics use average milking + dry cows as the denominator.

Example: Annual Culling Rate

Suppose:

  • 20 cows culled
  • Total time at risk = 90 cow-years
    (because cows leave during the year)

\[ Rate = 20 / 90 = 0.222 \text{ per cow-year} \]

👉 0.222 cullings per cow-year

This is a speed, not a probability.

Why They Are Not the Same

Risk asks:

What fraction of cows are culled during the year?

Rate asks:

How fast are cows being culled?

Different denominators:

  • Risk → cows

  • Rate → cow-time

Why words break math

  • “30% cull risk” - Over a month? year? lactation?

  • “0.35 removals per cow‑year” - interpretable

Rule

  • If you can’t attach a time window, you don’t have a rate.

Definitions that won’t betray you

Each metric has a:

  • numerator

  • denominator

  • time window

  • population scope

Metrics

Removal / Culling rate — definition

  • Exits / cow‑year
  • Confusion
    • Exits may include sold (alive) + culled + deaths (be explicit)
    • Sometimes used as synonyms
    • In rigorous use: removal includes all exits; cull may exclude deaths/live culls
  • Your job: define numerator explicitly

Mortality / Death rate — definition

  • Deaths / cow‑year
  • Always specify population:
    • cows
    • calves
    • heifers

Replacement rate — definition

  • First‑lactation entries / cow‑year
  • In a steady state (no growth) :
    • replacement rate ≈ exit rate

Calving / Freshening rate — definition

  • Calvings / cow‑year
  • Sometimes operationalized as fresh cows per month (be explicit)

Herd turnover rate — definition

  • Proportion replaced over time
  • Think “stall slots” being refilled

Involuntary vs voluntary removals

  • Voluntary culling → economically driven decision
    • Low milk yield
    • Reproductive decisions
    • Strategic replacement
  • Involuntary culling → biological constraint
    • Mastitis
    • Lameness
    • Mortality

Inventory math

Build it from components

Inventory is not one number.

It is:

  • entries

  • exits

  • time

The simplest dynamic identity

\[ N_{t+1} = N_t + \text{Entries} - \text{Exits} \]

Stable size implies:

\[ \text{Entry rate} \approx \text{Exit rate} \]

What changes herd size?

If you want growth:

  • increase entries
  • decrease exits
  • or both

…but constraints intervene.

Herd constraints (farm growth realism)

  • housing / stalls
  • heifer capacity
  • repro performance
  • calf survival
  • transition cow health

Visual

Constraints as a funnel

flowchart LR
A[Pregnancy performance] --> B[Calvings]
B --> C[Heifer survival]
C --> D[Heifers to breed]
D --> E[Heifers calving‑in]
E --> F[Milk cow slots]

Fertility: the pipeline driver

Pregnancy performance changes:

  • timing of calvings

  • replacement flow

  • age structure

Sexed semen

Inventory consequences

  • increases female calf supply
  • may reduce conception
  • adds lag & variability

Where sexed semen fits in the pipeline

flowchart LR
A[Semen choice] --> B[Preg outcomes]
B --> C[Calves born]
C --> D[Heifer survival]
D --> E[Replacements]

Beef semen

Inventory consequences

  • shifts calves away from replacements
  • increases calf value
  • requires replacement confidence

Use beef semen only when:

  • replacement pipeline is secure

  • growth targets are compatible with heifer supply

Synonym trap

Often treated as synonyms:

  • death rate ≈ mortality rate (if same denominator/time)

  • cull rate ≈ removal rate (IF deaths included)

Not guaranteed synonyms:

  • replacement rate vs turnover rate (context‑dependent)

  • calving rate vs pregnancy rate (related but not same)

Lab skill

Create defensible snapshot

A snapshot is defensible if it:

  • is date‑anchored

  • reconciles across reports

  • defines denominators

  • documents inclusion/exclusion

Grow CDREC (CURC) responsibly

Levers:

  • reduce involuntary exits

  • improve pregnancy performance

  • tune semen strategy (sexed vs beef)

  • manage heifer inventory

Lab deliverable

Students submit:

  • Snapshot (counts)

  • Dynamics sheet (rates)

  • Strategy presentation for growth

Usefull commands

Use of sexed and beef semen

BREDSUM\XB*

Reproductive performance

BREDSUM\E

Culling rate (sold and died) Mortality rate (died)

EVENTS\5SI FOR LACT>0
ECON\ID

DC 305 cheet sheets

DC305 cheet sheet.pdf

DC305 Farm evaluation