UCL

ESPO/IAG/POMS

PROD 2800PRODUCTION AND OPERATIONS MANAGEMENTGestion de la production et des opérations

Per AGRELLagrell@poms.ucl.ac.be

Lecture 4 Inventory Control

PROD 28002

Outline

InventoriesLotsizingFixed order quantity

– Assumptions– EOQ– EPQ– All-units Discounts

PROD 2800

Purposes of Inventory

1. Decoupling of processes.

2. Variation in demand.

3. Variation in raw material lead time.

4. Flexible production scheduling.

5. Economies of scale in processes.

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Fixed order quantity assumptions

1. Demand constant, deterministic, known2. Q continuous and unconstrained3. Independent demand and replenishment4. Delivery in batches5. Infinite planning horizon

– Replenishment rates– Unit value v(Q)– Backlog– Inflation

PROD 2800

Inventory Costs

Holding (or carrying) costs.– Costs for storage, handling, insurance, etc.

Setup (or production change) costs.– Costs for arranging specific equipment setups, etc.

Ordering costs.– Costs of someone placing an order, etc.

Shortage costs.– Costs of canceling an order, etc.

PROD 2800

Independent vs. Dependent Demand

PROD 28007

General expression

rQQvQDQA

QDvQTRC21

Discounts

Cycle time

InflationDiscounts

PROD 2800

Cost Minimization Goal

Q* Order Quantity (Q)

Cost

PROD 28009

EOQ I

PROD 280010

EPQ

P Replenishment rate

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All-units discount

PROD 280012

All-units discount

Let price ci be valid for Li Q < Li+1 for i = 1, 2, … N

1. Find Qi = Q*(ci)

2. If Qi is feasible– let calculate TCi = TC (Qi ) and

Else– use Qi = Li and calculate TCi = TC (Li)

3. Optimal Q** = argmin {TC (Qi ) }

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All-units discountQ 200 210 5000

0 1000 2000 3000 4000 50001 10

5

1.01 105

1.02 105

1.03 105

1.04 105

C c1 Q( )

C c2 Q( )

C c3 Q( )

Q

PROD 280014

Summary

Lotsizing single level systemsEOQ

– Robustness– Flexibility (parameters, assumptions)