Optimization

Supply Chain Planning Using Optimization

Optimization

Introduction to Optimization Models

Optimization

Optimization-Based Planning Models

• In constraint-based planning, production processes can be represented as optimization models.

• A production model based on optimization consists of Objective Function(s), Decision Variables, and constraints based on market conditions, physical processes, and resources/capacity.

• These kinds of models are usually called mathematical programs.

Optimization

Decision Variables

• Decisions variable are the independent variables of the problem. Typically, decisions take the form of Production lot sizes, Transport lot sizes, Purchase of additional capacities and so on.

• Examples of Decisions Variables:– How much do we invest in new machines?– How much do we spend in labor?– How many units to make?– Repair or replace?

Optimization

Objective Functions

• The Objective Function is the single benchmark for evaluating all combinations of decisions that satisfy the constraints. It usually represents a quantifiable goal, and sometimes 2 or more goals.

• Examples of Objective Functions:– Minimize total production costs– Minimize total material costs– Maximize total sales revenue– Minimize total inventory costs– Minimize total lead time

Optimization

Constraints

• Constraints represent limitations on which decision can be made and how decisions can be made. For example, the production capacity is 5000 Units/day.

• Constraints are also used to apply business rules when solving a problem. For example, all inventory must be non-negative.

• Other examples of constraints:– Market conditions/demand– Material/supplies– Capacity/resources– Transportation/logistics– Policy/managerial

Optimization

Steps for Constructing a Planning Model

• Typically, a simplified production model comes from performing VAT analysis on the existing production process that we want to model.

– What are the decisions variables?

– What are the constraints?

– What is the objective function?

Optimization

Objectives DecisionVariables

Constraints

SNP,Distribution& PP

Lateness,Storage Costs,Transportation Costs,Production Costs,Purchase of additional CapacitiesProduction Resources,Transportation (Fleets)Products

LatenessProduction Lot SizesTransportation Lot SizesPurchase of AdditionalCapacities

Production CapacitiesTransportation CapacitiesHandling CapacityDue DatesSafety StockDiscrete ValuesProduction Lot Size,Transportation Lot Size,Extra Shifts

DS LatenessMakespanSetup Costs

Resource Allocation(AlternativeMachines/Storage)Start DatesNOT Lot Sizes orAlternative Recipes

Time Constraints (maximal duedate, shelf life – Minimalproduction stages, campaign)Due DatesSetup Times,ProductivityResource networkCalendarShifts,Effectivity of receipts

Objective Functions, Decision Variables, Constraints in APO

Optimization

SNP Optimization

One time period (bucket)

Demand at a location

Dependent demand at a location

Processing flow

Optimization

Optimization of the Network

ForecastsCustomers orders

ForecastsCustomers orders

Sourcing production &purchasing

requirements

Sourcing production &purchasing

requirements

Priorities for:demand typesdefined viacosts

Control costsPenalty costs

$

Goal: Minimize costs

Goal: Maximize Profits*

Optimization

Optimization Methods

• Linear Programming– Continuous Linear Optimization Problems

• Primal Simplex Method• Dual Simplex Method• Interior Point Method

– Discrete Linear Optimization Problems• Mixed Integer Linear Programming

• Prioritization

• Decomposition

• Vertical Aggregated Planning

• Horizontal Aggregated Planning

Optimization

Optimization Methods

• Discretization

– Discretization until a certain date*

– Detailed Discretization for different restrictions for daily, weekly, or monthly buckets*

– Maintain discretization in PPM or transportation lane individually

Optimization

• Decision Variables– Production lot sizes– Transportation lot sizes– Capacity increase

• Objectives– Lateness – Storage costs – Transportation costs – Production costs– Penalty for increasing

capacity– Penalty cost for not

maintaining safety stock*– Penalty cost for late or

non delivery*

Optimization Parameters

• Constraints– Production capacities– Transportation capacities– Handling capacity– Due dates (demands)– Safety stock– Discrete Values

• Production Lot Size• Transportation Lot Size

Optimization

Cost Maintenance function

$

UseUse this function to maintain all costs used by the Optimizer and assigned to the master data from a single point of access. If you maintain the costs using this function, the master data for the selected planning version is automatically updated.

IntegrationThis function integrates costs assigned to PPM, Resource, and Product master data. These costs include Production, Handling, Storage, Transportation, Procurement, and Delay/Non-Delivery costs.

Optimization

Optimizer Profile

30

Costs Due date violation

Optimization

Optimizer Profile

A

A BCD

Storage CapacityTransport Capacity

Handling Capacity

Production Capacity

Safety Stock Violation

Determines which constraints are

considered

Other Constraints

Optimization

SNP Cost Profile

A

A BCD

$0 1 2 x

Penalty for fallingbelow the minimum

safety stock limit

Penalty for fallingbelow the minimum

safety stock limit

Optimization

Optimization Bound Profile*

• Specifies the time buckets where the new plan is constrained by an upper and lower limit on the allowable change.

• For example, you change the plans in the first month only within 10% of the original value. The basis for the change is the last optimization run for the same planning area

Optimization

Optimization Run - Interactive Planning Desktop

• Range of location products can be selected.

• Predefined Optimizer profiles can be selected

• Changes to the predefined profiles is allowed

Optimization

Costs in the APO Environment (I)

• Model considers the following costs:– Higher non-delivery cost results in:

• forced production– Higher relative storage cost results in:

• moving products from one location to another ahead of requirement

– Higher delay cost results in:• control lateness/build early scenarios

– Maximum delay used to:• control number of days demand fill is delayed by

– Transportation cost used to:• prioritize source location

• Costs are Interdependent!

Optimization

Costs in the APO Environment (II)

• To specify a site manufacturing priority: Production cost in preferred site Transportation cost from preferred site

• To influence inventory storage location: Relative storage costs between sites

• To ensure meeting inventory targets: Safety stock violation penalties

Optimization

Costs in the APO Environment (III)

• To meet delivery date early/late– Meet Early:

Delay Cost Storage Cost

– Meet Late: Maximum Delay Allowed Delay Cost Storage Cost

• To use stock before build Storage Cost

• To prioritize a site for downstream supply– Vary Transportation Cost

Optimization

SNP Decisions

Optimization

Optimization Total Costs

Total Cost (Sum Total) Source of cost data

Production PPM

Storage Resource

Production resource expansion Resource

Storage expansion Resource

Penalty cost for safety stock Cost Profile

Transport cost Resource

Transport capacity expansion Resource

Penalty for non-delivery Master data

Handling capacity expansion Resource

Procurement costs Master data

Delay Penalty Master data

Optimization

Relevant Costs for the Optimizer

Resource costs Standard (variant 1) Increase (variant 2)

Additional costs

ProductionTransportTransport (mat)StorageStorage (mat)Handling

(X)X

(X)X

XX

X

X

PPM-header: Variable costs

Safety stock: Penalty (cost profile)

Material priority: Late delivery (penalty)

Non delivery (penalty)

Optimization

Product Master Data: Global Data

• Penalty Costs for Requirements and Customer Forecast– Penalty costs for non-delivery– Penalty costs for delayed delivery– Maximum allowed delay (in days)

$

Salesorder

Fore-cast

30

Optimization

Input Parameters for SNP Optimization Run

• Planning Version

• Level ID

• Product and Location

• Planning Book and Data View

• Planning Start and End Date

• Optimizer and Cost Profile

• Optimizer Bound Profile

• Modify Quota Arrangement

Optimization

SNP Optimization Run Results

• Distribution Plan

• Production Plan

• SNP Resulting Costs

• Alerts