Chapter 18 of Business Dynamics

The Manufacturing Supply Chain This chapter adapts the stock

management structure of the previous chapter to represent the supply chain in manufacturing firms

The stock management structure… Is broken up into

An order fulfillment structure A production starts structure A demand forecasting component

Stock S

Adjustment forStock AS

Desired Stock S*

Stock AdjustmentTime SAT

Loss Rate

Desired AcquisitionRate DAR

Supply Line SLAcquisition Rate

AROrder Rate OR

Acquisition LagAL

Expected LossRate EL

IndicatedOrders IO

Adjustment forSupply Line ASL

Desired SupplyLine SL*

Supply Line Adjustmenttime SLAT

AverageLifetime L

Expected AcquisitionLag EAL

Overview Production Model

Work in ProcessInventory

InventoryProduction Rate Shipment RateProduction Start

Rate

Customer OrderRate

Order Fulfillment

demandForecasting

ProductionScheduling

B

WIP Control

B

Inventory Control

B

Stockout

InventoryShipment Rate

InventoryCoverage

Customer OrderRate

Desired ShipmentRate

Order FulfillmentRatio

MaximumShipment Rate

Table for OrderFulfillment

Work in Process InventoryProduction RateProduction Start

Rate

Adjustment forWIP

Desired ProductionStart Rate

ManufacturingCycle Time

Desired WIPWIP Adjustment

Time

DesiredProduction

ExpectedOrder Rate

Desired Inventory Desired InventoryCoverage

Safety StockCoverage

Minimum OrderProcessinig Time

Adjustment forInventory

InventoryAdjustment Time

Key management decisions are made by Order Fulfillment Production Scheduling

Three Balancing Loops

Stockout loop regulates shipments as inventory varies

Inventory and WIP Control Loops adjust production starts to move the levels of inventory and WIP toward their desired levels

In this initial model there are…

No capacity constraints (from either labor or capital)

No stocks of materials

Production Structure

InventoryWork in Process

InventoryProduction StartRate

Production Rate

ManufacturingCycle Time

Production

Production Rate =

DELAY3(Production Start Rate, Manufacturing Cycle time)

Terms

Manufacturing Cycle Time—the average transit time for all items aggregated together in the model

Manufacturing delay is being modeled as a fourth-order material (flow) delay

An Order Fulfillment Structure

InventoryShipment Rate

InventoryCoverage

Customer OrderRate

Desired ShipmentRate

Order FulfillmentRatio

MaximumShipment Rate

Table for OrderFulfillment

Desired InventoryCoverage

Safety StockCoverage

Minimum OrderProcessinig Time

InventoryAdjustment Time

Table for Order Fulfillment

From Fig. 18-3

Desired Shipment Rate =

Customer Order Rate

Order Fulfillment Ratio =

Table for Order Fulfillment(Maximum Shipment Rate/Desired Shipment Rate)

Minimum Order Processing Time = 6 Is a constant

Maximum Shipment Rate =

Inventory/Minimum Order Processinig Time

Safety Stock coverage =

6 Is a constant

Time to Average Order Rate =

6 Is a constant

Desired Inventory coverage =

Minimum Order Processing Time = 6 Is a constant

Desired Inventory =

whatever

Adjustment for Inventory =

Difference between desired inventory and actual inventory, all divided by the Inventory Adjustment Time

Inventory Adjustment Time =

6 Is a constant

A production starts structure

Work in Process InventoryProduction RateProduction Start

Rate

Adjustment forWIP

Desired ProductionStart Rate

ManufacturingCycle Time

Desired WIPWIP Adjustment

Time

DesiredProduction

ExpectedOrder Rate

Desired Inventory

Adjustment forInventory

InventoryAdjustment Time

Manufacturing Cycle time =

6 Is a constant

Desired WIP =

Manufacturing Cycle Time * Desired Production

This is an implementation of Little’s Law

WIP Adjustment Time =

6 Is a constant

Adjustment for WIP =

Guess: f(Desired WIP, WIP Adjustment time, Work in Process Inventory)

Desired Production =

MAX(0, Expected Order Rate + Adjustment for Inventory)

Desired Production Start Rate = Adjustment for WIP + Desired

Production

Production Start Rate =

MAX(0, Desired Production Start Rate)

A demand forecasting component This structure simply smoothes the

customer order rate, much like exponential smoothing would do to provide a realistic model of the forecasting process used in many firms

The demand forecasting structure

Customer OrderRate

ExpectedOrder Rate Change in Exp

Orders

Time to AverageOrder Rate

What is the equation for Change in Exp Orders?

Typical constants

Minimum order processing time = 2 wks Safety Stock Coverage = 2 wks Manufacturing Cycle Time = 8 wks Inventory Adjustment Time = 8 wks WIP Adjustment Time = 2 wks

Initial Stocks for Equilibrium

Initial Inventory = Desired Inventory\ Initial WIP = Desired WIP Initial Expected Order Rate = Customer

Order Rate

These are all the initial conditions needed to create an initial equilibrium

Behavior—Inventory

Inventory drops below desired inventory

Inventory vs. Desired Inventory60,000

50,000

40,000

30,000

20,0000 5 10 15 20 25 30 35 40 45 50

Time (Week)

Inventory : run2Desired Inventory : run2

Behavior—The RatesThe Rates

15,000

13,250

11,500

9,750

8,0000 5 10 15 20 25 30 35 40 45 50

Time (Week)

Customer Order Rate : run2Production Rate : run2Shipment Rate : run2Production Start Rate : run2

What the rate BOT charts tell us Amplification of the customer order rates

by the production starts rate is unavoidable This is what causes the bull whip effect in

supply chains, especially when suppliers are linked to the manufacturer by JIT Kanban or signaling systems

There is a phase lag between receipt of the order and its fulfillment

There is no significant oscillation

What about backlogs?

Boeing, like not other manufacturer, carries backlogs stretching out years.

Boeing is a make to order manufacturer Consideration of backlogs modifies the

order fulfillment structure

The backlog structure

InventoryShipment

RateB

-

+

DesiredShipment

Rate

+

BacklogOrderRate

OrderFulfillment

Rate

+

++

TargetDelivery

Delay

-

B

OrderFulfillment

DeliveryDelay+ -

Backlog equations

What is the equation for backlog? The equation for delivery delay is

formulated from one of the most important principles in Operations Management—Little’s Law: Delivery delay = backlog/order fulfillment

rate Desired Shipment Rate = Backlog/Target

Delivery Delay

More Backlog Equations

Order fulfillment rate = shipment rate These are, however, totally different

entities Shipment rate is a physical flow Order fulfillment rate is an information

accounting that reduces the amount of backlog within the computer’s database

Materials Inventory

ProductionStart Rate

DesiredProductionStart Rate

B

WIP Control

+

+

+

<ShipmentRate>

-

MaterialsInventoryMaterial

DeliveryRate

MaterialUsage Rate

MaterialUsageRatio

Table forMaterialUsage

MaximumMaterial

Usage Rate

MinimumMaterial

InventoryCoverage

+-

+

+B

MaterialsStockout

DesiredMaterial

Delivery Rate

Adjustmentfor MaterialInventory

DesiredMaterial

Inventory

MaterialSafety Stock

Coverage

+

+

-

+

B

MaterialsControl

MaterialsInventoryCoverage

<MaterialUsageRate>

<MaterialsInventory>

+-

MaterialUsage per

Unit

DesiredMaterial

Usage Rate

+

+

FeasibleProductionStarts fromMaterials

-

++

+

+

+

+

MaterialInventory

AdjustmentTime

- DesiredMaterial

InventoryCoverage

+

+

+

The final single supplier model

InventoryProduction

RateShipment

Rate

DesiredProduction

Adjustmentfrom Inventory

DesiredInventory

ExpectedOrder Rate

Change inExp Orders

InventoryAdjustment

Time

DesiredInventoryCoverage

Time to AverageOrder Rate

OrderFulfillment

Ratio

Table forOrder

Fulfillment

Work inProcess

InventoryProductionStart Rate

ManufacturingCycle Time

Adjustmentfor WIP

Desired WIP

DesiredProductionStart Rate

WIPAdjustment

Time

B

Stockout

B

InventoryControlB

WIP Control

-

-

+

+

+

++

--

+

+

-

-+

+

+

+

+

-

DesiredShipment

Rate

MaximumShipment

Rate

MinimumOrder

ProcessingTime

+

+

-

+ SafetyStock

Coverage

+

BacklogOrderRate

OrderFulfillment

Rate

+

++Target

DeliveryDelay

-

<Customer OrderRate>

+

B

OrderFulfillment

DeliveryDelay+ -

<DesiredShipment

Rate>-

InventoryCoverage

<Inventory>

+

<ShipmentRate>

-

MaterialsInventoryMaterial

DeliveryRate

MaterialUsage Rate

MaterialUsageRatio

Table forMaterialUsage

MaximumMaterial

Usage Rate

MinimumMaterial

InventoryCoverage

+-

+

+B

MaterialsStockout

DesiredMaterial

Delivery Rate

Adjustmentfor MaterialInventory

DesiredMaterial

Inventory

MaterialSafety Stock

Coverage

+

+

-

+

B

MaterialsControl

MaterialsInventoryCoverage

<MaterialUsageRate>

<MaterialsInventory>

+-

MaterialUsage per

Unit

DesiredMaterial

Usage Rate

+

+

FeasibleProductionStarts fromMaterials

-

++

+

+

+

+

MaterialInventory

AdjustmentTime

- DesiredMaterial

InventoryCoverage

+

+

+