Scheduling and lot sizing

Содержание

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JAP Scheduling means the allocation of resources over time to accomplish

JAP

Scheduling means the allocation of resources over time to accomplish specific

tasks.
Workforce scheduling determines when employees work.
Operations scheduling assigns jobs to machines or workers to jobs.
Operations schedules are short-term plans designed to implement the master production schedule (MPS).
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JAP The two basic manufacturing environments are: A JOB SHOP (Process

JAP

The two basic manufacturing environments are:
A JOB SHOP (Process focused system)

is a process focused production system which specializes in low- to medium-volume production utilizing job or batch processes ( tasks in this type of flexible flow environment are difficult to schedule because the variability in job routings and the continual introduction of new jobs to be processed) and
A FLOW JOB (Product focused system) specializes in medium- or high-volume production and utilizes line or continuous processes (tasks are easier to schedule because in flow facility the jobs have a common flow pattern through the system).
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JAP Single Processor Scheduling (no alternative routing) In some cases an

JAP

Single Processor Scheduling (no alternative routing)

In some cases an entire plant

can be viewed as a single processor (for example paper machine, car manufacturing production line).
Sometimes a single processor is a bottleneck (machine or cell) that controls the output of the plant because its limited capacity. Try to maximize the utilization of a bottleneck to raise the capacity.

Decide the work priority according
to the importance of customers,
tardiness (minimize the lateness or earliness)

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JAP Allocate your customers to ABC-classes A class –strategic customers /

JAP

Allocate your customers to ABC-classes
A class –strategic customers / most profitable

(or other vice important) customers which you serve the best way
B-class ok but the service level may vary
C-class – one might try to get rid of these especially if the are not highly profitable (their purchases are very small compared to total sales)
Try always to keep your promises, but if you cannot do that prefer your A-class customer’s service level
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JAP Typically scheduling is divided to: Rough planning - > Master

JAP

Typically scheduling is divided to:
Rough planning - > Master Production

Schedule MPS
(months and weeks of factory load and biddings)
and
Fine Scheduling -> weeks, days, and hours on operation level including routing
-> Work orders start implementation and controlling phase
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JAP Rough planning – MPS What are the main objectives, reasoning and steps of it?

JAP

Rough planning – MPS
What are the main objectives, reasoning and

steps of it?
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JAP TASK 1: Estimating realistic delivery times Specially needed for sales – for customer promises

JAP

TASK 1:
Estimating realistic delivery times

Specially needed for sales – for customer

promises
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JAP TASK 2: Ensuring the resources needed Specially needed to keep

JAP

TASK 2:
Ensuring the resources needed

Specially needed to keep the delivery time

promises given to customer
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JAP TASK 3: Controlling / managing the work load Specially needed

JAP

TASK 3:
Controlling / managing the work load

Specially needed for production planning

in order to react to changes and at the same time keep the customer promises and the costs low or at least reasonable
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JAP MPS + Bids

JAP

MPS + Bids

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JAP MPS + Bids + probability for order

JAP

MPS + Bids + probability for order

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JAP MPS + Bids + capacity utilization + bid ratio

JAP

MPS + Bids + capacity utilization + bid ratio

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JAP

JAP

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JAP Fine Scheduling -> weeks, days, and hours on operation level including routing

JAP

Fine Scheduling -> weeks, days, and hours on operation level including

routing
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JAP GANTT CHART can be used as a tool for sequencing

JAP

GANTT CHART can be used as a tool for sequencing work

on machines and monitoring its progress. The chart takes two basic forms: the job or activity progress chart and the machine chart.
The progress chart displays graphically the current status of each job relative to its scheduled completion date (under).

The planned prod. time

lateness 3

earliness is 1

The tardiness of a job (how much has been done)

tardiness is 0

Current date

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JAP A machine chart depicts the sequence of future work at

JAP

A machine chart depicts the sequence of future work at three

machines and also can be used to monitor progress.

HW

VAIS.

The planned prod. time

lateness 1

earliness is 1

The tardiness of a job (how much has been done)

tardiness 0 ENE.

Current date

ENERM.

VAISALA

HW

ENERM.

NONPRODUCTIVE TIME

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JAP CRITICAL PATH METHOD (CPM) offers a systematic procedure for selecting

JAP

CRITICAL PATH METHOD (CPM) offers a systematic procedure for selecting the

critical (shortest in time) path. In addition, the amount of slack or free time on noncritical paths may be determined.
The essential characteristics of the graphs:
A circle represents a node. Arrows, or activities leaving the node, cannot be started until all activities incoming to the node have been completed. The completion of all activities incoming to a node is considered an event, as is the start of a project.
An arrow represents one of the activities of the project. Its length is of no significance. (time is expressed by numbers)
A dashed arrow represents a dummy activity. Dummy activities are used to represent precedence relationships. They are not activities in the real sense and have duration of zero.
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G A B E F H C D Problem 12a. Critical

G

A

B

E

F

H

C

D

Problem 12a. Critical Path, missing dummy arrow
You have the following list of

dependencies. How ever the picture is not quite correct. You need to add one Dummy activity arrow to fix the error, and calculate the shortest possible throughput time.
operation Depends on operation Time of operation (days)
A - (which means that operation cannot start 2
B - before this – below - is finished) 4
C A 4
D B , G 6
E C , D 2
F D 6
G A 4
H E 3


JAP

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JAP

JAP

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JAP

JAP

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JAP Problem example: Rain gauge/wind sensor installation data

JAP

Problem example: Rain gauge/wind sensor installation data

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JAP 1 2 3 4 5 6 7 8

JAP

1

2

3

4

5

6

7

8

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JAP 1 2 3 4 5 6 7 8

JAP

1

2

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5

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7

8

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JAP PERFORMANCE MEASURES: The amount of shop time for the job

JAP

PERFORMANCE MEASURES:
The amount of shop time for the job is called

JOB FLOW TIME (= time of completion – time the job was available for first processing operation) or THROUGHPUT TIME
The total amount of time required to complete a group of jobs is called MAKESPAN (= time of completion of last job – starting time of first job)
PAST DUE or TARDINESS can be expressed as the amount of time by which the job missed its due date or as the percent of total jobs processed over a period of time that missed their due dates.
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JAP PERFORMANCE MEASURES: WIP, WORK-IN-PROCESS or PIPELINE INVENTORY The sum of

JAP

PERFORMANCE MEASURES:
WIP, WORK-IN-PROCESS or PIPELINE INVENTORY
The sum of scheduled receipts

for all items and on-hand inventories is THE TOTAL INVENTORY.
UTILIZATION is the percent of work time productively spent by machine or worker.
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JAP Problem of Economic batch quantity? If you consider a factory

JAP

Problem of Economic batch quantity?
If you consider a factory that needs

to produce an output of 1000 units per year, you might think that this could be achieved by producing one batch of l 000, two batches of 500, five batches of 200, and so on, the quantity in the batch defining the frequency with which a batch of products needs to be produced. The number of batches made and the quantities in the batch will have implications for the company in terms of storage requirements, both in-progress and in the store area. It will also have implications for the amount of control required over the particular work areas, suppliers and subcontractors, and for the costs involved. A method that is used to optimise these parameters is called economic batch quantity (EBQ).
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JAP Economic Production Quantity, EPQ Economic Batch Quantity, EBQ costs lot

JAP

Economic Production Quantity, EPQ
Economic Batch Quantity, EBQ

costs

lot size

(planning) fixed cost

storage costs

setup

costs

EPQ

2 * demand of a year * setup cost per lot

production cost per unit * storage costs %

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JAP The costs associated with batch production can be categorized as

JAP

The costs associated with batch production can be categorized as direct

and ancillary. Direct costs are those that are associated directly with the production of the product and would include parts costs and process costs. The ancillary costs are those that exist independently of the numbers of product. These will include the costs of equipment maintenance and set-up costs for internally supplied goods, and the purchasing costs for those goods provided by external suppliers. It is usual to divide the ancillary costs for a batch evenly over the number in the batch.
Consequently, because of the stability of the ancillary cost the proportion allocated to each product is lower, the larger the number of products in a batch. However, the problem of producing goods in large batches is that they require you to have a large stockholding, the cost of which increases with the number of units in the batch.
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JAP The use of the EBQ method is designed to analyse

JAP

The use of the EBQ method is designed to analyse these

problems and provide an optimum solution. The EBQ can be shown graphically and it can be calculated according to the formula:
EBQ = SQR(2SD/IC)
S= ancillary (set up) cost per batch
D = annual usage (units)
I= annual holding cost as a fraction of the stock value
C= unit cost of the item
The main advantage of using the EBQ is that it gives a value which is optimized for a certain data set. There are, however, a number of problems associated with its use that have to be considered. The main problems relate to the assumptions that have to be made, i.e. that unit price and ancillary cost remain constant throughout the year. There is also the problem that the ancillary costs, and more particularly the stockholding costs per batch, can be very difficult to assess. Finally, the EBQ will not often produce a number that is consistent with supply systems.
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JAP EXAMPLE of EPQ / EBQ A company makes telephone booths,

JAP

EXAMPLE of EPQ / EBQ
A company makes telephone booths, for a

stable market where the demand is 450 units per month. The booths are made in batches, with all the units in each batch being completed at the same time. Given the following information, calculate the economic batch quantity: Machine set-up cost per batch 150 €, Stockholding cost = 10% of stock value per annum, Unit cost = 37.50 €
EPQ = EBQ = SQR((2 * 450 * 150)/(10% * 37,50)) =
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JAP Problem 28. ECONOMIC BATCH SIZE / REPETITIVE ORDER QUANTITIES Replacement

JAP

Problem 28. ECONOMIC BATCH SIZE / REPETITIVE ORDER QUANTITIES
Replacement parts are

supplied from an inventory by a manufacturer of industrial tools. For a particular part, the annual demand is expected to be 750 units. Machine setup costs are $50, carrying costs are 25 % per year, and the part is valued in inventory at $35 each.
a) What is the economic order quantity placed on production?
b) What is the ROP (reorder point quantity) if it takes 1,5 weeks to set up production and make the parts ?
c) The production rate for these parts is 50 units per week. What is the production run quantity?
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JAP Very difficult EPQ and lot size problem: The demand of

JAP

Very difficult EPQ and lot size problem:
The demand of an item

is 20000 units in a year, and there are 250 working days in the factory per year. The rate of production is 100 units a day and lead time is 4 days. The unit cost of production is € 40,00 per unit, holding cost 25 %, and the set up cost € 20,00 per run.
What are the economic production quantity (lot size),
the number of runs in a year,
the reorder point, and
What would be the practical lot size in this case, EPQ or something else?
the annual cost in both cases?
How does the 99,7 % requirement of availability of finished goods affect to questions a-d, when you know that the standard deviation of demand during production lead time (throughput time) is 80 units?
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JAP EPQ= SQR((2*20000*20)/(0,25*40))= ( 282 units) 280 units which lasts for

JAP

EPQ= SQR((2*20000*20)/(0,25*40))= ( 282 units) 280 units which lasts for 280/80=3,5

days and it is produced in 280/100=2,8 days
Number of runs is 20000/282=71 runs
In normal case Reorder Point would be 4 days before the storage gets empty: Safety stock + usage (demand) from production order to production start up = 0 + 4 days*(20000 units/250 day)= 0 + 4 * 80 = 320 units
But in this case the picture tells you the truth better. The reorder takes place when storage level gets to 40 one production cycle earlier.

Storage max 56 = 2,8 * 20

Fill rate 100-80=20/day

Demand 80/day

2,8 days

56/80 = 0,7 day

2,8 + 0,7 = 3,5 days

4 days earlier => ordering point is 0,5*80= 40

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JAP 99,7% safety one gets by safety storage of 3 *

JAP

99,7% safety one gets by safety storage of 3 * standard

deviation (80 units) during the lead time (4 days)
=> 3*80 = 240 safety storage

Average usage during lead time

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85 103 130 127 162 30 88 51 72 32 20

85

103

130

127

162

30

88

51

72

32

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60

105

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40
BEGIN
END
I II III IV
Work Phases

Problem 11. Arranging the Production Flow

– Routing Problem – dynamic programming
Your job is to plan the production flow in a factory. The product is manufactured in four work phases ( I, II, III and IV ), and you can choose four different machines/methods for each job ( A, B, C and D ).
You know the machine hour prices and those combinations in workflow which are possible for manufacturing. All combinations are not suitable, because of technological restrictions. The possible production flows and machine hour prices are shown in the picture below:

Your task is to plan the most economic solution for manufacturing for the case. By doing that you should be able to choose also the next economical solution and so on, for the case you need to increase the capacity or there is a machine breakdown in production.
It is possible to solve the problem in this simple case only by testing and calculating the different possibilities, but when the situation gets more complicated you need to have a computer and an algorithm to solve the problem.
This task is a typical example of dynamic programming, which is a method for finding out optimum solution in a situation of sequence decisions - The previous decision affects the next one.

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