Fundamentals of Industrial Plants Prof. Andrea Sianesi academical year 2011/2012

Fundamentals of Industrial Plants Prof. Andrea Sianesiacademical year 2011/2012 Push Techniques: Material Requirements Planning & Short Term Scheduling

Inventory systems for dependent demand • Overall view (taxonomy) • The planning of requirements consists of the determination of • What • How much and • When to order at every stage of the production process Push systems (needs based) (requirements based) Dependent demand Planning systems Traditional Pull systems (stock based) Independent demand Just in Time

Inventory systems for dependent demand • Pull (stock based) systems • Objective: having “always” the required product stored in the warehouse • According to the service level • Required information:order issuing criteria (re-order policy): the triggering mechanism • E.g. Economic Order Quantity • Implicit hypotheses: • Smoothed and even stock consumption • Independent demands among finished products • Reduced demand variance • Distinctive feature:to manage the inventory level of components, each phase of the production process only “sees” the warehouse immediately downstream • while it is completely blind with reference to the remainder of the production / inventory system

Inventory systems for dependent demand Manufacturing lead time Inventory level Finished products Re-order point Re-order time r3 r2 r1 Inventory level Components time r3 r2 r1 Inventory level Raw materials time r2

Inventory systems for dependent demand • Push (needs / requirements based) systems • Objective: calculating which, how many and when components, sub-assemblies, parts, raw materials etc. are required to put a plan into operation i.e. to ensure that the customers’ orders due dates (deadlines) are respected • Requirements of components directly depend on a plan (e.g. the master production schedule) • Requirements of components are therefore calculated and not estimated (i.e. derived from statistical analyses) as under pull systems • In the end, the objective lies in coordinating the production dates (rendezvous) of components to manufacture finished products (or higher level components in the bill of materials) • Required information:It is much greater than under pull systems, as it is needed to know the master production schedule, the bills of materials and to consider at the same time all the data referred to all the products and departments involved

Inventory systems for dependent demand • Push (needs / requirements based) systems • MRP means Materials Requirements Planning and it represents the procedure that implement the data processing needed by the push approach to manage inventories • MRP procedure consists of planning, on a time horizon • made up of periods of a predetermined length over time in the future, the inventory level (i.e. the availability) of each item of the bill of materials:finished products, components, raw materials etc.

Inventory systems for dependent demand MPS Front end DETAILED Inventory BOMs Routing MATERIAL status file PLANNING data MRP RESOURCE PLANNING MATERIAL AND Engine CAPACITY PLANS Back end

Inventory systems for dependent demand • Push (needs / requirements based) systems • MRP procedure operates according to the so-called “3S” approach • Sum • The requirements of the same component coming from different orders and referred to the same period • Split • The overall requirements per period of each component according to the lot-sizing policy • Shift (backward) • The lot-sized requirements along the time-related dimension (i.e. over time) according to the lead times reported in the bills of materials (to take into account the production routings) • This leads to a plan of purchasing and manufacturing order proposals which in turn generates • falling to the lower level of the bill basis • gross requirements of lower-level components • The interactive procedure is finished with the analysis of raw materials also called “leaves” of the bill of materials

To clarify the concept of BOM Inventory systems for dependent demand Motorcycle Chassis Power Train Gear Engine Exhaust Rear Wheel Front Wheel Frame Brake

Inventory systems for dependent demand • Example of MRP running Other re-order policies are e.g. Lot-for-lot (L4L) policy and Dynamic EOQ (Wagner & Whitin Model) Product A data Higher-level item (e.g. motorcycle) M Coefficient of use A X A–C tie data A–B tie data 2 1 B C Raw material (*) Notice that, while under pull systems safety stocks are used to face demand (and/or lead time) variance, under push systems safety stocks (due to the presence of MPS) are used to face the forecasting error

Inventory systems for dependent demand Reserved _ stocks safety stocks Initial _ inventory 120 = 200 – 30 – 50, i.e.: • Example of MRP running + = - = x 1.1 (30 – 20 ) x 1.1 = 11 55 – (48 – 11 – 22) = 40 LT = 3 periods x 2.2 LT correction = 1 period “2.2” factor comes from a twofold effect: “x 2” comes from the coefficient of use and additional “x 1.1” comes from the 10% additional scraps

Inventory systems for dependent demand • Example of MRP running

Example of MRP running: the next iteration (item B and C) Now, on the basis of the data referred to product B and C (not included in the example presented here and italicized) you can apply the MRP procedure and find the orders to be issued for B and C Inventory systems for dependent demand B C

Inventory systems for dependent demand • MRP running: some remarks • Some ties may be further specified through the “validity” over time of the tie; this helps to mange the engineering change process • Orders issuing is “timed” (i.e. placed in a given time bucket of the horizon) according to the standard lead time, which has not to be confused with the standard time and/or cycle time • The (standard) lead time is the time span between the time an order of a given product by a customer and the time the product is made available for use (i.e. it is sent, received and “approved”) by the customer • i.e. the order is fulfilled • The (standard) time and/or cycle time is the “technical” time required to finish a given phase of a production / logistic process, without setting reference to the queues • E.g. the tool-piece contact time during lathe machining • Various reports are available at the end of the iterative running • Production and/or purchasing orders to issue • i.e. the ones that fall in “period 1” (none in the example) • Urgent orders to issue • Customers orders tracking • if the specific MRP software tool keeps the connection (i.e. pegs) between the quantity of customers orders and the requirements of the products

Inventory systems for dependent demand • Limits of MRP procedures • Three major areas are referred to as “critical system design features” (Orlicky, 1974) • Production capacity • Lead times • Data • MRP basically operates at infinite capacity • Loading of work centers is optimized only indirectly, through lot-sizing rules. • Lead times are assumed as fixed and pre-determined • Lead times are used as input variables and they are not considered as function of (dependent on) the work load • No protection is assured against the “orders in the past” phenomenon • i.e. the orders that fall in periods prior to period 1, i.e. orders that would have had to be issued “in the past” (yesterday, last week / month etc.) • MRP requires a high volume of data and it needs a tight control and a careful updating and management of information

Short term scheduling: Objectives • Define WHAT, HOW MUCH, WHEN and WHERE to produce • At the level of single batch of each item and at machine level • On a short term horizon (normally weekly) • With temporal detail level the day or the hour • Data • Production orders generated in the previous planning phases • Resource availability • Actual state of production system and inventory level

Short TermScheduling: The steps • Loading of the production plan defined in the MPS-MRP phases in the production system and generation of production orders • Production operations allocation to available resources • Sequencing of production, taking into account plant situation and characteristics

Short Term Scheduling: Critical issues • Huge amount of data both technical and managerial to take into account • Uncertainty of working data • Variability (e.g. product variants, urgent jobs, ecc.) • Unpredictability (e.g. failures) • Uncertainty (e.g. working times, efficacy, ecc.) • Difficulties in the objective definition: • Better to aim to efficacy (e.g. machine saturation, low WIP,…) or to effectiveness (low completion time, delays minimization,…)? • Till the end of the ’90s: Many research activities… • …but few practical applications

Today the number of applications is rising • Growing thrust to lead time reduction and to efficient use of resources • Growing production processes automation level • Growing use of information technology in production systems • Higher power of data processing systems based on distributed architectures • Easier real time data transmission

Production orders What Howmuch Forwhen Bill ofMaterials Forassembly Raw material / semifinishedproduct Production or assemblycycles Machines Tools Processing times Efficacy Set-up Calendar of availability of resources Machines Workforce Tools System status In-progess works Resources status Inventory levels Requested (updated) data

Vocabulary • SCHEDULING: “planning” • In general, synonymous of Operative Planning • JOB: working unit composed by physical units that are all of the same kind • It could be a single piece or a box or a batch • It could happen that there is no correspondence between job and client order • ROUTING: sequence of the operations that are in the job production or assembly cycle • It should include information about the machines on which these operations can be performed • DUE DATE: date in which a job should be completed (forced by higher planning levels or by final client) • PREEMPTION: stopping of the processing of one job on a machine in order to process another one that is more urgent • PASSING: overtaking between jobs waiting to be processes, for urgency reasons

Hypothesis • It is not possible to call the decisions taken at higher planning level into question. • Quantity and delivery date are fixed • Available resources (workforce, machines,tools) are completely known and it is not possible to change them • Normally it is supposed to have only one critical resource (generally the machines) • In this case, the other resources (e.g. workers) are supposed to be always available • Jobs are completely defined from a technical point of view (cycles, processing and set-up times, machines that can be used for every operation) • No alternative routings are allowed

Hypothesis • Transportation time between two following phases are unimportant • A job is available for an operation as soon as it has finished to be processed by the previous one • Presence and influence of decoupling point is not taken into account • A machine can process only one job at any given time • A job can only be processed by one machine at any given time • It can not be processed in parallel by two identical machines • It can not begin processing on a new machine until it has not completed processing on the previous one • Stock keeping costs are neglected • Due to the short planning horizon

Classification profiles • Production system typology • Plant configuration • Type of constraints considered Specific objectives Used resolution technique

Possible machine environments • SINGLE-MACHINE (or comparables), there is only one machine and all jobs must be processed on it. Once a job has been processed by the machine, it is completed • PARALLEL MACHINES, each of them can perform the only operation required for all the jobs • Identical • Not identical (processing time dependent on the machine) • OPEN SHOP: consists of many machines or shops, each of them can perform a different operation (e.g. drill, lathe…), in which the jobs routing has not been fixed a priori on technological basis. • Used essentially for checking available production capacity, disregarding the constraints raised by fixed job routing • FLOW SHOP: consists of many machines or shops, each of them can perform a different operation (e.g. drill, lathe…); all job have the same pre-defined routing • JOB SHOP: each job must be processes on some or all the machines (or shops), but each job may have a unique routing

The constraints • Set-up times • Indipendent or dependent on the sequence • Eventually, dependent on machine state (past hystory) • Preemption allowed or not allowed • Passing allowed or not allowed • Processing time deterministic or stochastic

Objectives - symbols • Commonly used symbols • N: number of jobs to be processed • j: index of the job • M: number of machines • i: index of the machine • Variables known when problem is set • tjki: processing time of operation k of job j on the machine i • rj: data of possible “start” of processing of job j, i.e. the moment when the job is ready to be released • dj: due date (agreed) of job j • Variables known when scheduling is completed • Ij: date of start processing job j • Cj: completion date of job j • SUji: set-up time of job j on the machine i

Objectives (1) • LATENESS (for each job): Lj = Cj – dj • Delay considering anticipation as a “negative” delay • TARDINESS (for each job): Tj = max (0, Lj) • Delay without considering anticipation • FLOWTIME (for each job): Fj = Cj – Ij • Lead time of job: from the moment in which it starts to be processed to moment when it is completed • AVERAGE LATENESS: LM = • AVERAGE TARDINESS: TM = • AVERAGE FLOWTIME: FM = • For each indicator (L, T, M) it is also possible measure the maximum (among all jobs) or the weighted average (assigning a weight wj to each job)

Objectives(2) • NUMBER OF TARDY JOBS: number of jobs with Tardiness > 0 • MAKESPAN: MAK = maxj {Cj} – minj {Ij} • Time to complete the entire portfolio of jobs • SATURATION coefficient of machine i: Tsi • AVERAGE SAT. Coeff. : TSM • WORK IN PROGRESS: WIP • TOTAL SET-UP TIME: SUC

Solving techniques Solving tecnique Optimization Heuristic Substitution Short-sighted AI Interactive Analytical Algorithmic Continuos Discrete Space Time Generic Specific Algebrical Differential Computational Enumeration Esplicit Implicit In general, it is important to keep in mind the two steps: the GENERATION of the solution and the EVALUATION of the objective function for that solution

GANTT’s diagram Machines Time

Machine environment: Other constraints: Objective: Solving technique: Single machine Sequencedependent Set-up Sujk No preemption Minimum total set-up = minimum makespan Short-sighted (in time) heuristic Karg & Thompson’s algorithm

Karg & Thompson’s algorithm • Select randomly two jobs • Select a new job and put it in any position of the sequence, computing the corresponding total set-up time • Position the job according to the sequence with the lowest total set-up time and go back to step 2 until all jobs have been positioned • Repeat several times changing the two starting jobs and the order on which the other jobs are selected, looking for a better solution

Machine environment: Other constraints: Objective: Solving technique : Single machine No Set-up or sequenceindependent (included in processing time) No preemption Minimum numberoftardyjobs Algorithmicoptimization Hodgson’s algorithm

Hodgson’s algorithm • Define the two sets: L, that is the set of tardy jobs, and E, that is the set of not tardy jobs • Put all the jobs in set E and order them by increasing delivery date • Identify the first tardy job (k) in the set E; if there is no tardy job, the sequence is given by the jobs in E, taken in the order they are, followed by the jobs in L, taken in any order • Among the first k jobs in set E, choose the one with the highest processing time and put it in L • Go back to step 3

Machine environment: Other constraints: Objective: Solving technique : Flow shop withonly 2 machines No set-up or sequenceindependent (included in processing time) No preemption No passing (samesequence on the twomachines) Minimum makespan = maximumsaturation Algorithmicoptimization Johnson's Algorithm

Johnson's Algorithm • The algorithm works by defining the sequence in the extreme parts and moving towards the inner part. • Among all the available jobs find the job j with the lowest processing time on any of the two machines (minj {tj1, tj2}) • If this time is the processing time on the first machine (tj1 < tj2), put job j at the first free place in the sequence, if it is the time on the second (tj1 > tj2) put job j in the last free place • “Free place” means the first place next (after or before) to the already placed jobs respectively at the beginning or at the end of the sequence • Cancel job j from the list of available jobs and go back to step 1 until all the jobs have been placed.

Dispatching rules • Due to the complexity and the dynamic nature of the system analyzed by operation scheduling, a PLAN, that pre-defined allocations and operations sequences, is not formulated • Instead, RULES to take decisions each moment are provided • This approach is generally (with some rare exceptions) HEURISTIC but flexible and relatively easy to use

Optimization • The job to be loaded on the machine is chosen among the one available on the basis of a “degree of worthiness” • This “degree of worthiness” is computed for each job on the basis of one or more of the following variables: • Processing time • Set-up time • Due date • Job state • Machine/plant state • Delay costs

Static The reciprocal priority of two jobs in queue at the same machine does not change in time The value of worthiness of each job can be computed once for all when the job enters the queue at the machine Dynamic The reciprocal priority of two jobs in queue at the same machine can change in time The value of worthiness of each job must be re-computed any time a decision is taken Static and dynamic rules

Local The value of worthiness for a job on a machine is calculated only with information regarding the operations on that machine Global The value of worthiness for a job on a machine is calculated with information regarding also the operations on other machines Local and global rules

SPT - Shortest Processing Time • Variable: processing time • Static • Local • First the job with the shortest processing time on the considered machine • In case of single machine, it minimizes the average flowtime • In general, it provides very good results in terms of average flowtime • Risk of strong delays of the longest jobs

EDD – Earliest Due Date • Due date • Static • Local • First the job with the earliest due date • It provides very good results in terms of number of tardy jobs • It neglets the processing time therefore it penalizes the longest jobs

OPNDD – Operation Due Date • Due date, processing time, ongoing operation • Static • Global • Calculate for each operation a OPNDD by dividing the interval between the moment when the job enters the system and the due date among all the operations • In equal parts, or • In part proportional to processing times • First the job with the earliest OPNDD for the ongoing operation

S/OPN – Slack per Operation • Due date, processing time, actual moment • Dynamic • Global • Compute for each job the SLACK = due date – actual moment – residual total processing time • Compute the rate S/OPN = SLACK / residual number of operations • First the job with lowest S/OPN • It provides very good results in terms of puntuality (especially if the due date have been “reasonably” defined) • It needs to replicate a computation every time the rule is applied

The benefits of the dispatching rules • Simple • Limited number of information needed • Flexibility of use • Easy to transfer and to reconfigure • They are not strictly linked to production system characteristics • Decision taken at the latest • A plan defined a priori becomes obsolete after few hours • Good practical results • Few valid alternatives for a job shop

Fundamentals of Industrial Plants Prof. Andrea Sianesi academical year 2011/2012