Aggregate and Workforce Planning (Huvudplanering)

Transcription

1 Aggregae and Workforce Planning (Huvudplanering) Producion and Invenory Conrol (MPS) MIO030 The main reference for his maerial is he book Facory Physics by W. Hopp and M.L Spearman, McGraw-Hill, 200.

2 Wha is he Role of Aggregae Planning? Role of Aggregae Planning Long-erm planning funcion Sraegic preparaion for acical acions Aggregae Planning Issues Producion Smoohing: invenory build-ahead Produc Mix Planning: bes use of resources Saffing: hiring, firing, raining Procuremen: supplier conracs for maerials, componens Sub-Conracing: capaciy vendoring Markeing: promoional aciviies 2

3 Aggregae Planning is Long Term Markeing Parameers FORECASTING Produc/Process Parameers CAPACITY/FACILITY PLANNING WORKFORCE PLANNING Labor Policies Capaciy Plan Personnel Plan AGGREGATE PLANNING Aggregae Plan Sraegy WIP/QUOTA SETTING Cusomer Demands Maser Producion Schedule DEMAND MANAGEMENT WIP Posiion SEQUENCING & SCHEDULING Tacics REAL-TIME SIMULATION Work Schedule Work Forecas SHOP FLOOR CONTROL PRODUCTION TRACKING Conrol 3

4 Basic Aggregae Planning Siuaion Problem: plan producion of single produc over planning horizon. Moivaion for Sudy: mechanics and value of Linear Programming (LP) as a ool inuiion of producion smoohing Inpus: demand forecas (over planning horizon) capaciy consrains uni profi invenory carrying cos rae 4

5 A Simple Aggregae Planning Model (I) Noaion: = an index of he ime periods, =,...,. d = demand in period. c = capaciy in period. r = uni profi (no including holding cos) h = cos o hold one uni of invenory for one = quaniy produced during period. S = quaniy sold during period. I = invenory a he end of period. period. 5

6 A Simple Aggregae Planning Model (II) Formulaion summed over planning horizon max = rs hi sales revenue - holding cos subjec o I S =, S I, I d c + 0 S, =,... =,... =,... =,... demand capaciy invenory balance non-negaiviy 6

7 Produc Mix Planning (I) Problem: deermine mos profiable mix over planning horizon Moivaion for Sudy: linking markeing/promoion o logisics. Boleneck idenificaion. Inpus: demand forecas by produc (family?); may be ranges uni hour daa capaciy consrains uni profi by produc holding cos 7

8 Produc Mix Planning (II) Verbal Formulaion maximize subjec o: profi producion capaciy, a all worksaions in all periods sales demand, for all producs in all periods Noe: we will need some echnical consrains o ensure ha variables represen realiy. 8

9 Produc Mix Planning (III) Noaion i j d a c r d i h i S I i ij j i i i i = an index of produc, i =,..., m = an index of worksaion, j =,..., n = an index of period, =,..., = maximum demand for produc i in period. = minimum sales allowed of produc i in period = ime required on worksaion j o produce one uni of produc = capaciy of worksaion j in period. = ne profi from one uni of produc i = cos o hold one uni of i for one period. = amoun of produc i produced in period = amoun of produc i sold in period. = invenory of produc i a end of. i. 9

10 Produc Mix Planning (IV) Mahemaical Formulaion max = m i= r i S i h i I i (sales revenue - holding cos) subjec o I i i d i =, S m i= I i, I S a i i i ij + d i 0 i i c j S i, for alli, for all j, for alli, for alli, (demand) (capaciy) (invenory balance) (non-negaiviy) 0

11 A Produc Mix Example (I) Assumpions: Daa: wo producs, P and Q consan weekly demand, cos, capaciy, ec. Objecive: maximize weekly profi Produc P Q Selling price $90 $00 Raw Maerial Cos $45 $40 Max Weekly Sales Minues per uni on Workcener A 5 0 Minues per uni on Workcener B 5 35 Minues per uni on Workcener C 5 5 Minues per uni on Workcener D 25 4

12 A Produc Mix Example (II) A Linear Programming (LP) Approach: Formulaion: Soluion: max 45 P + 60 Q 5000 subjec o : 5 P + 0 Q P + 35 Q P + 5 Q Opimal Objecive * P * Q P = $ = = Ne Weekly Profi : Round soluion down (sill feasible) o: Q * P * Q = 75 = 36 To ge $ $ $5,000 = $535. 2

13 Exensions o he Basic Produc Mix Model (I) Oher Resource Consrains: Noaion: b k ij j i = unis of resource j required per uni of produc i = number of unis of resource j availablein period = amoun of produc i produced in period Consrain for Shared Resource j: m i= b ij i k j Uilizaion Maching: Le q represen fracion of raed capaciy we are willing o run on resource j. m i= a ij i qc j for all j, 3

14 Exensions o he Basic Produc Mix Model (II) Backorders: Subsiue Ii = Ii Ii Allow I i o become posiive or negaive + Penalize I, differenly in objecive if desired max Overime: i I i + Define O j as hours of OT used on resource j in period and β j he cos of one overime hour in worksaion j Add O j o c j in capaciy consrain. m i= a ij { m } + r S h I π I = i= i i i i i + O Penalize O j in objecive if desired max c j j for all j, { m } + n r S h I π I β O = = i i i i i i = i i i j j j 4

15 Workforce Planning Problem: deermine mos profiable producion and hiring/firing policy over planning horizon. Moivaion for Sudy: hiring/firing vs. overime vs. Invenory Build radeoff ieraive naure of opimizaion modeling. Inpus: demand forecas (assume single produc for simpliciy) uni hour daa labor conen daa capaciy consrains hiring/ firing coss overime coss holding coss uni profi 5

16 A Workforce Planning Model (I) Noaion j d d a b c j r h l l e e j = an index of worksaion, j =,..., n = an index of period, =,..., = maximum demand in period. = minimum sales allowed in period = uni hours on worksaion j = number of man hours required o produce one uni. = capaciy of work cener j in period. = ne profi from one uni. = cos o hold one uni for one period. = cos of regular ime in dollars / man - hour = cos of overime in dollars/ man - hour = cos o increase workforce by one man - hour = cos o decrease workforce by one man - hour 6

17 A Workforce Planning Model (II) Noaion (con.) S I W H F O = amoun produced in period = amoun sold in period = invenory a end of = workforce period in man - hours of regular ime = increase (hires) in workforce from period o in man - hours. = decrease (fires) in workforce from period o in man - hours. = overime in period in hours Noe, his model only considers a single produc. Generalizaions o m producs are sraighforward! 7

18 8 { } F H W O I S O W b F H W W S I I c a d S d e F eh O l lw h I S r j j for all 0,,,,,, for all for all for all, for all for all subjec o max + + = + = = A Workforce Planning Model (III) Formulaion

19 A Workforce Planning Example (I) Problem Descripion 2 monh planning horizon 68 hours per monh 5 workers currenly in sysem regular ime labor a $35 per hour overime labor a $52.50 per hour $2,500 o hire and rain new worker $2,500/68=$4.88 $5/hour $,500 o lay off worker $,500/68=$8.93 $9/hour 2 hours labor per uni demand assumed me (S =d, so S variables are unnecessary) 9

20 A Workforce Planning Example (II) Soluion: LP opimal Soluion: layoff 9.5 workers Add consrain: F =0 resuls in 48 hours/worker/week of overime Add consrain: O 0.2W Reasonable soluion? 20

21 Aggregae Planning Conclusions No single AP model is righ for every siuaion Simpliciy promoes undersanding Linear programming is a useful AP ool Robusness maers more han precision Formulaion and Soluion are no separae aciviies. 2