Planning of Capacity and Inventory in a Manufacturing Supply Chain: Under Uncertain Demand. Acknowledgements. Outline

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1 Planning of Capacity and Inventory in a Manufacturing Supply Chain: Under Uncertain Demand B. Dominguez Balletero,, C. Luca, G. Mitra,, C. Poojari Acknowledgement European Project SCHUMANN: Supply Chain Uncertainty Management Iberdrola,, Daimler-Chryler, Ford-Spain, Yamanouchi, LCP, Univ. Politect.. Valencia, Brunel Univ. UNILEVER Reearch: OSIRIS Project Outline Strategic and tactical model for the upply chain Combining trategic and tactical deciion Model decription Future uncertaintie and hedged deciion Beyond hedging: rik meaure and rik quantification Dicuion

LCP, Univ. Politect.. Valencia, Brunel Univ.

2 Strategic and Tactical Model for the Supply Chain Strategic (Long-Term) Activitie Tactical (Medium-Term) Activitie Operational (Short-Term) Activitie Strategic and Tactical Model for the Supply Chain Deciion upport in the upply chain baed on optimum reource planning and cheduling Reource baed view of the Firm..(Shapiro..Wernerfelt..Mahoney Shapiro..Wernerfelt..Mahoney) ) reource acquiition, divetment..deployment There i a wide range of mathematical programming model in the literature for both, trategic and tactical deciion Combining Strategic and Tactical Deciion Importance of inter-temporal temporal integration of upply chain activitie a well a their functional and geographical integration i well known (Porter, 1985) Preferably, deciion are aigned jointly when they are trongly related (e.g.,capacity and inventory), or interact in a way that notably affect the overall performance Finding the appropriate balance involve identifying the combination of different activitie (e.g., capacity and inventory) that allow performance criteria to be met while optimiing a firm financial criteria (Bradley & Arntzen,99)

.deployment There i a wide range of mathematical programming model in the literature for both, trategic and tactical deciion Combining Strategic and Tactical Deciion Importance of inter-temporal

3 Combining Strategic and Tactical Deciion Capacity planning: typically concerned with deciion of location, retooling, ize, and acquiition or hut-down of capacity in order to optimie the profit over a planning horizon. Inventory planning: concerned with deciion of location, acquiition or rental of warehoue, and mainly with the holding level of WIP and FGI. Thee deciion are important conidering (1)uncertain upply or demand, (2)eaonal demand, or (3) promotional ale. Combining Strategic and Tactical Deciion The trade-off between capacity and inventory invetment implie that a greater level of one of thee aet can be employed to reduce the reliance upon the other The cot of capacity invetment increae relative to the cot of inventory.. Iue :return on aet (ROA) and economic value added (EVA) Capacity i expenive i a common managerial belief Seaonal Demand Pattern Demand pattern 25 2 Demand Qty Time period (month)

Thee deciion are important conidering (1)uncertain upply or demand, (2)eaonal demand, or (3) promotional ale.

4 Combining Strategic and Tactical Deciion Strategic Deciion Capacity Trade-off Capacity/Inventory Tactical Inventory Deciion Hedging Deciion Planning and utiliation of production & ditribution capacitie.optimal deciion Leading problem in manufacturing and upply chain logitic Need for regular evaluation of trategic aet allocation deciion (rolling plan) uncertain buine environment Determinitic Optimiation Model LP cannot be applied!! We do not know Demand Production Rate with certainty! With hind ight we can make Optimum Deciion. Wait-and-See for actual realiation? But the deciion mut be made Here-and-Now

optimal deciion Leading problem in manufacturing and upply chain logitic Need for regular evaluation of trategic aet allocation deciion (rolling plan)

5 Anwer: Buy flexibility Hedge againt uncertainty Make robut deciion Three world Determinitic: in a determinitic world all parameter known with certainty Probabilitic (Uncertain): in an uncertain world we have random parameter probability ditribution Pragmatic: in a pragmatic world we have alternative cenario and dicrete weight probability crude but poibly acceptable approximation to the actual randomne Role of time Wait and See optimum deciion Here and Now deciion to be made

ditribution Pragmatic: in a pragmatic world we have alternative cenario and dicrete weight probability crude but poibly

6 Here and Now Future Scenario 1 P 1 Scenario 1 P 1 Strategic Deciion Recoure (bet corrective action) Stochatic Programming with recoure model are ideally uited.. two perpective (near) optimum reource allocation hedge againt uncertain future outcome Deciion not optimum for any one outcome, good for many outcome! Two tage model Firt Stage: Here-and and-now aet allocation deciion take into conideration cenario(outcome) Second Stage: : Recoure deciion optimal corrective action a future unfold Model Decription Product Configuration Product Product External Supplier Cutomer Warehoue Factory Cutomer Warehoue Factory Cutomer Warehoue External Supplier Cutomer FZ WH CZ Warehoue

Two tage model Firt Stage: Here-and and-now aet allocation deciion take into conideration cenario(outcome) Second Stage: : Recoure deciion optimal corrective action a

7 Model Decription Three-echelon echelon manufacturing upply chain (factorie, warehoue, and cutomer zone) A factory can adopt different capacity configuration A factory can revie the capacity configuration every three month Production may be outourced. Contract agreed three month in advance External warehouing may be ued. Contract agreed three month in advance A cutomer can be erved either from a warehoue or directly from a factory The planning horizon i one year The demand i eaonal and uncertain Model Decription Two tage: Firt-tage tage deciion: Outourced production External warehouing Configuration reviion Second-tage deciion: Production quantitie Inventory quantitie Sale quantitie meeting demand and hortage quantitie Model Decription Contraint: Strategic capacity contraint Strategic outourcing and torage rental contraint Combined capacity and operational inventory contraint Tactical demand and hortage contraint Objective: Maximie expected profit

Contract agreed three month in advance A cutomer can be erved either from a warehoue or directly from a factory The planning horizon i one year The demand i eaonal and uncertain Model Decription Two

8 P: min Z = cx + ubject to Ax Bx + Dy n x {,1} y Ey 1 Model & Data Intance p fy = b h = d P1: x'' x y { 1,...,S} { 1,...,S} min Z = cx + fy ubject Ax Bx x' = + {,1} n 1 (x',x'') to Dy Ey h = d Strategic Contraint Combined... TacticalDemand Contraint Second - tage variable tage variable = b Firt Dicrete - Contraint Variable Model Dimenion-WS Variable: 468 Integer: 192 Contraint: 418 Nonzeroe: : 1642 Demand cenario: 43 Single product Model Dimenion- Determinitic Equivalent Variable: 1195 Integer: 192 Contraint: Nonzeroe: : Demand cenario: 43

.. TacticalDemand Contraint Second - tage variable tage variable = b Firt Dicrete - Contraint Variable Model Dimenion-WS Variable: 468

9 Beyond Hedging: Rik Meaure and Rik Quantification What i the maximum lo with a pecified confidence level?: Value-at at-rik (VaR( VaR) Mean exce lo: average lo for the wort x% cenario (e.g., 5%): Conditional Value-at at-rik (CVaR( CVaR) Beyond Hedging: Rik Meaure and Rik Quantification 35 3 Frequency VaR Maximum Lo Probability (1-ß) CVaR Lo Decriptive Simulation Model Rik Modelling Rik Deciion Model of Randomne Contraint Optimiation Technology Single Period Model Optimum Deciion VaR Downide CVaR SP Technology 1) Multi-time time period 2) Hedged Optimum Deciion Computation of rik for a given deciion SP Technology Extended Optimum Rik Deciion (include 1 and 2 above)

10 9 Computational Reult Profit per cenario auming expected 1t tg deciion Profit ( ) cenario Computational Reult Profit per cenario Profit ( ) cenario Computational Reult Profit, VaR (95%) and CVaR EV HN Profit CVaR (95%) VaR (95%)

Profit ( ) 3 25 2 15 1 5 37 38 18 19 39 4 41 31 2 32 43 22 23 34 36 25 27 9 2 6 7 8 cenario Computational Reult Profit,

11 Computational Reult CVaR (95%) veru HN Profit 1,4, 1,2, 1,, Profit ( ) 8, 6, 4, 2, 128, , ,78 154,13 16, , , , ,24 192,662 24,222 CVaR (95%) Dicuion The model revie deciion every quarter The model ue much more flexible outourcing deciion along with rental of torage pace Determinitic olution i not good enough Two-tage tochatic model lead to hedged (robut, flexible) olution CVaR and VaR need to be captured to model the rik

model ue much more flexible outourcing deciion along with rental of torage pace Determinitic olution i not good

Risk Management for a Global Supply Chain Planning under Uncertainty: Models and Algorithms

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