Design of Global Supply Chains

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1 Design of Global Supply Chains Marc Goetschalckx Carlos Vidal Tjendera Santoso IERC Cleveland, Spring 2000 Marc Goetschalckx Overview Global Supply Chain Problem Bilinear Transfer Price Formulation Iterative Heuristic Global Optimization Procedure Computational Example Conclusions Marc Goetschalckx 1

2 Global Logistics Systems Models Domestic Plus Exchange Rates, Duties, Taxes Objective is Worldwide After-Tax Profit Maximization Decisions are Material Flows, Transportation Cost Allocations, and Transfer Prices Tax Rates and Profit Realization 34% 17% 12% 40% or more Marc Goetschalckx 2

3 Previous Research Nieckels (1976) NLP to solve TPP iteratively, local opt. Single commodity, no BOM Cohen et al. (1989) Dyn. NL MIP, solved iteratively, local opt. TP are markup Strong country tax reduction (feasible?) Implementation Cohen and Lee (1989) Previous Research Continued Arntzen et al. (1995) Comprehensive model for DEC No TP and taxes part of production costs Specialized MIP algorithms Canel and Khumawala (1997) TP fixed a priori at LB or UB MIP model Marc Goetschalckx 3

4 Previous Research Summary TP either Set a priori Determined iteratively, local optimum, and no bound Not included Global Transactions and Tax Rates a x,t,p b Country A Country B Tax Rate Net Income Before Tax Marc Goetschalckx 4

5 Impact of Transfer Prices on After Tax Profits A and B profit A loses, B profits A profits, B los es Transfe r price t Net income after tax A and B los e x = 20,000 x = 15,000 x = 12,000 x = 8,000 x = 6, The basic model Maximize global after tax profit: Subject to: After tax profit of internal suppliers + After tax profit at plants + After tax profit at distribution centers - Inventory costs Nonlinear expressions for the net income before tax Suppliers capacity (internal and external suppliers) Production capacity at plants Customer demand constraints Bill of materials (at plants) Balance constraints at DCs Minimum profit for internal suppliers, plants and DCs (optional) Bounds on decision variables Marc Goetschalckx 5

6 Before and After Tax Profit Objective and Constraint + max :(1 taxratek) ibtwfk ibtwfk subject to : 1 1 MPRICE w HANDC + TRCWM W w VPkp H TTWM klm + ( CSF ) SHIPFREQklm + SSFWkp l C( k) m T( k, l) p P E k TTWM klm wklmp lp klmp kp klm p klmp l C( k) m T( k, l) p P El l C( k) m T( k, l) p P Ek 1 tppldc ( 1 + DUTY ) + ( 1 propw ) TRCPW W x j M m T( j, k) p P( j) E j 1 + f FIXDCk = ibtwf k ibtwfk k W Ek jp jkp jkm jkm p jkmp The Basic Model (General Structure) Max s. to: T c x T T T P( x, t, p) c x + x A t + x B p = b ; r = 12,,..., m r Cx d 0 T t T 0 p 1 x 0, t 0 r + r r Marc Goetschalckx 6

7 Solution Methodology An optimization-based heuristic: Substitution of proportion variables Redefinition and substitution of TP variables Relaxation of nonlinear constraints Iterative procedure Global optimization Tightening of Dual Bound with Primal Heuristics Substitution of Transportation Cost Proportion Variables prosp W s = z i S, j M( i), m T( i, j) ijm r ijmr r R( i) R( j) ijm propw W x = z j M, k W, m T( j, k) jkm p jkmp p P( j) jkm Marc Goetschalckx 7

8 Transfer Prices Substitution and Constraints tpsupl s = y i S, j M( i), r R( i) R( j) ijr ijmr ijr m T(, i j) tppldc x = y j M, k W, p P( j) jkp jkmp jkp m T( j, k) y ij r ij r n = n+ 1 n+ 1 ijnmr ijn+ 1mr m T(, i j ) m T(, i j ) y n jk p jk p n = n+ 1 n+ 1 jknmp jkn+ 1mp m T( j, k ) m T( j, k ) n s x y y s x Transformed Formulation Max s. to: d v T 0 T T T T c x+ d v+ e y+ g z = f ; r = 1,2,..., m r r r r r Cx b l u Dx y Dx z Ex 0 T x F y = 0; q= 1,2,..., h (constraints to be relaxed) q x 0, y 0, v 0, z 0 Marc Goetschalckx 8

9 Optimization-Based Heuristic Solve RP(x, y, z): Upper Bound on P(x, t, p) and starting point Feasible? No Yes Optimal Solution to P(x, t, p) Solve P(x, t, z x) Solve P(x, t, z t) No Convergence criterion? Yes Local optimum of P(x, t, p) Starting Points for Heuristic Procedure Optimal TP (From Relaxation) Optimal Flows (From Relaxation) Tax Heuristic Lower Bound TP Upper Bound TP Middle Point TP Interval Zero Initial Flows Marc Goetschalckx 9

10 Computational Test Case 50 Raw Material Suppliers 8 Plants, 10 Distribution Centers 80 Customers 35 Components, 12 Finished Products 3.1 Modes per Channel Variables, 2900 Constraints Heuristic Computation Results MEDIUM INSTANCES a No. Starting Point % gap from the upper bound Solution time (s) 3 Opt_Flows Opt_TP Heu_TP LB_TP UB_TP Mid_TP Init_Flows = No. of iterations b 4 Opt_Flows Opt_TP Heu_TP LB_TP UB_TP Mid_TP Init_Flows = Opt_Flows , Opt_TP , Heu_TP LB_TP , UB_TP , ,356 Mid_TP , ,177 Init_Flows = , ,028 Marc Goetschalckx 10

11 Global Optimization Procedure Specified Optimality Gap ε Ben-Tal (1994) Branch and Bound Method for Reducing Duality Gap f max g i g T i Acceleration Techniques Branching rule: largest TP interval Branching rule: interior transfer prices Computational Experiment Global Optimization Procedure No. Target Tolerance ε (%) MEDIUM INSTANCES % gap achieved Solution time (s) No. of branches b 3 N/A a (0.405) d c N/A a (0.568) d e e 5 N/A a (0.28) d e e Marc Goetschalckx 11

12 Profit Increases for Optimal Transfer Prices Transfer Price Heuristics Instance Middle Tax Lower Upper Point Rate Bound Bound Impact of Transfer Price on Corporate Profits NET INCOME AFTER TAX [$/YEAR] vs. TRANSFER PRICE FACTOR 24,000,000 23,500,000 23,000,000 22,500,000 Net Income After Tax [$/year] 22,000,000 21,500,000 21,000,000 20,500,000 20,000,000 What is the maximum transfer price factor that satisfies the operating profit constraints of all countries? 19,500,000 NIAT 19,000,000 18,500, Transfer Price Factor Marc Goetschalckx 12

13 Conclusions Transfer Price Formulation is Bilinear Iterative Heuristic Efficient, Case Dependent Gap Global Optimization Procedure A Priori Gap Efficient with Acceleration Techniques Significant Impact on After Tax Profits Supply Chain Modeling Challenges Multiple Periods Periodic demand Dynamic strategic systems Global Taxes and profit realization Local contents, duty drawback Stochastic Flexibility, robustness, risk, scenarios Marc Goetschalckx 13

14 Supply Chain Solution Algorithms Challenges Large Scale Models Non-Linear Models Stochastic Models Standard MIP Linear Algorithms Cannot Solve Very Large Cases NL-MIP or Stochastic Algorithms Only for Small Cases or Nonexistent Supply Chain Design Challenges Integrated models are large and complex Accommodate diversity of local characteristics Cost, flexibility, and responsiveness tradeoffs for performance measures Strategic design as a continuous effort Technology transfer to logistics professionals and students Marc Goetschalckx 14

15 From a Multicommodity Case......and Configuration by a Current Design Tool Marc Goetschalckx 15

16 To Design Tools for the Next Century Marc Goetschalckx 16

Capacity Planning with uncertainty in Industrial Gas Markets

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