1. Integrated Production/ Distribution Model 2000. 01. 27 Byun, Myunghee SNU. IEFALab.

2. Contents • Two papers’ presentation • “IPDM for a multi-national company operating under varying exchange rates” • Incorporate exchange rates in the model • “Synchronized Development of Production, Inventory, and Distribution Schedules” • Capacity management, inventory allocation, vehicle routing을 고려하는 모델.

3. An Integrated production-distribution model for a multi-national company operating under varying exchange rates Zubair M. Mohamed Department of Management & Information Systems, Western Kentucky University, USA IJPE 58(1999) 81-92

4. Introduction-MNC environment • Multi-national company(MNC)’s condition • The number of countries of operation • The proportion of overall revenues • The growth of international trade • Liberalizing import restrictions • Diffusion of knowledge and technology • Transnational corporations : 24,000 in the world’s 14 richest countries(by UN Conference)

5. Introduction • Relevant factors to research • Cost of production(manufacturing) • Distribution(logistics), labor costs(capacity) • Expertise in production and distribution(efficiency) • Currency exchange regulation & stability of foreign exchange(exchange rate)

6. Integrated Production/Distribution model(PDM) efficiency Exchange rate Manufacturing cost Distribution cost Forecast coefficient for the exchange rate Base exchange rate

7. Numerical examples

8. Numerical examples

9. Impression for this paper • Facility capacity는 efficiency보다 cost가 주 factor • Exchange rate를 모델에 고려. • 수식을 너무 간소화했다.(setup variable) • 가정 사항의 타당성 • Capacity change. • Exchange rate를 고려할 때와 고려하지 않을 때의 비교.

10. Synchronized Development of Production, Inventory, and Distribution Schedules F. Fumero and C. Vercellis Dipartimento di Economia e Produzione, Politecnico di Milano, Italy Transportation Science Vol. 33, No. 3, 1999

11. Introduction • Inventory/Routing problem • Production details-capacity allocation, lot size, setup • Distribution plan-vehicle routing • “Coordination of production and distribution”-by Chandra & Fisher(EJOR, 1994) • Multi-period horizon,multi-product, lot sizing & delivery routing problems

12. Descriptions of model

13. Integrated production/distribution model(IPDM) N = W{0} product vehicle time setup Binary vehicle travel Transported quantity production demand Resource level Delivered qty to customer k

14. IPDM-continue Vehical capa. absorption

15. The Decomposition Procedure • 앞의 model, constraints 2, 8 relaxation • Constraint 2 : to separate the lot-sizing and vehicle routing problems • Constraint 8 : to separate the integer and continuous Lagrangian multipliers jt, iltv Lagrangian dual problem : max, (PROD + INV + DIS + ROU) subject to iltv >= 0

16. The Decomposition Procedure • 1. Production(PROD) • 2. Inventory(INV)

17. The Decomposition Procedure • 3. Distribution(DIS)

18. The Decomposition Procedure • 4. Routing(ROU)

19. Solution Algorithms • Upper bounds(for Lagrangian dual problem) • Optimal value Pjt 를 이용해서, delivery schedule 결정 • 모든 customer k에 대해서, demand를 fully loaded vehicles과 residual demand로 나눈다. • One customer 이상을 serve 해야 하는 vehicles을 위한 route결정(by nearest neighbor heuristics) • At insertion step, a capacity check is executed.  The best results were summed up to compute the desired upper bound

20. Solution Algorithms • Primal feasible solution • 1. a reasonable delivery plan • 2. Production volume Pjt V’ v V’ v v 0 v V’ v Possible routes associated to a feasible solution of DIS

21. Computational Results

22. References • P. Chandra & M. L. Fisher, “Coordination of Production and Distribution Planning”, EJOR. 72, 503-517(1994) • F. Fumero, C. Vercellis, “Integrating distribution, machine assignment and lot-sizing via Lagrangean relaxation”, IJPE, 49, 45-54(1997) • S. S. Erenguc, N.C. Simpson, A.J. Vakharia, “Integrated production/distribution planning in supply chains : An invited review”, EJOR, 115, 219-236(1999) • M. Minoux, “Mathematical Programming : Theory and Algorithms”, John Willey & Sons, 1986