Journal of the Korean Operations Research and Management Science Society (한국경영과학회지)

The Korean Operations Research and Management Science Society (한국경영과학회)
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An Integrated Control Problem of Secondary Sourcing and Inventory in A Supply Chain

공급체인에 있어서 이차원천과 재고의 통합적 통제에 관한 연구

  • Published : 2007.03.31
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Abstract

We consider a supply chain where products are shipped to warehouse from manufacturing system to customers. Products are supplied from either in-house regular manufacturing or the secondary source such as subcontractor. The inventory in warehouse is controlled by base-stock policy, that is, whenever a demand arrives from customer, an order is released to the manufacturing system. Unsatisfied demand is backlogged. The manufacturing system is modeled as M/M/s+1/c queueing system, and the orders exceeding the given limit care blocked and lost. The steady state distribution of the outstanding orders and the throughput of the manufacturing system are functions of the level of engagement In the secondary source. There is a profit obtained from throughput and cost not only due to the engagement of the secondary source in the manufacturing system but also inventory positions. We want to maximize the total production profit minus the total cost of the production system by simultaneously determining the optimal level of engagement of the secondary source and the optimal base-stock level of the inventory. We develop two algorithms : one without guarantee of the optimal solution but with the small number of computations, the other optimal but with more computations.

Keywords

References

  1. Benjaafar, S., M. ElHafsi, and F. de Vericourt, 'Demand Allocation in Multiple-product, Make-to-Stock Systems,' Management Sciece, Vol.50, No.10(2004), pp.1431-1448 https://doi.org/10.1287/mnsc.1040.0250
  2. Bradley, J.R., 'Optimal Control of a Dual Service Rate M/M/1 Production Inventory Model,' European Journal of Operational Research, Vol.161(2005), pp.812-837 https://doi.org/10.1016/j.ejor.2003.08.052
  3. Chen, F. and Y. Zheng, 'Lower Bounds for Multi-echelon Stochastic Inventory Systems,' Management Science, Vol.40(1994), pp.1426-1443 https://doi.org/10.1287/mnsc.40.11.1426
  4. Clark, A. and H. Scarf, 'Optimal Bounds for a Multi-echelon Inventory Problem,' Management Science, Vol.6(1960), pp.475-490 https://doi.org/10.1287/mnsc.6.4.475
  5. Crabill, T.B., 'Optimal control of a Service facility with Variable Exponential Service Times and Constant Arrival Rate,' Management Science, Vol.18(1972), pp.560-566 https://doi.org/10.1287/mnsc.18.9.560
  6. Dellaert, N.P. and M.T Melo, 'Make-to-order Policies for a Stochastic Lot-sizing Problem Using Overtime,' International Journal of Production Economics, Vol. 56(1998), pp.56-57, 79-97
  7. Duenyas, I., W.J. Hopp, and Y. Bassok, 'Production Quota as Bounds on Interplant JIT Contracts,' Management Science, Vol. 43, No.10(1997), pp.1372-1386 https://doi.org/10.1287/mnsc.43.10.1372
  8. Fox, B., 'Discrete Optimization via Marginal Analysis,' Management Science, Vol. 13(1969), pp.210-216 https://doi.org/10.1287/mnsc.13.3.210
  9. Gordon, P.J., Contract Manufacturing form a Global Perspective: 1999 Update, Technology Forecasters, Inc., Alameda, CA, 1999
  10. Iyer, A.V. and A. Jain, 'Modeling the Impact of Merging Capacity in Production-Inventory Systems,' Management Science, Vol. 50(2004), pp.1082-1094 https://doi.org/10.1287/mnsc.1040.0245
  11. Johnson, M.E., and S. Whang, 'E-Business and Supply Chain Management : An Overview and Framework,' Production and Operations Management, Vol. 11(2002), pp.413-423 https://doi.org/10.1111/j.1937-5956.2002.tb00469.x
  12. Kelly, F.P., Reversibility and Stochastic Networks, John Wiley & Sons Ltd., 1979
  13. Prasad, R., 'SMT Vender Selection, Qualification and management,' In : Proceedings of the Electronic Manufacturing Services Conference, San Jose, CA, (1995), pp.31-36
  14. Rubio, R. and L.M. Wein, 'Setting Base Stock Levels Using Product-form Queueing Networks,' Management Science, Vol.42, No.2(1996), pp.259-268 https://doi.org/10.1287/mnsc.42.2.259
  15. Sobel, M.J., 'Optimal Average Cost Policy for A Queue with Start-up and Shut-down Costs,' Operations Research, Vol.17(1969), pp.145-162 https://doi.org/10.1287/opre.17.1.145
  16. Zheng, Y.S. and P. Zipkin, 'A Queueing Model to Analyze the Value of Centralized Inventory Information,' Operations Research, Vol.38(1990), pp.296-307 https://doi.org/10.1287/opre.38.2.296