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Ye shanshan Friday, May 11, 2012 1/20

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Problem Literature Review Mathematical Model Conclusion My idea 参考文献： Gupta, S., and Dutta, K., Modeling of financial supply chain, European Journal of Operational Research, Vol. 211, No. 1, 47-56, 2011. 2/20

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Imformation Flow Downstream Flow of good Upstream Flow of cash wholesaler Supplier Up-stream Partners Down-stream Partners Distributor Fig.1. Supply chain of goods and cash for a wholesaler. 3/20

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Motivation & Subjective ： Focus on the upstream flow of money in the supply chain. Develop an optimization model to schedule payments can benefit the wholesaler. 4/20

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Hausman(2005), Killen(2002) and SAP(2005): focus on the improvement of actual business process interactions across multiple organizations in financial supply chain systems. Farris and hutchison(2002, 2003): show the importance of C2C as a metric in the supply chain. Obayrak and Akgun(2006): focus on cash conversion cycle between the time a purchase or investment is made and the time of sales revenue received from goods produced by that purchase or investment. 5/20

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Ashford et al. (1988) and Steuer and Na(2003): give good overviews of applying operational research techniques for financial decision making including both the short term and long term cash management in investments. Feinberg and Lewis (2007): proposed solution conditions for optimizing average cost of inventory for the cash balance problem. Gormley and Meade (2007): presented a policy to minimize transaction cost based on cash flow forecast and uncertainty associated with the forecast. Bar-Ilan et al. (2004): impulse control model has been developed for cash management or money demand. 6/20

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Rajamani et al. (2006): proposes a framework to analyze the cash supply chain structure and provide a framework for the physical transportation of money, similar to that of flow of materials, in a supply chain. Gupta et al. (1987): developed an integer programming model for the loan payment policies. Vanderknoop and Hooijmans (1989): a similar study by manipulating incoming receipts and outgoing cash-flows. 7/20

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Set K = set of all invoices Parameters: L k = invoice amount for invoice k νk ∈ K u k = discount rate on the invoice k’s amount ∨ k ∈ K b k = the time on or before which the invoice k needs to paid to get the discount uk ∨ k ∈ K d k = due date for the invoice k ∨ k ∈ K v k = penalty or interest rate per period if the invoice k is not paid on or before due date d k ∨ k ∈ K s k = time at which invoice was generated by the upstream partner ∨ k ∈ K, s k ≤ b k ≤ d k r = interest rate that can be earned per day for accumulated cash by the wholesaler (r < v k ) q t = total amount received from all downstream partners at time t δ= cash in hand at the beginning time 0 8/20

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Integer programming modeling Consider the problem from the viewpoint of a wholesaler: Objective: develop this model to minimize the net present value of the cash out flow to make payments to the upstream partners. Assume the future cash in-flows from downstream partners and future invoices along their terms from upstream partners are known. 9/20

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AkAk as the amount paid for the invoice k PV k as the present value X kt ＝ 1, if k is paid on day t, 0 otherwise. 10/20

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following constraints to balance the cash inflow and outflow on each day: 11/20

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Relax the constraints to have the following Lagrangian objective function for: Lower bound determination For larger problem sizes, cannot find the optimal solution, so there is no way to judge the quality of Lagrangian Relaxation solution for large size problems 12/20

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Interval heuristic Create a new problem which is obtained by merging n number of time intervals of problem P into one interval. accuracy or the problem complexity ？ For n =1 ， the new problem is reduces to the original problem. As n is increased ， the accuracy of the heuristic solution reduce. If n =7 ， one interval is a week. 13/20

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If each interval is composed of more than 7 days will perform poorly. For a very large size problem, even the interval heuristic problem becomes impossible to solve optimally. 14/20

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Dynamic invoice in-flow problem The wholesaler has two choices: (I) pay j first and then k ; (II) pay k first and then j. The real life situations are dynamic. The set of pending invoices is dynamic in nature because of the receipt of new invoices. 15/20

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When total amount received from all downstream partners at time t are known before hand, the algorithm can be run. For limited number of future time periods, the algorithm will perform well also. But if all invoices are known before hand for distant future, this algorithm will not perform well. when both the future cash in-flow and the invoice flow is dynamic and unknown, we develop an alternate heuristic. 16/20

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Dynamic invoice and dynamic cash in-flow problem 17/20

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The above algorithm is based on the assumption that it is always better to pay the invoices that have crossed the deadline. 18/20

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However, if the penalty for crossing the deadline of an invoice is very small, it may be beneficial to hold the payment of that invoice to pay for other invoices before the deadline, Where penalty is high, the heuristic decision of the algorithm will not perform well. Thus, if the variance in penalty of invoices is high, the result of the algorithm will not be as good as in other scenarios. 19/20

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Both dynamic heuristics are more time efficient than the interval heuristic. For very large problems of several years and hundreds of invoices the dynamic heuristic may be preferred over the interval heuristic. The research may be expanded to multiple echelons involving several currencies. 20/20

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