Dynamic Control and Optimization of CapitalConstrained Stochastic Inventory Systems

doi:10.12005/orms.2015.0039

Abstract

Abstract: For most firms, especially the small-and medium-sized ones, the operational decisions are affected by their internal capital and ability to obtain external capital. However, the majority of the current studies on dynamic inventory control ignore the firm’s financial status and financing issues completely. An important question that arises is: what are the dynamic optimal inventory and financing policies for firms with limited capital and limited access to external capital? In this paper, we review some of the latest developments in this area. After a brief review of single period models, we focus on multi-period dynamic control of the firm who aims to optimize its xpected terminal wealth. Two cases are discussed in detail: self-finance and short term finance. In the first case, the firm has to rely on its own capital for all ordering decisions, while in the second, the firm can borrow short term loan from lenders. A detailed characterization of the optimal policy is presented and its managerial insights are discussed. Several possible extensions are suggested.

Key words: dynamic inventory control, capital constraint, self-finance, short-term financing, optimal policy

摘要： For most firms, especially the small-and medium-sized ones, the operational decisions are affected by their internal capital and ability to obtain external capital. However, the majority of the current studies on dynamic inventory control ignore the firm’s financial status and financing issues completely. An important question that arises is: what are the dynamic optimal inventory and financing policies for firms with limited capital and limited access to external capital? In this paper, we review some of the latest developments in this area. After a brief review of single period models, we focus on multi-period dynamic control of the firm who aims to optimize its xpected terminal wealth. Two cases are discussed in detail: self-finance and short term finance. In the first case, the firm has to rely on its own capital for all ordering decisions, while in the second, the firm can borrow short term loan from lenders. A detailed characterization of the optimal policy is presented and its managerial insights are discussed. Several possible extensions are suggested.

关键词: dynamic inventory control, capital constraint, self-finance, short-term financing, optimal policy

ZHAO Xiu-li, WANG Shou-yang. Dynamic Control and Optimization of CapitalConstrained Stochastic Inventory Systems[J]. Operations Research and Management Science, 2015, 24(2): 1-19.

ZHAO Xiu-li, WANG Shou-yang. Dynamic Control and Optimization of CapitalConstrained Stochastic Inventory Systems[J]. 运筹与管理, 2015, 24(2): 1-19.

References

[1] Alan Y, Gaur V. 2012. Operational investment and capital structure under asset based lending. technical report, owen graduate school of management, vanderbilt university.
[2] Archibald T L, Thomas J, Betts Johnston R. 2002. Should start-up companies be cautious? inventory policies which maximize survival probabilities. management science 48(9): 1161-1174.
[3] Axsater, S. 2000. Inventory control. kluwer academic publishers.
[4] Aytekin U, Birge J R. 2004. Optimal investment strategies and production across markets with stochastic interest rates. working paper. department of industrial engineering and management sciences, northwestern university, evanston, Illinois.
[5] Babich V, Aydin G, Brunet P Y, Keppo J, Saigal R. 2010. Risk, financing and the optimal number of suppliers. managing supply disruptions(eds H. Gurnani, A. Mehrotra, S. Ray). Springer-Verlag London Ltd.
[6] Babich V, Sobel M J. 2004. Pre-IPO operational and financial decisions. management science, 50(7): 935-948.
[7] Bradley D. 2000. Lack of financial and location planning causes small business bankruptcy. technical report, university of central arkansas, conway, AR.
[8] Birge J R. 2000. Option methods for incorporating risk into linear capacity planning models. manufacturing & service operations management, 2(1): 19-31.
[9] Birge J R, Xu X. 2011. Firm profitability, inventory volatility, and capital structure. technical report, university of chicago, chicago, IL
[10] Boyabatli O, Toktay B. 2010. Stochastic capacity investment and technology choice in imperfect capital markets. technical report, georgia institute of technology, atlanta, GA.
[11] Buzacott J A, Zhang R Q. 2004. Inventory management with asset-based financing. management science, 50(9): 1274-1292.
[12] Cai G, Chen X, Xiao Z. 2013. The roles of bank and trade credits: theoretical analysis and empirical evidence. productions and operations management. forthcoming.
[13] Chao X, Chen J, Wang S. 2008. Dynamic inventory management with cash flow constraints. naval research logistics, 55(8): 758-768.
[14] Chen J. 2008. Risk management of cash flow in supply Chains. Ph.D. thesis, academy of mathematics and systems science, Chinese academy of sciences. Beijing, China.
[15] Chen J B, Zhang W. 2001. The report of China’s industrial development in 2001. development and research center of the state council. report number 2001-181-185, Beijing, China.
[16] Chen X F, Cai G. 2011. Value of third-party logistics(3PL)to the supply Chain with a budget-constrained retailer. european journal of operational research, 214(3), 579-587.
[17] Chopra S, Meindl P. 2012. Supply Chain management: strategy, planning, and operations. fifth edition, prentice hall.
[18] Ciarallo F W, Akella R, Morton T E. 1994. A periodic review, production planning model with uncertain capacity and uncertain demand-optimality of extended myopic policies. Management Science, 40(3): 320-332.
[19] Dada M, Hu Q. 2008. Financing newsvendor inventory. operations research letters, 36: 569-573.
[20] Ding Q, Dong L, Kouvelis P. 2012. On the integration of production and financial hedging decisions in global markets. working paper, washington university, st. loius, MO.
[21] Eeckhoudt L, Gollier C, Schlesinger H. 1995. The risk-averse(and prudent)newsboy. management science, 41(5): 786-794.
[22] Federgruen A, Zipkin P. 1986a. An Inventory model with limited production capacity and uncertain demands I: the average-cost criterion. mathematics of operations research , 11(2): 193-207.
[23] Federgruen A, Zipkin P. 1986b. An inventory model with limited production capacity and uncertain demands II: the discounted-cost criterion. mathematics of operations research, 11(2): 208-215.
[24] Gong X, Chao X, Simchi-Levi D. 2012. Dynamic replenishment policy with cash flow constraint and short-term financing. technical report, department of industrial and operations engineering, university of michigan, ann arbor.
[25] Goyal S K. 1985. Economic order quantity under conditions of permissible delay in payments, journal of operational research society, 36: 335-338.
[26] Gupta D, Wang L. 2009. A stochastic inventory model with trade credit. manufacturing & service operations management, 11(1): 4-18.
[27] Haley C W, Higgins R C. 1973. Inventory policy and trade credit financing. management science, 20(4): 464-471.
[28] Henig M, Gerchak Y, Ernst R, Pyke D. 1997. An inventory model embedded in designing a supply contract. management science, 43(2): 184-189.
[29] Heyman D P, Sobel M J. 1984. Stochastic models in operations research, Vol. II: stochastic optimization. McGraw-Hill, NY.
[30] Hu Q, Li L, Sobel M J. 2012. Production/inventory management and capital structure. chapter 12 in the handbook of integrated risk management in global supply Chains(eds P. Kouvelis, L. Dong, O. Boyabatli, R. Li), john wiley & wons, Inc.
[31] Hu Q, Sobel M J. 2005. Capital structure and inventory management. technical report, case western reserve university, cleveland, OH.
[32] Hu Q, Sobel M J. 2007. Echelon base-stock policies are financially sub-optimal. operations research letters, 35: 561-566.
[33] Hu Q, Sobel M J, Turcic D. 2012. Optimization of inventory and dividends with risky debt. manufacturing & service operations management, forthcoming.
[34] Hua Z, Sun Y, Xu X. 2011. Operational causes of bankruptcy propagation in supply chain. decision support wystems, 51(3), 671C681.
[35] Jing B, Chen X, Cai G. 2013. Equilibrium financing in a distribution channel with capital constraint. productions and operations management. 21(6), 1090-1101.
[36] Karatzas I. 1996. Lectures on the mathmatics of finance, CRM monograph series, american mathematics society.
[37] Kouvelis P, Zhao W. 2011. The newsvendor problem and price-only contract when bankruptcy costs exist. production and operations management, 20(6): 921-936.
[38] Kouvelis P, Zhao W. 2012. Financing the newsvendor: supplier vs. bank, and the structure of optimal trade credit contracts. operations research, forthcoming.
[39] Lai G, Debo L G, Sycara K. 2009. Sharing inventory risk in supply chain: the implication of financial constraint. omega, 37(4): 811-825.
[40] Li L, Shubik M, Sobel M J. 2009. Control of dividends, capital subscriptions, and physical inventories. working paper, weatherhead school of management, case western reserve university, cleveland, OH.
[41] Martínez-de-Alb′eniz V D. Simchi-Levi. 2005. A portfolio approach to procurement contracts. production and operations management, 14(1): 90-114.
[42] Maddah B S, Jaber M Y, Abboud N E. 2004. Periodic review(s, S)inventory model with permissible delay in payments. journal operational research society, 55:147-159.
[43] Manheim website http://www.manheim.com/products/financing.
[44] Modigliani F, Miller M H. 1958. The cost of capital, corporation finance, and the theory of investment. american economic review, 48(3): 261-297.
[45] Nahmias S. 2001. Production and operations analysis, 4th edition. mcGraw-hill/Irwin, boston.
[46] Pliska S R. 1997. Introduction to mathematical finance: discrete time models. blackwell publishers.
[47] Porteus E L. 2002. Foundations of stochastic inventory theory. stanford university press, stanford, CA.
[48] Protopappa-Sieke M, Seifert R. 2010. Interrelating operational and financial performance measurements in inventory control. european journal of operational research 204(3): 439-448.
[49] Robb D J, Silver E A. 2006. Inventory management under date-terms supplier trade credit with stochastic demand and leadtime. journal of operational research society 57: 692-702.
[50] Rosenblatt M J, Rothblum U G. 1990. On the single resource capacity problem for multi-item inventory systems. operations research, 38(4): 686-693.
[51] Shi J, Katehakis M N, Melamed B. 2012. Cash-flow based dynamic inventory management. technical report, rutgers business school, rutgers university, newark and new brunswick, NJ.
[52] Simchi-Levi D, Kaminsky P, Simchi-Levi E. 2007. Designing and managing the supply Chain, third edition, McGraw-Hill/Irwin.
[53] Wang Y, Gerchak Y. 1996. Periodic review production models with variable capacity, random yield, and uncertain demand, management science, 42(1): 130-137.
[54] Xu X, Birge J R. 2004. Joint proudction and financing decisions: modeling and analysis. working paper, northwestern university, evanston, IL.
[55] Xu X, Birge J R. 2006. Equity valuation, production, and financial planning: a stochastic programming approach. Naval Research Logistics, 53: 641-655.
[56] Xu X, Birge J R. 2008. Operational decisions, capital structure, and managerial compensation: a news vendor perspective. the engineering economist, 53(3): 173-196.
[57] Yang S, Birge J R. 2011. How inventory is(should be)financed: trade credit in supply chains with demand uncertainty and costs of financial distress. working paper, university of chicago,IL.
[58] Zakrajek E. 1997. Retail inventories, internal finance, and aggregate fluctuations: evidence from U.S. firm level data. research paper No. 9722, federal reserve bank of new york, newyork, NY 10045.
[59] Zipkin P H. 2000. Foundations of inventory management. McGraw-Hill, boston, MA.