A capital Flow-constrained lot-sizing problem with trade credit

Document Type : Article

Authors

School of Economics and Management, Beihang University, Beijing, P.R. China

Abstract

This paper incorporates capital flow constraints and trade credit to lot sizing problems. Capital flow constraint is different from traditional capacity constraints: when a manufacturer begins to produce a certain number of products, its present capital should not be less than its total production costs of that period; otherwise, the manufacturer must decrease production quantity or suspend production, or it could delay payment using trade credit. Moreover, the capital of each period should also be greater than zero to avoid bankruptcy. We formulate a mathematical model for the single-item lot sizing problem.  Based on dynamic programming, we approximate this mixed integer problem to a traveling salesman problem finding the longest route, divide the model into sub-linear problems without integer variables, and propose a dynamic programming algorithm with heuristic adjustment to solve it. The sub-linear problems can be easily solved by interior point algorithm. Our algorithm could obtain optimal solutions under certain situations. Numerical analysis shows our algorithm has small optimality deviation percentage under other situations and holds computation efficiency advantage compared with CPLEX 12.6.2. It also indicates capital flow constraints and the application of trade credit in lot sizing problems could affect optimal production decisions.

Keywords

Main Subjects


References
1. Andriolo, A., Battini, D., Grubbstrom, R.W., Persona,
A., and Sgarbossa, F. A century of evolution from
Harris's basic lot size model: Survey and research
agenda", Int. J. Prod. Econ., 155, pp. 16-38 (2014).
2. Glock, C.H., Grosse, E.H., and Ries, J.M. The lot
sizing problem: A tertiary study", Int. J. Prod. Econ.,
155, pp. 39-51 (2014).
3. Wagner, H.M. and Whitin, T.M. Dynamic version of
the economic lot size model", Manage. Sci., 5(1), pp.
89-96 (1958).
4. Wagelmans, A., Van Hoesel, S., and Kolen, A. Economic
lot sizing: an O (n log n) algorithm that runs
in linear time in the Wagner-Whitin case", Oper. Res.,
40(1-supplement-1), pp. S145-S156 (1992).
5. Karimi, B., Ghomi, S.F., and Wilson, J.M. The
capacitated lot sizing problem: a review of models and
algorithms", OMEGA, 31(5), pp. 365-378 (2003).
6. Maes, J. and Van Wassenhove, L. Multi-item singlelevel
capacitated dynamic lot sizing heuristics: A
general review", J. Oper. Res. Soc., 39(11), pp. 991-
1004 (1988).
7. Brahimi, N., Dauzere-Peres, S., Najid, N.M., and
Z. Chen and R.Q. Zhang/Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2775{2787 2787
Nordli, A. Single item lot sizing problems", Eur. J.
Oper. Res., 168(1), pp. 1-16 (2006).
8. Jans, R. and Degraeve, Z. Meta-heuristics for dynamic
lot sizing: A review and comparison of solution
approaches", Eur. J. Oper. Res., 177(3), pp. 1855-
1875 (2007).
9. Buschkuhl, L., Sahling, F., Helber, S., and Tempelmeier,
H. Dynamic capacitated lot sizing problems:
a classi cation and review of solution approaches",
Or Spectrum, 32(2), pp. 231-261 (2010).
10. Aksen D., Altnkemer K., and Chand S. The singleitem
lot sizing problem with immediate lost sales",
Eur. J. Oper. Res., 147(3), pp. 558-566 (2003).
11. Aksen, D. Loss of customer goodwill in the uncapacitated
lot sizing problem", Comp. Oper. Res., 34(9),
pp. 2805-2823 (2007).
12. Absi N., Detienne B., and Dauzere-Peres S. Heuristics
for the multi-item capacitated lot sizing problem with
lost sales", Comput. Oper. Res., 40(1), pp. 264-272
(2013).
13. Sereshti, N. and Bijari, M. Pro t maximization in
simultaneous lot sizing and scheduling problem", Appl.
Math. Model., 37(23), pp. 9516-9523 (2013).
14. Coughtrie, D., Morley J., andWard, T. Restructuring
in bankruptcy: recent national case examples" (2009).
https://www.eurofound.europa.eu/sites/default/ les/
ef les/docs/erm/tn0908026s/tn0908026s.pdf/
15. Elston J.A. and Audretsch D.B. Financing the entrepreneurial
decision: An empirical approach using
experimental data on risk attitudes", Small. Bus.
Econ., 36(2), pp. 209-222 (2011).
16. ACCA and IMA. Surviving the recession and the
recovery: the SME story" (2013).
http://www.accaglobal.com/content/dam/acca/global/
PDF-technical/small-business/pol-tp-stra.pdf
17. Cu~nat, V. and Garcia-Appendini, E. Trade credit and
its role in entrepreneurial nance", In Oxford Handbook
of Entrepreneurial Finance, Douglas C., Ed., pp. 526-
557, Oxford University Press, New York, USA (2012).
18. Fitzpatrick, A. and Lien, B. The use of trade credit
by businesses", RBA Bulletin, pp. 39-46 (2013).
19. Goyal S.K. Economic order quantity under conditions
of permissible delay in payments", J. Oper. Res. Soc.,
36(4), pp. 335-338 (1985).
20. Chang, C.T., Teng, J.T., and Goyal, S.K. Inventory
lot-size models under trade credits: a review", A. Pac.
J. Oper. Res., 25(01), pp. 89-112 (2008).
21. Teng, J.T., Min, J., and Pan, Q. Economic order
quantity model with trade credit nancing for nondecreasing
demand", OMEGA, 40(3), pp. 328-335
(2012).
22. Liao, J.J., Huang, K.N., and Chung, K.J. Lot sizing
decisions for deteriorating items with two warehouses
under an order-size-dependent trade credit", Int. J.
Prod. Econ., 137(1), pp. 102-115 (2012).
23. Jaggi, C.K., Yadavalli, V.S.S., Verma, M., and
Sharma, A. An EOQ model with allowable shortage
under trade credit in di erent scenario", App. Math.
Comput., 252, pp. 541-551 (2015).
24. Ouyang, L.Y., Ho, C.H., Su, C.H., and Yang, C.T. An
integrated inventory model with capacity constraint
and order-size dependent trade credit", Comput. Ind.
Eng., 84, pp. 133-143 (2015).
25. Yadav, D., Singh, S.R., and Kumari, R. Retailer's
optimal policy under in
ation in fuzzy environment
with trade credit", Int. J. Syst. Sci., 46(4), pp. 754-762
(2015).
26. Zhou, Y.W., Zhong, Y., and Li, J. An uncooperative
order model for items with trade credit, inventorydependent
demand and limited displayed-shelf space",
Eur. J. Oper. Res., 223(1), pp. 76-85 (2012).
27. Seifert, D., Seifert, R.W., and Protopappa-Sieke, M.
A review of trade credit literature: Opportunities for
research in operations", Eur. J. Oper. Res., 231(2),
pp. 245-256 (2013).
28. Bitran, G.R. and Yanasse, H.H. Computational complexity
of the capacitated lot size problem", Manage.
Sci., 28(10), pp. 1174-1186 (1982).
29. Potra, F.A. andWright, S.J. Interior-point methods",
J. Comput. Appl. Math., 124(1), pp. 281-302 (2000).
30. Zhang, Y. Solving large-scale linear programs by
interior-point methods under the Matlab* environment",
Optim. Methods. Softw., 10(1), pp. 1-31 (1988).