SUPPLY LEAD TIME UNCERTAINTY IN A SUSTAINABLE ORDER QUANTITY INVENTORY MODEL

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Abstract

Transport plays a key role in inventory management since it affects logistic costs as well as environmental performance of the supply chain. Expected value and variability of supply lead time depend on the transportation means adopted, and influence the optimal values of order quantity, reorder level, and safety stock to be adopted. Fast transportation means allow reducing expected value of the lead time; they are characterized by the highest costs of externalities (i.e. air pollutant emission, noise, congestion, accidents). On the contrary, slow transportation means require high inventory level due to large order quantity; in this case costs of externalities tend to decrease. The Sustainable Order Quantity (SOQ) [1] allows identifying optimal order quantity, reorder level, safety stock as well as transportation means which minimize the sum of the logistic and environmental costs in case of stochastic variability of product demand. In this paper, the authors propose a new SOQ analytical model considering stochastic variability of supply lead time (LT). A solution procedure is suggested for solving the proposed model. The approach is applied to a real industrial case study in order to evaluate the benefits of applying it if compared with the traditional one.

[1] Digiesi S., Mossa M., Mummolo G., A SustainableOrder Quantity Model under Uncertain Product Demand, in Manufacturing Modelling, Management, and Control, IFAC Proceedings Volumes, 7, 664-669, 2013.

[2] Harris F., How many parts to make at once, in Operations Research, 38, 6, 947-950, 1990 (reprint from Factory, The Magazine of Management, 10, 2, 135-136, 1913.

[3] Zhang X., Gerchak Y., Joint lot sizing and inspectionpolicy in an EOQ model with random yield, IIE Transactions, 22, 1, 41-47, 1990.

[4] Salameh M.K., Jaber M.Y., Economic productionquantity model for items with imperfect quality, Int. J. of Prod. Econ., 64, 1-3, 59-64, 2000.

[5] Khan M., Jaber M.Y., Bonney M., An economic orderquantity (EOQ) for items with imperfect qualityand inspection errors, Int. J. of Prod. Econ., 133, 1, 113-118, 2008.

[6] Ghare P.M., Jaggi C.K., A model for exponential decayinginventory, The J. of Ind. Eng., 14, 238-243, 1963.

[7] Covert R.P., Philip G.C., An EOQ model for itemswith Weibull distribution deterioration, AIIE Transaction, 6, 323-326, 1973.

[8] Aggarwal S.P., Jaggi C.K., Ordering policies of deterioratingitems under permissible delay in payment, J. of Oper. Res. Soc., 46, 5, 658-662, 1995.

[9] Buzacott J.A., Economic order quantities with inflation, Oper. Res. Quart., 26, 3, 553-558, 1975.

[10] Horowitz I., EOQ and inflation uncertainty, Int. J. of Prod. Econ., 65, 2, 217-224, 2000.

[11] Liao H.-C., Tsai C.-H., Su C.-T., An inventory modelwith deteriorating items under inflation when adelay in payment is permissible, Int. J. of Prod. Econ., 63, 2, 207-214, 2000.

[12] Hou K.-L., Lin L.-C., An EOQ model for deterioratingitems with price- and stock-dependent sellingrates under inflation and time value of money, Int. J. of System Science, 37, 15, 1131-1139, 2006.

[13] Baumol W.J., Vinod H.D., An inventory theoreticmodel of freight transport demand, Management Science, 16, 7, 413-421, 1970.

[14] Swenseth S.R., Godfrey M.R., Incorporating transportationcosts into inventory replenishment decisions, Int. J. of Prod. Econ., 77, 2, 113-130, 2002.

[15] Ertogral K., Darwish M., Ben-Daya M., Productionand shipment lot sizing in a vendor-buyer supplychain with transportation cost, Europ. J. of Oper. Res., 176, 3, 1592-1606, 2007.

[16] Tersine R.J., Barman S., Economic inventory/transport lot sizing with quantity and freight ratediscounts, Decision Sciences, 22, 5, 1171-1179, 1991.

[17] Burwell T.H., Dave D.S., Fitzpatric K.E., RoyM.R., Economic lot size model for price dependent demandunder quantity and freight discounts, Int. J. of Prod. Econ., 48, 2, 141-55, 1997.

[18] Darwish M.A., Joint determination of order quantityand reorder point of continuous review modelunder quantity and freight rate discounts, Computers & Oper. Res., 35, 12, 3902-3917, 2008.

[19] Alstrøm P., Numerical computation of inventorypolicies, based on the EOQ/xvalue for order-pointsystems, Int. J. of Prod. Econ., 71, 1-3, 235-245, 2001.

[20] Louly M.-A.O., Dolgui A., Calculating safety stocksfor assembly systems with random component procurementlead times: A branch and bound algorithm, Europ. J. of Oper. Res., 199, 3, 723-731, 2009.

[21] Park K.S., Inventory model with partial backorders, Int. J. of Systems Science, 13, 12, 1313-1317, 1982.

[22] Grubbstr¨om R.W., Erdem A., The EOQ with backloggingderived without derivatives, Europ. J. of Oper. Res., 59, 1-3, 529-530, 1999.

[23] Pasandideh S.H.R., Niaki S.T.A., Nia A.R., An investigationof vendor-managed inventory applicationin supply chain: the EOQ model with shortage, The Int. J. of AdvancedManuf. Techn., 49, 1-4, 329-339, 2010.

[24] Hariga M., Ben-Daya M., Some stochastic inventorymodels with deterministic variable lead time, Europ. J. of Oper. Res., 113, 1, 42-51, 1999.

[25] Pan J.C.-H., Lo M.-C., Hsiao Y-C., Optimal reorderpoint inventory models with variable lead time andbackorder discount considerations, European Journal of Operational Research, 158, 2, 488-505, 2004.

[26] Ben-Daya M., Hariga M., Integrated single vendorsingle buyer model with stochastic demand and variablelead time, Int. J. of Prod. Econ., 92, 1, 75-80, 2004.

[27] Liberatore M.J., The EOQ model under stochasticlead time, Oper. Res., 27, 2, 391-396, 1979.

[28] Bookbinder J.H., Cakanyildirim M., Continuous reviewinventory models where random lead time dependson lot size and reserved capacity, Europ. J. of Oper. Res., 115, 2, 300-313, 1999.

[29] Hayya J.C., Christy D.P., Pan, A., Reducing inventoryuncertainty: a reorder point system, Prod. and Inv. Manag. J., 28, 2, 43-49, 1987.

[30] Wang P., Hill J.A., Recursive behavior of safetystock reduction: the effect of lead-time uncertainty, Decision Sciences, 37, 2, 285-290, 2006.

[31] He X.J., Kim J.G., Hayya J.C., The cost of lead-timevariability: the case of the exponential distribution, Int. J. of Prod. Econ., 97, 2, 130-142, 2005.

[32] Bonney M., Jaber M.Y., Environmentally responsibleinventory models: Non-classical models for anon-classical era, Int. J. of Prod. Econ., 133, 1, 43-53, 2011.

[33] Hua G., Cheng T.C.E., Wang S., Managing carbonfootprints in inventory management, Int. J. of Prod. Econ., 132, 2, 178-185, 2011.

[34] Ortolani C., Persona A., Sgarbossa F., External costeffects and freight modal choice: research and application, Int. J. of Log. Res. and Appl., 14, 3, 199-220, 2011.

[35] van Essen H., Nelissen D., Smit M., van Grinsven A., Aarnink S., Breemersch T., Martino A., Rosa C., Parolin R., Harmsen J., An inventory of measuresfor internalizing external costs in transport,final report of contract move/a3/350-2010 impactassessments and evaluations (ex-ante, intermediateand ex-post) i the field of the transport, European Commission, Directorate-General for Mobility and Transport, DM 28- 0/110-Archives B-1049 Brussels, Belgium.

[36] European Commission, Strategy for internalisationof external costs, Communication from the Commission, 2008, COM(2008) 435 final (8.7.2008), Brussels.

[37] European Commission, Roadmap to a Single EuropeanTransport Area - Towards a competitive andresource efficient transport system, 2011, white paper, 2011, COM(2011) 144 final (28.3.2011), Brussels.

[38] Wahab M.I.M., Mamun S.M.H., Ongkunaruk P., EOQ models for a coordinated two-level internationalsupply chain considering imperfect items and environmentalimpact, Int. J. of Prod. Econ., 134, 1, 151-158, 2011.

[39] Digiesi S., Mossa M., Mummolo G., A loss factorbased approach for sustainable logistic, PP&C, 23, 2-3, 160-170, 2012.

[40] Rubino S., Mossa G., Digiesi S., Sustainable OrderQuantity of Repairable Spare Parts, Adv. Maint. Eng., IFAC Proceedings Volumes, 2, 1, 181-186, 2012.

[41] Rubino S., Mossa G., Digiesi S., A Sustainable EOQModel for Repairable Spare Parts Under UncertainDemand, IMA J. of Manag. Math., in press.

[42] Jonkers C.O., The loss factor of transport, F¨orden und Heben, 31, 2, 98-101, 1981.

[43] European Environment Agency, Climate for atransport change, Term 2007: indicators trackingtransport and environment in the EuropeanUnion, 2008, Available from: http://www.eea.europa. eu/publications /eea report 2008 1 [Accessed October 2012].

[44] European Commission, Regulation (EC) no715/2007 on type approval of motor vehicles withrespect to emissions from light passenger and commercialvehicles (Euro 5 and Euro 6) and on accessto vehicle repair and maintenance information, 2007.

[45] European Commission, Directive (EC) 30/2009 onspecification of petrol, diesel and gas-oil, 2009.

[46] Runhaara H., van der Heijden R., Public policy interventionin freight transport costs: effects on printedmedia logistics in the Netherlands, Transport Policy, 12, 35-46, 2005.

[47] Forkenbrok D.J., External costs of intercity truckfreight transportation, Transp. Res. Part A, 33, 7-8, 505-526, 1999.

[48] Forkenbrok D.J., Comparison of external costs ofrail and truck freight transport, Transp. Res. Part A, 35, 4, 321-327, 2001.

[49] Janic M., Modelling the full costs of an intermodaland road freight transport network, Transp. Res. Part D, 12, 1, 33-44, 2007.

[50] van Essen H., Schroten A., Otten M. Sutter D., Schreyer C., Zandonella R., Maibach M., Doll C., External Costs of Transport in Europe - UpdateStudy for 2008, Delft, CE Delft, 2011. Available from: www.cedelft.eu. [Accessed July 2013].

[51] Schreyer C., Schneider C., Maibach M., Rothengatter W., Doll C., Schmedding D., External costs oftransport - update study, Paris, International Railway Union, 2004.

[52] http://rivaluta.istat.it/ [Accessed July 2013].

[53] Parry M.L., Canziani O.F., Palutikof J.P., van der Linden P.J., Hanson C.E., Climate Change 2007:Impacts, Adaptation and Vulnerability, IPPC Working Group II, Contribution to the Fourth Assessment Report, Cambridge (UK); New York (USA), Cambridge University Press, 2007.

[54] Gnoni M.G., Iavagnilio R., Mossa G., Mummolo G., Modelling dynamics of a supply chain under uncertainty:a case from the automotive industry, Int. J. of Autom. Techn. and Manag., 3, 3, 354-367, 2003.

[55] Gnoni M.G., Iavagnilio R., Mossa G., Mummolo G., di Leva A., Production planning of a multi-site manufacturingsystem by hybrid modelling: A case studyfrom the automotive industry, Int. J. of Prod. Econ., 85, 2, 251-262, 2003.

[56] UK Department for Transport, Free Flow VehicleSpeeds in Great Britain 2011, http://www.dft.gov.uk/statistics/releases/freeflow- vehicle-speeds-in-great-britain-2011/ (accessed September 2012).

[57] EEA - European Environment Agency, 2007, EMEP/CORINAIR Emission Inventory Guidebook - 2007, http://www.eea.europa.eu/publications/EMEP CORINAIR5 (accessed September 2012).

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