A model and an analytical method for conveyor systems in distribution centers

Abstract

The design and operation of high volume conveyor systems in distribution centers are important due to its high cost, large footprint and critical role in the system. However, there is no analytical model available. In this paper, we study the characteristics of the conveyor sortation system, develop a generic model of a complex conveyor network. We then use the Delay and Stock abstraction to develop an approximate analytical method using sample path analysis and dynamic network flow model. The decision variables include length of accumulation segments and the speeds of conveyor components aforementioned decision variables. This analytical solution provides faster analysis, insights and useful subgradient with respect to the decision variables.

Keywords

Conveyor system / sortation system / network / accumulation / sample path analysis / dynamic network flow

References

[1] Apple, J.M. (2009). Batch picking and sortation, the design of high-volume case picking operations. The Progress Group white paper. Available via DIALOG. http://www.theprogressgroup.com/publications/wp5_pick.html

[2] Atmaca T.. Approximation analysis of a conveyor system. International Journal of Production Research, 1994, 32(11): 2645-2655.

[3] Bozer Y.A., Sharp G.P.. An empirical evaluation of a general purpose automated order accumulation and sortation system used in batch picking. Material Flow, 1995, 2: 111-131.

[4] Bozer Y.A., Quiroz M., Sharp G.P.. An evaluation of alternate control strategies and design issues for automated order accumulation and sortation system. Material Flow, 1988, 4(4): 265-282.

[5] Bastani A.. Analytical solution of a closed-loop conveyor system with discrete and deterministic material flow. European Journal of Operation Research, 1988, 35(2): 187-192.

[6] Fleischer L.. Universally maximum flow with piecewise-constant capacities. Networks, 2001, 38(3): 115-125.

[7] Fleischer L., Tardos E.. Efficient continuous-time dynamic network flow algorithms. Operations Research Letters, 1998, 23(3–5): 71-80.

[8] Ford L.R., Fulkerson D.R.. Flows in Networks, 1962, Princeton, NJ: Princeton University Press.

[9] Gewekw J.. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. Bayesian Statistics, 1992, 4: 169-193.

[10] Gurkan, G., Ozge, A.Y. & Robinson, S.M. (1994). Sample-path optimization in simulation. In: Proceedings of the Winter Simulation Conference, 247–254

[11] Hoppe B., Tardos E.. The quickest transshipment problem. Mathematics of Operation Research, 2000, 25(1): 36-62.

[12] Johnson M.E.. The impact of sorting strategies on automated sortation system performance. IIE Transactions, 1998, 30(1): 67-77.

[13] Johnson M.E., Russel M.. Performance analysis of split-case sorting systems. Manufacturing and Service Operations Management, 2002, 4(4): 258-274.

[14] Kwo T.T.. A theory of conveyors. Management Science, 1958, 6(1): 51-55.

[15] Maxwell W., Wilson R.. Deterministic models of accumulation conveyor dynamics. International Journal of Production Research, 1981, 19(6): 645-655.

[16] Mayer H.. An introduction to conveyor theory. Western Electric Engineer, 1960, 4(1): 43-47.

[17] Ogier R.G.. Minimum-delay routing in continuous-time dynamic networks with piece-wise constant capacities. Networks, 1988, 18(4): 303-318.

[18] Plambeck E.L., Fu S.R., Robinson S.M.. Sample-path optimization of convex stochastic performance functions. Mathematical Programming, 1996, 75(2): 137-176.

[19] Russell M.L., Meller R.D.. Cost and throughput modeling of manual and automated order fulfillment systems. IIE Transactions, 2003, 35(7): 589-603.

[20] Schmidt L.C., Jackman J.. Modeling recirculating conveyors with blocking. European Journal of Operational Research, 2000, 124(2): 422-436.

[21] Shapiro, A. (2003). Stochastic Programming, Vol. 10 of Handbooks in Operations Research and Management Science. Elsevier North Holland

[22] Sonderman D.. An analytic model for recirculating conveyors with stochastic inputs and outputs. Internal Journal of Production Research, 1982, 20(5): 591-605.

[23] Wang Y., Zhou C.. Fluid-based simulation approach for high volume conveyor transportation Systems. Journal of System Science and System Engineering, 2004, 13(2): 297-317.

[24] Wang, Y. & Zhou, C. (2005). Fluid-based simulation model for high volume DC conveyor systems. In: Proceedings of Winter Simulation Conference

[25] Xue J., Proth J.M.. Closed loop conveyor system. INFOR, 1987, 25(1): 84-92.

[26] Zrnic D.J.N., Cupric N.L.J.. A study of material flow systems(input/output) in high-bay warehouses. International Journal of Production Research, 1992, 30(9): 2137-2149.