An analytical model for computing the optimal time-and-quantity-based policy for consolidated shipments

Abstract

The logistics literature reports that three different types of shipment consolidation policies are popular in current practice. These are time-based, quantity-based and Time-and-Quantity (TQ)-based consolidation policies. Although time-based and quantity-based policies have been studied via analytical modeling, to the best of the authors knowledge, there is no exact analytical model for computing the optimal TQ-based policy parameters. Considering the case of stochastic demand/order arrivals, an analytical model for computing the expected long-run average cost of a consolidation system implementing a TQ-based policy is developed. The cost expression is used to analyze the optimal TQ-based policy parameters. The presented analytical results prove that: (i) the optimal TQ-based policy outperforms the optimal time-based policy; and (ii) the optimal quantity-based policy is superior to the other two (i.e., optimal time-based and TQ-based) policies in terms of cost. Considering the expected maximum waiting time as a measure of timely delivery performance, however, it is numerically demonstrated that the TQ-based policies improve on the quantity-based policies significantly with only a slight increase in the cost.

Keywords:

• Shipment consolidation
• renewal theory
• Poisson processes

Acknowledgements

This research was supported in part by NSF Grant CAREER/DMI-0093654 and by NSERC (Natural Sciences and Engineering Research Council of Canada).

Notes

¹We generated the problems through a factorial design of the model parameters K and w while assuming λ = 1. Parameter K varies from 40 to 4000 with a factor of 1.2 whereas parameter w varies from 0.2 to 40 with a factor of 1.2.