Mathematical modeling for warehouse logistics: stock loading and order picking

Abstract

Logistics makes extensive use of human and material resources to achieve a

target level of customer service at the lowest possible cost. It has been recognized

as a major key to success in commerce and industry, and continues to

evolve radically and grow in importance in recent years. Warehousing, as one

of the most costly elements of logistics, is often the central operation in most

logistics networks. Its successful management is critical in terms of both cost

and service. In this thesis, two problem areas in warehouse logistics are studied:

stock loading and order picking.

Stock loading is an essential operation in modern logistics. Improvement on

container capacity utilization and loading efficiency significantly reduces costs.

For a given set of boxes in different sizes and an unlimited number of identical

containers, the basic cargo loading problem is to determine the minimum

number of containers required. The problem is proven NP-hard. To tackle this

problem, a Tabu search optimization with a tree-based cargo loading algorithm

as its inner heuristic is proposed. This approach has flexibility in taking different

box conditions into consideration, and can find better solutions on average

than other recent meta- or heuristic algorithms.

Decreasing order sizes and increasing fuel costs provide a strong incentive for

the inner-city truck loading operation to utilize container space more efficiently

in transporting goods to multiple clients during one trip. This considers not

only traditional loading constraints, but also multi-drop requirements. A wallbuilding

heuristics based on a binary tree data structure is proposed to handle

these side constraints. A dynamic space decomposition approach, together with

a repacking and space amalgamation strategy, permits an efficient and effective

loading plan.

Order picking, one of the most critical warehousing operations, is the second

problem studied in this thesis. An analytical approximation model is proposed

based on probability modeling and queueing network theory applied to a synchronized

zone picker-to-part order picking system with different routing and

ABC-class inventory storage policies. The numerical results are compared and

validated via simulation. The resulting model can therefore be usefully applied

in the design and selection process of order picking systems.

The routing versus storage issues are further investigated with a simulation

model. This extends the existing research by evaluating multiple routing and

storage policies under varying operating conditions. Results show that the midpoint,

return and traversal routing policies generally perform best when paired

with perimeter, across-aisle and within-aisle storage strategies, respectively. Yet

performance is indeed dependent on demand patterns, zone sizes, batch sizes

and order sizes.

At first glance, order picking and stock loading operation seem to pursue

different objectives. However, they are two related operations conducted sequentially

from internal to the outbound side of warehousing. An efficient

order picking system is a precondition for an effective loading operation at the

shipping dock, especially when multiple orders need to be selected for consolidation

in shipment. The proposed loading algorithms and the order picking

system performance evaluation models can be used to further study the effective

integration of these two functions.