Document Type

Research Paper

Publication Date



The unit load storage assignment problem determines the assignment of a set of unit loads with known arrival and departure times to a set of unit storage locations in a warehouse. The material handling device(s) can carry at most one unit load at the time. In this research it is assumed that each of the storage locations can be accessed directly without load relocations or rearrangements and that the travel times between the storage locations and from and to the warehousing docks can be computed in advance. The objective is to minimize the total travel time of the material handling device for performing a number of storage and retrieval operations. This type of storage system is in widespread use and implemented in both mechanized and automated systems. It is by far one of the most common storage system architectures for unit loads. The formulation of this problem belongs to the class of Assignment Problems (AP) but finding the optimal solution for the most general variant is provably hard for large problem instances. A classification of the different variants of the APs for unit loads will be presented. The size of the instance problem is proportional to the product of the number of loads and the number of locations and the number of periods in the planning horizon and is typically very large for real world problem instances. Efficient solutions algorithms only exist for product-based

storage policies or for the very special case of a perfectly balanced warehouse for load-based storage policies. However, for load-based storage policies the integrality property is not satisfied in general. This results in very large binary programming problems that to date cannot be solved to optimality. However, the formulations have special structure that can be exploited to design efficient solution algorithms. Properties and the special structure of the formulation will be presented. A specialized compound solution algorithm combines primal and dual approaches and heuristics to reduce the optimality gap. Initial computational experience will be shared. It is anticipated that the solution algorithm can either be directly implemented in commercial warehouse management systems or that it becomes a tool to evaluate the performance of commercially implemented storage policies. The above formulation is the sub problem in a decomposition algorithm for the design of unit load storage systems that identifies the tradeoffs between efficiency and risk of the performance of the storage system. Different risk measures such as the standard deviation and the downside risk can be used. An example based on realistic data values shows that in this case operator-controlled systems are less expensive and more risky than automated systems. However, if the same level of risk is mandated then the automated system is less expensive.


Paper 5

Publication Title

Progress in Material Handling Research: 2014