Model for Warehouse Product Allocation and Design
Allocating the warehouse space to the 3 typical functional areas within a warehouse- Reserve-where products(SKUs) are typically stored for a longer uration prior to shipping Forward-where fast moving products are stored for a shorter duration and also activities like collating, processing and other value added activities may be carried out prior to shipping. Cross-Dock-where products are taken in from the receiving dock and immediately transferred to the shipping dock 2.
Allocating the products (SKI-I’s) to these functional areas within the warehouse. The author argues that current practitioners make these decisions sequentially, however for an optimum design, these two criteria have to be analyzed together. Once the warehouse space has been distributed among the functional areas, the allocation of products gets limited to the constraints set by the previous design problem. However, if carried out in tandem, the result will be lower costs and optimum allocation considering the warehouse space and product flow.
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The focus of the paper is on development of a mathematical model to solve the problem and a heuristic which is typically used for a larger number of SKUs where a mathematical model will not be able to handle vast amounts of data. The author starts by describing the literature review for the paper and also a general verview of the functional areas within a warehouse and the decision making procedure currently used by practitioners. They then go on to formulate the mathematical model followed by the heuristic and a practical example.
Mathematical model: This is a linear programming problem where the authors identify several parameters associated with warehouse design and product allocation. The costs involved in the process are the storage costs and handling costs per SKU per allocated flow (receive- crossdock-ship, receive-reserve-ship, receive-reserve-forward-ship, receive-forward- ship). The problem is formulated to find out —% of total if Product i is assigned to flow J, otherwise.
To find out the storage and handling costs, the authors have suggested an equation to get these values based on warehouse investment/leasing costs, material handling equipment costs, labor costs etc. However, they require the knowledge of which product (SKIJ) is assigned to which flow… a decision variable in the primary problem. Hence they suggest to make an initial allocation to find the costs and then go on solving the problem to determine the optimum allocation and design as a 2 stage rocess. This model can be solved for upto 3000 SKU’s on a conventional solver like LINGO.
However for larger warehouse design problems the authors also suggest a heuristic which, as described in the example gives extremely close results as the mathematical model itself. The organization of the heuristic is an iterative process which starts by considering each product and then allocating it to a particular flow where the costs are the least. Based on these allocations and using the equations (constraints) in the LP model the % allocation to the functional areas is calculated. If these values are within the limits prescribed for these areas, we have arrived at the optimal solution.
If not then the products which cause the areas to exceed the bounds are identified and transferred to the other areas such that the total cost remains as low as possible. The author finally compares the results obtained by these two methods on a cost, allocation and CPU time/memory perspective by considering an example. The author concludes by re-iterating the fact that the decisions involving warehouse functional area design and product allocation should be carried out together for optimum results.