Economic analysis of warehouse operations

There is vast research studding particular aspects of warehouse design – layout, material handling, order picking, and operating policies – when, in fact, the decisions involved in the process are interrelated. These produces models and techniques that consider only part of the picture. “It is the synthesis of these techniques that appears to be lacking to act as a basis for the overall warehouse design” (Rouwenhorst et al., 2000).

When designing a warehouse there is a vast solution space and the interrelation between decision makes the process highly complex . In the absence of a scientific method, practitioners “must consider some very complex trade-offs, many of which are not yet fully articulated”, and “based on intuition, experience, and judgment, makes some initial design decisions about the overall system architecture” (Govindaraj et al., 2000).  “Too much of current warehousing practice is based on rules-of-thumb and simplistic ratios. This is fine as far as it goes; but there is much more that can be done.” (Bartholdi and Hackman, 2017)

Even if there are provide more comprehensive approaches to the warehouse design problem, there are still many complex trade-offs that the designer needs to face without a formalized process. For example, when deciding the number of cross aisles in a traditional warehouse layout, the designer wishes to determine the best number for the operation of his or her particular situation. Current methods only provide with the best number of cross aisles to minimize the travel time of pickers, when, in fact, there is trade-off between the administration of picking labor and the use of space. At the end, the optimal number of cross aisles will depend of the cost of this to critical resource for the warehouse operation. That is why, it is critical to make decisions based on the overall performance of the operation. The following is a systematic method to assess the total operation cost in terms of its four critical resources: labor, space, working capital and equipment and system dynamic model to describe the interrelation between warehouse design decisions and their impact to the total operational cost.

Operational cost of warehouses

The annual operational cost of warehouses is based on four sources:

• Labor: It accounts for the salaries and extra benefits of workers. The main activities that could require labor in a warehouse are receiving, put away, replenishment, picking, packing/sorting and shipping. Nevertheless, these activities can also be performed by automated equipment.  There are also activities that can require labor like cycle counting, and returns processing.
•  Space: the cost of space comes two fold. The rental cost and the operational cost – utilities, infrastructure amortizations. The main areas of the warehouse are: receiving, bulk area, picking area, Shipping.  It can also be support areas like a battery station for forklifts, returns processing, and maintenance room.
• Working capital: The financial cost of the money invest in inventory.
• Equipment: the amortization and operational cost of equipment like conveyors, industrial trucks, and racks.

Labor Cost

The labor cost will be given by the salaries, bonuses and overtime of the workforce.

$LaborCost = \sum_{ip} \left( Workers_{ip} (Salaries_{i} + Bonus_{i}) + Overtime_{ip} (HourCost_i) \right)$

where $i$ represents the activity that workers are assigned to (receiving, put away, replenishment, picking, packing/sorting and shipping), and $p$ represents periods of time.

Space Cost

The space cost is a fixed cost depending rental cost and the operational cost. The rental cost is mostly settled by the cost of land in the location of the warehouse but it can also be affected by the building characteristics like ceiling height, docks, roof structure, etc.

The operational cost refers to utilities and amortization of infrastructure. These costs are may vary through time, but their variations are negligible for our study and we will consider them as fixed costs. We refer as infrastructure, for example,  pharmaceutical products require an environmental management system  – that controls temperature, humidity, and/or ventilation – or redundant power systems.  These systems require a big investment upfront investment that we amortize and also have high operational cost in energy. We calculate it in terms of the marginal cost per square feet of rent and operation times the area of the warehouse.

$SpaceCost = (Rental + BuildingOperational) Area$

Equipment

“Material handling equipment is used for the movement and storage of material within a facility “ Michael G. Kay. We calculate the equipment cost as the sum of the amortization of each equipment $k$ plus its operational cost, for example, maintenance or charging batteries.

$EquipmmentCost = \sum_{k} \left( Amortization_k + EquipOperational_k)\right)$

Inventory Cost

The inventory cost accounts opportunity cost of holding the working capital invested in inventory. We calculate it as the average working capital times – the opportunity cost interest rate $(r)$ as follows:

$InventoryCost = \left( \sum_{ip} \frac{InvLevel_{jp}*C_j}{P} \right) r$

where $InvLevel_{jp}$ is the inventory level of product $j$ in period $p$$C_j$ is the cost of product $j$ , and $P$ is the number of periods considered.

In the figure below, we show the interaction of all these costs.  We color the leaves of the diagram depending on whether they are of direct decisions of warehouse designer (Green) or are better model as external parameters (Gray).

In the labor cost, the salaries, bonuses, and cost of an overtime hour are determine mostly by the environment of the warehouse and its location- minimum wage, payroll taxes and regulations. Even if the warehouse manager can influence how much he is going to pay in salaries, it will be decision that will hardly change from period to period, and it will require to work with human resources. On the other hand, the number of workers $(Workers_{ip})$ and number of hours overtime $(Overtime_{ip})$ are decision of the warehouse manager. It is typical that warehouse managers have absolute control over they labor staffing.

In the space cost, the rental cost and building cost will be defined mostly by the location of the warehouse, nevertheless the ceiling height is a design decision that may influence these costs depending on the industrial property appraisal of the region. On the other hand, the warehouse area is a decision of the warehouse designer, in fact the most critical one.

In the equipment cost, the prices of material handling equipment – racks, conveyors, forklifts, cranes, palletizers, etc – are determine by suppliers. But the warehouse designer selects what equipment to use.

Finally, in the inventory cost, the cost of products is defined by the manufacturing process or the suppliers, both out of the control of the warehouse designer. On the other hand, the inventory levels are in most cases under the umbrella of the logistics division of the company even if they can not solely decided by the warehouse manager.

All factors that affect the total operational cost of a warehouse can be divided into resources and the cost of resources.

 Resources Labor hours Area Equipment Working Capital Resources cost Cost of an Overtime hour Salaries Bonuses Rental cost Building operational cost Equipment prices Equipment operation costs Products cost Opportunity cost interest rate

The resources are the direct responsibility of warehouse managers,  and the cost of resources are defined by the environment where the warehouse is located. When choosing where to locate a new warehouse, engineers must look into labor cost and availability, leasing costs, tax benefits, and transportation costs.  However, once the warehouse start operating, the manager cannot directly influence those factors. Therefore, we will leave the discussion on resource costs for a future post and focus on the resources.

Warehouse manager focus

Following our cost model, the management of a warehouse is summed up to the administration of labor hours, area, equipment, and working capital to ful fil customer orders with a desired service level.

Managers can control the use of these four resources through the number workers, the number of overtime hours, the area, and the selection of the material handling equipment. In this section, we analyze the factors that affect the use of these four resources.

The figure below presents the analysis of the most typical activities – receiving, put away, replenishment, picking, packing/sorting and shipping – that require labor in a warehouse. The activities in dark red are generating labor hours requirements. In light gray are the process design decisions that will defined the labor requirements of these activities and that can be directly controlled by the warehouse manager. And, in green are factors that affect the labor hour requirements, but that are external to the process decision of the warehouse operation.  The support activities vary depending on the material handling equipment and level of IT support of the warehouse. We are referring to activities like cycle counting, handling of returns, inbound inspections, equipment maintenance, and/or maintenance of areas.

The figure below shows the use of space for warehouse operations. In dark red are the areas where the warehouse space is being used. In light gray are warehouse design decisions that affect this areas. And, in green are factors that affect the labor hour requirements, but that are defined by external to the in the warehouse design.

The selection of the material handling equipment will fully determine the equipment in the warehouse, reason for which it is a design decision itself.

Finally, the figure below shows how the working capital is define by purchasing policies, the customer orders, and the product cost.