Background and problem definition

This thesis focused on the settings within a production warehouse and the mathematical program models the following operations: the production, the storage and handling of the items. Attention will be focused on items that are produced in the facility and placed in the warehouse for storage, and then are sent to the output point for delivery to customers. The process of item flow within the observed warehouse was as follows:

- Items were produced in the production area of the facility

- Items were sent by conveyors to automatic palletizers, and were placed on pallets.

- The items were then picked up at from these palletizers using a forklift truck and placed into specific storage locations. (One unit of item i occupied one storage location, and it should be noted that pallets were floor stacked and could be stacked approximately 3 pallets high. However for simplicity of the model it was assumed that products will be moved in stacked columns of 3 pallets).

46 - From these specific storage locations a fork lift truck was used to bring items

to the I/O point.

This product flow was modified for the model within this thesis, so that the model is generic enough to mirror the general flow of items within any production warehouse. The modified item flow is listed below:

- Items are produced in the production area of the facility

- The item are picked up from the production area and placed into the warehouse in storage locations

- From these specific storage locations items are brought by a fork lift truck to the output point.

Figure 2 depicts the flow of items from the production area to the output point of the facility. The areas of interest associated with each section of the process have been highlighted in the figure.

47 In the production area of the warehouse the model was concerned with

production, setup, inventory, demand, and the production constraints. Production was considered to address the cost of minimizing how many items were produced during a given period. This cost was only incurred when items were produced, and these costs usually varied per item. In this model the different product lines on which products were produced was not considered, a general production area where all items are produced was assumed. Setup costs were related to the amount of time an operator would spend

prepping a machine for production. The operator salary per hour was used and was multiplied by the amount of time that the operator needed to perform the setup operation. This data was taken from a time study that was conducted, and the cost for each setup varied based on the production line and the type of item that was going to be produced. Inventory was considered and was based on which items were in the warehouse at the end of the period, and the cost of holding products at the end of the period was

minimized. Demand was forecasted and known and production was performed to meet demand at a minimal cost. The production constraints were what limited production, and it was found that while it may be cheaper to produce more product and hold them in inventory, the model assumed that you could not produce more items than you had space for. Therefore in the production area the focus was on production costs, setup costs and inventory costs. These costs were constrained by product demand and key production resource constraints.

From the production area to the warehouse storage locations the cost of distance travelled was required. This cost was incurred whenever a product was carried by a fork lift truck from the production area to the storage locations. Each storage location had its

48 own individual address that items could be delivered to, and a cost was proportional to the distance travelled in feet by the forklift operator from the production area to that specific storage location.

. A dedicated storage assignment policy was used to organize the warehouse space, by assigning locations to each item. These policies have been examined in the literature review found in Chapter 2, and have been proven to increase the amount of space utilization. While it was determined that a class based storage assignment policy would be the best option for this specific warehouse, for the purpose and simplicity of this model a dedicated storage assignment policy has been used. A dedicated storage assignment policy also has industrial relevance to the warehouse as it allows order pickers to become familiar with item locations, and it typically reduces the material handling costs. The optimal storage locations were determined based on cost; this cost was proportional to the distance travelled in feet by the forklift operator during the placement and retrieval of items in the warehouse. The cost was based on the wage of the operator, order processing, labelling, and shrink wrapping of the items. Figure 3 is a depiction of the general warehouse layout that would be used in the above scenario.

Inventory level and demand were also considered in the warehouse storage location stage because at this stage the amount of inventory carried over to the next period is minimized while accounting for the customer demand. An example of the general idea for the warehouse layout that was considered for the model is depicted below in Figure 3.

49

Figure 3: General Warehouse Layout

This figure depicts the layout of the warehouse that was considered for the mathematical model. This is not the warehouse layout of the industry sponsor but is an example of the general layout considered within the thesis. It was assumed that products came into the system at the top of the figure from the production area and exited in the bottom left hand corner of the figure at the output point. Examples of different scenarios can be found in Chapter 4.

The travel costs associated with the movement of product from the storage locations to the output point and from the production area to the storage locations was calculated based on operator travel. The only different was the starting and ending points which alters the cost of travel. Therefore in most cases the distance from the production

50 area to the storage locations differed from the distance from the storage locations to the output point.

At the output point, demand was considered for each item and was considered as the pull mechanise in the item flow process. The forecasted demand which was known determined how many items would flow to the output point each period to be shipped to customers and this was where the item flow ended in the model.

Based on the area of research identified at the industry sponsor, the item flow in a general production warehouse, and the noted gap in research a mathematical model was developed. This thesis combined a dedicated storage location assignment with the capacitated lot sizing problem into a single mathematical model that minimized travel distance, reserved storage space costs, handling, production, inventory holding, and setup costs. In the next section is the formulation of the mathematical model.