SPR distributes wholesale office products. Each DC accepts orders until 5PM and ships overnight for next day delivery. Orders are received, filled, and shipped on the same day.

There are three distinct picking zones: palletized product, light bulk, and small parts. We will be concerned with small parts, which are picked manually into totes. The totes then are placed on a conveyor to packing stations.

The warehouse management system used by SPR examines each customer order, converts order-lines to pick-lines, and assigns the pick-lines to a set of boxes. All the items assigned to a box are picked together. The packer then prepares the recommended boxes and fills them with their assigned items plus dunnage. An efficient packing will use fewer boxes, with each (nearly) filled.

Here is a copy of the class presentation by SPR representatives.

- Given its current cubing algorithm, what box sizes should SPR
stock? Should the same sizes be used at all DCs? Or can all DCs
standardize on the same set of sizes?
- If too few box sizes, then it will be more difficult to pack well and cost of cardboard will be unnecessarily high.
- If too many box sizes, then it will be more expensive to stock and handle boxes. Also, there will be fewer of each size and so the cost per box will be higher. Finally, orders may be packed into multiple boxes, with higher consequent costs of shipping.

- Can the current cubing algorithm be improved? An effective
algorithm must account for the following:
- To reduce shipping costs, minimize the number of boxes used for each order.
- Each box should be large enough that it can be packed easily, without having to figure out precise placement of each item; but the box should not be too large, because it will be more expensive to purchase, use more dunnage, and, possibly, be more expensive to ship.

Miscellaneous notes:

- For ergonomic reasons, no box should be loaded to exceed 50 pounds.
- Boxes being shipped via UPS should be small enough to avoid the UPS surcharge for Over Maximum Limits.
- Some items are too large to fit into any box of reasonable size. Custom packages are built for them as needed.
- Boxes can be manufactured in essentially any size.
- A given box size may have different costs in different regions of the country.

**The company data is copyrighted and proprietary. You may
use it for the purposes of this course only. (If you would like to use
it for something else, please contact me to discuss.)**

- Box sizes, usage, costs from some representative warehouses. (The box sizes on the spreadsheet tab labeled “New standard box list” are five sizes that SPR is considering as possible standards, but these were not derived by any detailed analysis.) Note that the envelopes that were distributed in class may be considered additional types of box (less expensive ones).
- Order history. Note that SPR recycles order numbers. The first two digits of the order number represent the Distribution Center number. The last 6 digits begin at 100000, and when they reach 999999, they start over again at 100000. The order number and the date should make the order unique. (NB: All full-case picks have been removed from the order history. Everything remaining was a piece-pick.)
- Cartons into which items were packed
- Item master
- Definitions of the fields in the three preceding data sets.

The warehouse management system (WMS) assigns virtual cartons (that is, sets of pick-lines) to carts sufficient to (nearly) fill the capacity of the cart, which is approximately 13,000 cubic inches. This assignment is guided by logic such as this: Assume zones A and B are on the mezzanine and zones C and D are downstairs, on the ground floor. Then the WMS may assign picks to carts according to the following logic: Group together cartons (sets of pick-lines) that have similar extent in the warehouse. More specifically, Group together cartons that

- are for zone A picks only
- are for zone B picks only
- are for zone C picks only
- are for zone D picks only
- start in zone A and end in zone B
- start in zone C and end in zone D
- start in zone A or B and end in zone C or D

Each group of cartons (sets of picks) that have similar extent would be assigned to the same cart, as much as possible.

Here are the zones in which small parts are stored:

- Baltimore (DC 19): Zones A, B, C, L, O
- Philadelphia (DC 23): Zones A, B, C, D, L
- Columbus (DC 09): Zones A, B, C, D, S
- Pittsburgh (DC 38): Zones A, C

The client suggests assuming that air pillows are used for dunnage in parcel orders and that paper is used for non-parcel orders. The use of air pillows is roughly proportional to the length of the longest dimension of a box; the use of paper is roughly proportional to the unoccupied volume in a box. A reasonable price for air pillows would be $80 per roll, with the roll being 2900-feet in length and the pillows perforated every 8 inches. Paper dunnage comes in a number of different sizes and shapes. A typical version would be a roll 36-inches wide by 1,500 feet long at $17 per roll.

- Search literature on packing. This will fall into two distinct categories: analysis of algorithms for simple idealizations of the problem, and lists of issues to be dealt with in practice. Look first at the “Next Fit” heuristic and its relatives (First/Best/Worst Fit, First Fit Decreasing, etc.)
- Secure a computer with a database program and some general programming language (recommendation: Java)
- Make sure you understand the meaning of each of the fields in the database.
- Filter out all pick-lines for skus that are not in the small-parts zones of the warehouse. We can ignore them because the warehouse will handle them separately.
- Generate some initial statistics. For example: How many orders are there per day? How many lines per order? What are the most popular SKUs? What are the distributions of the dimensions and weights of SKUs? More importantly, what are the distributions of the weights, volumes, and maximum measurements of the orders?