WH-AS2 - Storage Location Assignment and Space Requirements
This assignment defines the storage part of your group’s final management report. Build on the data pipeline, layout representation, and profiles your group developed while diagnosing the warehouse status.
The following requirements are the minimum needed to meet the rubric criteria. Further analysis, discussion, and interpretation are encouraged to support your management argument.
Before you start, work through the storage optimization tutorial. It computes the distance matrix, the weights, and the SLAP on a small example.
Aims
In this assignment, we will:
- Formulate and solve a storage location assignment problem (SLAP).
- Translate the analysis into storage recommendations for warehouse management.
Learning Objectives
After completing this assignment, students will be able to:
- Develop a mathematical optimization model for the classical storage location assignment problem.
- Derive model parameters (distances, trip frequencies, handling costs, and space requirements) from operational data and state the assumptions behind them.
- Evaluate a proposed product-location assignment against the current assignment.
- Communicate storage decisions, their expected effects, and their limitations to management.
Study Case
The study case and data are the same as in the activity profiling assignment (WH-AS1). Reuse your cleaning decisions, location coordinates, and activity profiles. If your peer feedback identified errors in these inputs, correct them first.
Table 22.1 lists some connections between the two phases (diagnosis and storage assignment) of the integrated project.
| Activity Profiling Artifact | Use in Storage Location Assignment |
|---|---|
| Warehouse heatmap (layout and location coordinates) | Distance matrix; visualization of current and proposed assignments |
| Item-activity profiles (popularity, cube movement, demand variability) | Trip frequencies and space requirements \(S_i\) |
| KPIs (e.g., picking productivity) | Handling costs and interpretation of the objective value |
Problem Description
Management wants to know whether the current assignment of SKUs to active locations is a sound basis for the combined picking of zones B and C. Your report part answers three questions:
- Which SKUs should occupy which storage locations?
- How many locations does each SKU need?
- How much travel cost does the proposed assignment save compared with the current assignment?
Modeling Steps
The steps below build the storage location assignment model from scope to recommendation. Each step produces evidence for the management report (see Requirements).
1. Model Scope
To model a conventional storage location assignment problem, the following elements are typically defined:
- Items \(i \in I\): the SKUs included (e.g., all SKUs stocked in active locations of a zone, or the SKUs responsible for a given share of picks).
- Storage locations \(j \in J\): the active locations included, their definition (e.g., whether a location holds one SKU or is shared), and their coordinates.
- I/O points \(k \in K\): the points through which items enter and leave the modeled area (e.g., the pickup station, the drop-off conveyor, or a reserve area that replenishes active locations), and their positions on the layout.
- Flows: the movements represented (e.g., picks from active locations, replenishments from reserve) and those left out.
- Resources: the equipment and labor assumed to perform those movements.
- Constraints: what limits the assignment (e.g., location capacity, item-location compatibility, replenishment frequency).
- Performance measures: what the model evaluates (e.g., total weighted travel cost, storage space required) and the units used.
Link every modeled element to a data field, an explicit assumption, or a documented data gap. Leave out detail the data cannot support, and record it as an evidence gap instead.
If you discover that the model is too large to solve, propose a smaller scope (e.g., a subset of SKUs or locations) and justify it.
2. Distance Matrix
Compute the distance \(d_{kj}\) between each I/O point \(k\) and storage location \(j\). Choose a distance measure that reflects how pickers travel through the aisles (for example, rectilinear distance along the main aisles), explain it, and report the units. Show how accurately your distance measure reflects the actual travel paths in the warehouse, and state any assumptions or simplifications you made.
3. Weights
Calculate the weights \(w_{ij}\) for each item \(i\) and storage location \(j\):
\[ w_{ij} = \frac{\sum_{k \in K} c_{ik} f_{ik} d_{kj}}{S_i} \]
where:
- \(f_{ik}\) is the frequency of trips for item \(i\) to/from I/O point \(k\);
- \(c_{ik}\) is the cost of moving a unit load of item \(i\) to/from I/O point \(k\);
- \(d_{kj}\) is the distance between I/O point \(k\) and storage location \(j\); and
- \(S_i\) is the number of storage locations required for item \(i\).
Your group defines how \(f_{ik}\), \(c_{ik}\), and \(S_i\) are obtained from the data. For each parameter, state the data source, the time window, the unit, and the assumptions. For example, \(c_{ik}\) may reflect handling requirements such as weight, volume, or fragility, and \(S_i\) may follow from the replenishment maximum, the item’s dimensions, and the location dimensions.
4. Mathematical Model
Formulate and solve the SLAP that assigns the items to storage locations such that the total travel cost between the I/O points and the storage locations is minimized. Determine:
- The mathematical model (sets, parameters, decision variables, objective, and constraints), including any constraint that prevents assigning an item to a location into which it does not fit.
- The objective value of the optimal assignment.
- The objective value of the current assignment, evaluated with the same weights, and the relative difference.
- A graphical representation of the current and proposed product-location assignments on the warehouse layout.
5. Storage Policy and Feasibility
State the storage policy that follows from your model precisely enough for SPR (S. P. Richards Co.) to implement it. The policy specifies which product characteristics determine a location, how new or changed SKUs are slotted, and when the assignment should be recalculated.
Check that the proposed assignment is feasible:
- Capacity: the locations assigned to each item hold the inventory the item requires.
- Compatibility: each item fits the locations it is assigned to (e.g., shelf depth, height, weight, and any handling requirement).
- Replenishment: the assignment implies a workable replenishment frequency from reserve, given the minimum and maximum levels and the space assigned.
- Service: the risk of an empty active location during a picking wave remains acceptable, or you state how it is controlled.
Report the checks you performed, their results, and any constraint you could not verify with the available data.
6. Management KPIs
Interpret the trade-offs and express them using KPIs that are meaningful to management: how much travel cost is saved? How much space is required? How much labor is freed for other tasks? Choose the KPIs that best support your argument, and explain how they are calculated and what they mean.
Requirements
Management report
The WH-AS2 evidence forms part of your group’s integrated management report of no more than 12 pages. Write for warehouse management: lead with the decision and its expected effect, and support it with the key numbers, figures, and tables. The report part must present:
- the model scope and the main assumptions behind \(d_{kj}\), \(f_{ik}\), \(c_{ik}\), and \(S_i\), stated concisely;
- the mathematical model in compact form;
- the proposed assignment compared with the current assignment (objective values, relative difference, and a layout figure);
- the resulting storage policy and the capacity, compatibility, replenishment, and service checks; and
- the recommendation, its sensitivity to the main assumptions, its limitations, and what management should monitor.
You do not need to print full distance or weight matrices in the report. Show only what supports the argument, and refer to the code for the complete results. Figures and tables follow the same caption and visualization standards as WH-AS1.
Table 22.2 suggests one way to organize the WH-AS2 section of the report; adapt it to the argument your group builds.
| Section | Content |
|---|---|
| Storage decision | The proposed assignment and storage policy, and the expected effect on travel cost and space |
| Model and assumptions | Scope, parameters, and the assumptions and evidence gaps behind them |
| Results | Proposed vs. current assignment and layout figure |
| Feasibility | Capacity, compatibility, replenishment, and service checks |
| Recommendation | What to implement, under which conditions, with which risks and monitoring indicators |
Supporting code
You are free to use any tools or programming language, as long as the evidence used in your report is generated automatically by code and saved in a folder. This includes numerical results, KPIs, data tables, chart data, and charts.
Provide one entry point that processes the original files in data/raw/ and generates the evidence. Keep your README brief: state the setup, the command to run, and where the outputs are saved. A notebook entry point should execute the notebook from start to finish.
Import or copy the generated evidence into your LaTeX report. Submit the complete LaTeX project and PDF with the code. Follow the final project file requirements for submission details.
We assess whether the code reproduces the evidence used in the report. Clear functions and documentation help your team check and revise the analysis.
Your manager should be able to check the calculations and assumptions behind your recommendation. Give readers the code and instructions they need to repeat the analysis. These guides explain the main practices:
Assessment Criteria
The WH-AS2 rubric applies to the WH-AS2 part of the report and its supporting code. Table 22.3 lists the evidence expected for each criterion.
| Rubric criterion | Expected evidence |
|---|---|
| Model scope | Items, locations, I/O points, flows, resources, constraints, and performance measures |
| Evidence traceability | Data source, unit, and assumption for \(d_{kj}\), \(f_{ik}\), \(c_{ik}\), and \(S_i\), and the documented evidence gaps |
| Product-assignment logic | Distance matrix, weights, mathematical model, optimal assignment, and the implementable storage policy that follows from it |
| Feasibility and evaluation | Capacity, compatibility, replenishment, and service checks; and comparison with the current assignment |
| Decision insight | Interpretation of the improvement, its sensitivity to the chosen parameters, and what management should monitor |
Use the rubric as a guide when developing your own work, and make sure every criterion is addressed thoroughly.