11.8 Case Studies
Case Study 1: Aqua Fresh Spring Water
Aqua Fresh has established a distribution network for the supply of spring water critical to its bottling plants. Currently, there are two springs for water, which must be shipped to three bottling plants. The current distribution network is shown below:
| Transportation COSTS/Bottle | ||||
| (Spring to Plants) | Plant 1 | Plant 2 | Plant 3 | Spring Output |
| Spring 1 (West Mountain Range) | $6 | $8 | $9 | 400 Bottles |
| Spring 2 (East Mountain Range) | $4 | $7 | $3 | 600 Bottles |
| Bottling Plant Intake Capacity | ||||
| 500 Bottles | 500 Bottles | 500 Bottles | ||
The company has identified two potential sites for a third spring in the central mountain range; these are identified as Candidate A and Candidate B. From A, the costs to ship would be $9 to Plant 1, $10 to Plant 2, and $12 to Plant 3. From B, these costs would be $11, $14, and $8. The new spring, wherever it is located, will have a capacity of 500 units.
Tasks
(a) Expand the Distribution Network
Construct a transportation model that includes each candidate spring (A and B) as a third source. Represent the network using a transportation tableau for each scenario (i.e., one with Candidate A and one with Candidate B).
(b) Determine the Optimal Spring Location
Using transportation cost minimization techniques (e.g., the Transportation Simplex Method or software-based optimization), identify which candidate spring — A or B — should be selected to minimize total transportation costs.
(c) Evaluate Further Cost Reduction Opportunities
Analyze whether the total transportation cost, after selecting the optimal spring, can be further reduced. Consider possibilities such as:
- Reallocating supply among springs
- Adjusting plant intake capacities
- Introducing multi-modal transport or bulk discounts
Case Study 2: All Mats Services – Optimizing Delivery Logistics
Refer to the All Mats Services case in Chapter 5. The company completes a variety of mat orders daily, which are shipped using a fleet of three trucks. The trucks differ in capacity, cost efficiency, and delivery range. The current shipping process assigns orders to any available truck without a structured cost-minimization strategy.
Truck Fleet and Operational Details
| Truck Type | Capacity (Orders/Day) | Cost per Rubber Mat/Runner Job (USD) | Cost per Plush Job (USD) | Special Notes |
| 10-footer | 36 | $16 | $12 | Local deliveries only |
| 15-footer | 56 | $16 | $20 | Local deliveries only |
| 20-footer | 76 | $18 | $22 | Can handle out-of-town deliveries |
Currently, the company assigns orders to trucks randomly, without considering cost implications.
Tasks
(a) Estimate the Current Cost of Random Shipping
Assuming a random allocation of orders across the three trucks, calculate the expected daily shipping cost. Consider the mix of rubber mat/runner jobs and plush jobs in your analysis.
(b) Identify Opportunities for Cost Reduction
Can the current shipping cost be reduced through a more strategic allocation of orders to trucks? If so, determine the new optimized shipping cost using appropriate optimization techniques (e.g., linear programming or cost minimization models).
(c) Determine the Absolute Minimum Shipping Cost
Is the cost calculated in part (b) the lowest possible? If not, identify the absolute minimum shipping cost and describe the optimal allocation strategy that achieves it.
