Here$$s the problem:

Ernie$$s Market is a small independent chain of neighborhood grocery stores. Ernie$$s distributes high volume product to its stores from a company owned and operated warehouse. Additionally, the company is looking to start a back$-$hauling program with its suppliers in an effort to reduce its transportation costs.

Kimberly$-$Clark operates a factory in the vicinity of Ernie$$s stores and warehouse and will be the first participant in a pilot back$-$hauling program. Figure $1$ is a road map showing the locations of Kimberly$-$Clark and Ernie$$s warehouse and stores and the distances along each of the road segments.

Here are your tasks:

$1.$ Develop detailed cost minimizing outbound and backhaul routes for sending:

a$.$ A full truck from the warehouse to each store, then from each store to Kimberly Clark

b$.$ A full truck from Kimberly Clark to each store, then from each store to the warehouse

$2.$ Calculate the costs of:

a$.$ All outbound routes $($i$.$e$.$ the combined outbound cost$)$

b$.$ All return routes $($i$.$e$.$ the combined backhaul cost$)$

$3.$ Present your recommendations to your client in an easily understandable, and actionable, format; for example, the client should be able to clearly see and easily implement, the route from the warehouse to store E and then from store E to Kimberly Clark.

Be careful that you do not strand trucks at stores...

Ernie$$s has stated the following assumptions to help guide your efforts:

$$ Outbound transportation costs are directly proportional to travel distance

$$ Backhaul transportation costs are a linear function of the distance.

Table $1$ shows the reverse route cost ratios which can be used as multipliers $($i$.$e$.,$ multiply the ratio by the distance to determine the cost$)$ to calculate the relative transportation costs associated with traversing road segments in the reverse direction.

Figure $1-$ Road System showing Ernie's Warehouse, Stores, and Kimberly$-$Clark Factory

Your submission should be a client report $($i$.$e$.$ a professional document worthy of sending to your client$).$ As usual, it should contain the following sections:

$$ Executive summary

$$ Recommendations $($including immediate, intermediate, and long term as appropriate$)$

$$ Methodology and approach

$$ Analysis and findings.

Submissions will be graded according to the criteria outlined in the grading template $($see assignment folder$).$ Be sure that your recommended routes are easily identifiable $($the client should not have to work hard to understand how to implement your recommendations$).$ Moreover, take care to explain the business relevance of your recommendations.

Table $1-$ Reverse Route Cost Multipliers