This problem uses the Transportation Problem model to address whether demand that is

predicted to grow over the next three years should be met by expanding the Dallas supply point

$($origin$)$ in year $3$ or year $4.$

Year $1$ is the current year and the following table provides unit cost, supply and demand data in

year $1$ for $4$ supply points $($origins$)$ and $6$ destinations. The total supply is currently $2200$ which

exceeds the current total demand of $1550.$ Suppose the cost data will stay the same over the next

three years, but the demand will increase to reflect sales growth and the supply can increase in

either year $3$ or $4$ by expanding the Dallas supply point. The supply at the three other origins

$($Chicago$,$ San Diego, Toronto$)$ does not change.

$$/$unit Atlanta Boston Denver Miami Montreal Seattle Supply

Chicago $245535600$

Dallas $133614400$

San Diego $157372600$

Toronto $423526600$

Demand $150200200400300300$

In year $1,$ the demand is in the last row above $($totaling $1550),$ and the demand will grow by $100$

units at each destination except Montreal for each of the next $4$ years.

Thus, in year $2$ the demand totals $2050$ and is:

$$/$unit Atlanta Boston Denver Miami Montreal Seattle

Demand $250300300500300400$

In year $3$ the demand totals $2550$ and is:

$$/$unit Atlanta Boston Denver Miami Montreal Seattle

Demand $350400400600300500$

In year $4$ the demand totals $3050$ and is:

$$/$unit Atlanta Boston Denver Miami Montreal Seattle

Demand $450500500700300600$

If nothing is done, the increasing demand will exceed the current supply in year $3.$ When the

total demand exceeds the total supply, then there is unmet demand which incurs a cost of $$5/$unit$.$

To handle the increasing demand, the company is considering two expansion options at Dallas.

Option $1$ expands the Dallas origin to $800$ in year $3$ and option $2$ expands the Dallas origin to $800$

in year $4.$ There is a one$-$time cost for the expansion at Dallas in year $3$ or year $4$ of $$15,000.$

$2$

$1.$ Fill in the tables of costs below for option $1.$ For each row $($year$),$ solve a Transportation

Problem using the appropriate supply can demand to determine the minimum transportation

cost $($column $3).$ Then, calculate the Unmet Demand Cost $($column $4)$ for any unmet demand.

Then, sum each row for the total cost per year $($column $6).$

Option $1$: Expand Dallas in year $3$

Year

Dallas

Supply Transportation Cost Unmet Demand Cost Expansion Cost Total Cost$/$Yr

$1400-$

$2400-$

$3800$ $$15,000$

$4800-$

Sum $-$ $$15,000$