For the Paul & Giovanni Foods scenario (Example 14.7), conduct a what-if analysis by varying k, the

Question:

For the Paul & Giovanni Foods scenario (Example 14.7), conduct a what-if analysis by varying k, the number of distribution centers, from 1 to 4. Summarize your results and write a short memo to the supply chain manager explaining your findings and recommendation.

Data from Example 14.7

Paul & Giovanni (PG) Foods distributes supplies to restaurants in five major cities: Houston, Las Vegas, New Orleans, Chicago, and San Francisco. In a study to reconfigure their supply chain, they have identified four possible locations for distribution centers: Los Angeles, Denver, Pensacola, and Cincinnati. The costs of supplying each customer city from each possible distribution center are shown in the table below. PG Foods wishes to determine the best supply chain configuration to minimize cost.

Define X_ij = 1 if customer city j is assigned to distribution center i and 0 if not, and Y_i = 1 if distribution center i is chosen from among a set of potential locations. The integer optimization model is

X_ij ≤ Yi , for every i and j (e.g., X₁₁ ≤ Y₁, X₂₁ ≤ Y₁, and so on) X_ij and Y_i are binary

Figure 14.17 shows a spreadsheet model and the optimal solution for k = 2 (Excel file Paul & Giovanni Foods); Figure 14.18 shows the Solver model. We see that the distribution centers in Los Angeles and Cincinnati should be chosen, with Los Angeles serving Las Vegas, New Orleans, and San Francisco, and Cincinnati serving Houston and Chicago.

This model can easily be used to evaluate alternatives for different values of k. The supply chain manager can use this information to determine the trade-offs associated with opening different numbers of distribution centers.