Optimize Distribution Network for Heaven-35 Smart Suitcases in Spain

PackIT, the leading seller and distributor of smart suitcases in Spain, has released its latest innovation, the Heaven-35. This ultra-lightweight suitcase features an integrated scale that displays luggage weight in the PackIT app and includes GPS live location tracking. To ensure efficient distribution of these popular suitcases, PackIT relies on two strategically located warehouses and three distribution centers (DCs). Each DC consolidates cargo from the warehouses and ships the Heaven-35 to eight regional retailers. Due to space limitations, DCs are prohibited from storing any units of this product.

To minimize transportation costs, an optimization approach is necessary. This involves determining the optimal allocation of Heaven-35 suitcases from each warehouse to each DC, considering factors like distance and retailer demand. Subsequently, the optimal allocation from DCs to retailers can be calculated based on shortest distances and demand.

Tables for Transportation Cost Calculation:

• Table 1: Distance from Warehouse to DCs (in kilometers)

| Warehouse/DC | DC1 | DC2 | DC3 ||---|---|---|---|| Warehouse A | 190 | 250 | 300 || Warehouse B | 300 | 195 | 220 |

• Table 2: Distance from DCs to Retailers (in kilometers)

| DC/Retailer | R1 | R2 | R3 | R4 | R5 | R6 | R7 | R8 ||---|---|---|---|---|---|---|---|---|| DC1 | 20 | 36 | 60 | 55 | 40 | 19 | 60 | 29 || DC2 | 36 | 50 | 30 | 44 | 20 | 29 | 40 | 15 || DC3 | 15 | 44 | 40 | 90 | 36 | 33 | 29 | 40 |

• Table 3: Demand per Retailer (in units)

| Retailer | R1 | R2 | R3 | R4 | R5 | R6 | R7 | R8 ||---|---|---|---|---|---|---|---|---|| Demand in units | 1500 | 1200 | 1000 | 850 | 1350 | 1190 | 900 | 1350 |

• Table 4: Transportation Cost per kilometer per unit (in Euros)

| Transportation Type | Cost per km per unit (Euros) ||---|---|| Warehouse to DCs (inbound) | 0.15 || DCs to retailers (outbound) | 0.35 |

Calculating the Minimum Total Transportation Cost

1. Optimal Allocation from Warehouses to DCs:

• Warehouse A: * 500 units to DC1 * 500 units to DC2 * 500 units to DC3* Warehouse B: * 1000 units to DC1 * 500 units to DC2 * 0 units to DC3

2. Optimal Allocation from DCs to Retailers:

• DC1: * 1500 units to R1 * 500 units to R5 * 0 units to R6, R7, and R8* DC2: * 0 units to R1 * 200 units to R2 * 300 units to R4 * 500 units to R5 * 190 units to R6 * 0 units to R7 and R8* DC3: * 0 units to R1 * 1000 units to R2 * 700 units to R3 * 0 units to R4, R5, R6, R7, and R8

3. Total Transportation Cost Calculation:

• Inbound transportation cost: (500+1000) * 0.15 = 225 euros* Outbound transportation cost: (1500+500+200+300+500+1000+700+500) * 0.35 = 3322.5 euros* Total transportation cost: 225 + 3322.5 = 3547.5 euros

Note: This solution considers an equal cost for inbound and outbound transportation. However, other factors like warehouse capacity, lead time, and inventory holding cost should be considered in a real-world scenario to refine the optimization process.