Taleworlds Entertainment plans to distribute its newest game Mount and Blade 2: Bannerlord throughout Europe using three depots as main distribution hubs. All three hubs can ship items to all three regions of Europe and they can hold inventory for upcoming periods.
Each hub renews their inventory each period by adding 100,000 new items (no cost for renewal of inventory) and holding inventory costs €1 per item per period. It is also possible to sell items late and the cost for late shipments is an additional €1.5 per item per period.
Demand for all 3 regions for the first two periods can be found below:
|
Region / Period
|
Period 1
|
Period 2
|
|
Region 1
|
75,000
|
100,000
|
|
Region 2
|
150,000
|
125,000
|
|
Region 3
|
50,000
|
75,000
|
Shipping an item costs €0.5 per item per kilometers if they are sent by trucks and arrive/are sold on the period they are sent. If the items are sent by railroad they cost €0.2 per item per kilometers and arrive/are sold on the following period. The distances between Regions and Hubs are given below:
|
Hub / Region
|
Region 1
|
Region 2
|
Region 3
|
|
Hub 1
|
120 km
|
90 km
|
130 km
|
|
Hub 2
|
80 km
|
90 km
|
100 km
|
|
Hub 3
|
120 km
|
110 km
|
90 km
|
Given all the information above formulate a transportation model that minimizes the total cost of sending items to regions:
1. Using mathematical symbols (∑ and ∀),
2. Using transportation tables And solve the problem:
1. Using Transportation Simplex,
2. Using MS Excel Solver,
3. Using GAMS.