Lecture 10_Warehouse Location Flashcards
Add heuristic to Warehouse location problem
Start Solution
- find location which minimizes ∑ of invetment and transport cost to all customers and open it
Improvement (Iteration)
**for each undecided location: **
- calculate improvement in transport costs if opening location
- compare to required investment costs
- open location with highest positive saving
- forbid all locations with negative savings
Compare saving of remaining plant locations with the last added savings and subtract fi
- **repeat until all potential locations are either opened or forbidden **
Optimal solution of Warehouse Heuristic
- smallest transport cost among opoened plants
Time focused models
Problem Setting
Competition
Warehouse Problem
Problem Setting
- customers who should be delivered within a certain time window (24h, 48h)
- location configuration, so that x% of customers can be delivered within time t
Competition
- time competition instead of cost competition
Hotelling’s Beach
Time-Focused Model
2 competitors want to sell ice cream on a beach of length 1
Customers
* Uniformly distributed along the line of length 1
* Procurement from the closest location (if the distance is equal, the choice is randomly)
Location strategy
* If location of the competitor is given
− Directly next to the competitor, such that a maximum number of customers has the shortest distance to the ice cream shop
* Reaction/anticipation
− Both competitors place their ice cream shop in the middle of the beach
Set Covering Problem
2 problems
Problem 1
- minimize # of required locations
- all customers can only be delivered within given time window (alternative: max. distance)
- e.g. fire brigade / police
- e.g. spare parts warehouse with service legal agreements
Probelm 2
- max # of customers that can be attracted with given number of locations
Problem 1
Set Covering Problem
Mathematical Problem
Parameters
* Set of customers I, set of potential locations J
* dij distance (geographic, time) between customer i and location j
* Service requirement: maximum distance S
* N(i) set of locations which fulfil customer i‘s service target
N(i) := { j ∈ J | dij <= S}
Objective function [minimize # of locations]
min ∑ x(j) ∀ j ∈ J
Constraint
j ∈ N(i) ∑ x(j) >= 1 ∀ i ∈ I
x(j) = binary variable
Problem 2 of the Set Covering Problem
Mathematical model
Objective
max (j∈J) ∑ a(i) * y(i)
Constraints
** (j∈N(i)) ∑ x(j) >= y(i) ∀ i∈I**
(j∈J) ∑ x(j) = p
x(j) ∈ {0,1] y(i) ∈ {0,1}
∀ i∈I, j∈J
p = number of locations
a(i) = busines volume of customer i
xj and yi = binary variables
Transportation Processes
5 items
- direct transports: shortest way between A and destination Z; commuter tours, many-to-many
- relay traffic: one vehicle starts at A, the other at Z, meeting at B; vehicle exchange and return
- hub-spoke: central collection and distribution point
- disaggregation bundling: break down on smaller means of transport
- bundling
- freight consolidation, economies of scale
Hub-Spoke system
- each node delivers one unit to each other
- sternförmig
Cross Docking
- (almost) no inventories
- only **reallocation of incoming and outgoing goods **
Objectives
- Transport consolidation or service improvement by more frequent deliveries
- effective sorting e.g. from product based to store order based
- lowering inventory at certain nodes in the supply chain
- shorter lead time for products
Network Design
Problem Definition and Trade-Off
Problem Definition
- connection of a # of nodes (pipelines, roads)
- Objective: Minimize length of infrastrukture -> Steiner Graphs
Trade Off
- transportation costs
- political discussion:
- advantages of infrastructure
- provision of infrastructure: public good, toll systems
Example
- 4 points in a square with side length of 1 and exchange quantities of 1
- if you provide 3 sides (U-Shape) transport will be highest with value of 20
