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P SSCM V2 > Module6 > Flashcards

Module6 Flashcards

1
Q

Main Models (Module 6)

A
  • Capacitated plant location model (with single sourcing)
  • Gravity location model
  • Minimum spanning-tree problems
  • Traveling salesman problem
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2
Q

Facility Location Info

A
  • Location of supply sources and markets
  • Demand and/or forecast
  • Cost factors (facility, labor, production, material)
  • Inventory costs (region/site & function of quantity)
  • Transportation costs between regions/sites
  • Taxes and tariffs
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3
Q

Types of CPL Models

not very relevant / insightful in my opinion

A
  • Capacitated plant location models (Region)
  • Capacitated plant location models (Site)
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4
Q

CPL Model Structure

A
  • Decision: Open/close plants, how much to produce/ship
  • Fixed costs: If plant is open
  • Capacities: Max production per plant
  • Demands: Regions need certain amounts
  • Variable costs: For transporting each unit
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5
Q

CPL Model Parameters

A

Capacitated Plant Location

  • fi: Fixed cost to open Plant i
  • cij: Cost/unit from Plant i to Region j
  • Ki: Capacity of Plant i
  • Dj: Demand of Region j
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6
Q

CPL Decision Variables

A
  • yi ∈ {0,1}: 1 if Plant i is open, 0 otherwise
  • xij ≥ 0: Quantity shipped from Plant i to Region j
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7
Q

CPL Model Formulation

A

Objective: Minimize
∑(fi·yi) + ∑∑(cij·xij)

Constraints:
- Demand: ∑ xij = Dj for each j
- Capacity: ∑ Dj·xij ≤ Ki·yi
- Binary open/closed: yi = 0 or 1
- Nonnegative shipments: xij ≥ 0

Capacitated Plat Location

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8
Q

CPL with Single Sourcing

A
  • Similar to CPL, but each demand region is served by exactly one plant.
  • xij becomes binary: region j assigned to plant i or not.
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9
Q

Gravity Model Concept

A
  • Places customers as points on a plane (xn, yn)
  • Finds a center of gravity (x, y) that minimizes total distance cost
  • Continuous optimization in 2D
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10
Q

Gravity Model Objective

A

Minimize: ∑ (distancen · Dn · Fn)

  • distancen = (Euclidean from (x,y) to (xn, yn))
  • Dn = quantity
  • Fn = shipping cost/unit/mile
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11
Q

Gravity Model Solution

A
  • Non-linear objective (square root in distance)
  • Solved via iterative or quadratic programming methods
  • No closed-form formula for the final (x, y)
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12
Q

Minimum Spanning Tree

A
  • Goal: Connect all nodes with minimal total link cost
  • Applies to telecommunication, roads, pipelines, etc.
  • Ensures no cycles and all nodes are reachable
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13
Q

MST Algorithm

A

Minimum Spanning Tree

  1. Start with cheapest link.
  2. Repeatedly add the next cheapest link that connects a new node.
  3. Stop when all nodes are connected.
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14
Q

Traveling Salesman Problem

A
  • Must visit each city exactly once and return to start.
  • Objective: Minimize total travel cost/distance.
  • Known to be NP-complete (non-deterministic polynomial time).
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15
Q

Nearest Neighbor Heuristic (TSP)

A
  1. Pick a start node.
  2. Move to closest unvisited node.
  3. Repeat until all are visited, then return to start.
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16
Q

TSP Complexity

A

Travelling Salesman Problem

  • Number of routes grows factorially with number of cities
  • No efficient (polynomial-time) exact algorithm is known
  • Heuristics needed for large problems
17
Q

TSP & NP-completeness

A
  • TSP is a representative NP-complete problem
  • Clay Mathematics Institute offers $1M prize for a general solution
  • Illustrates computational complexity in supply chain optimization
18
Q

SunOil Case Example

A
  • Global petrochemical plants in 5 regions
  • Considering low (10M units) or high (20M units) capacity plants
  • Trade-off: Economies of scale vs. transportation costs
19
Q

Natural Beverages Example

to be deleted in my opinion

A
  • Considering a new bottling facility in Hamburg or Bremen
  • Possibly building one new warehouse in same city
  • Capital limit: €1 million
20
Q

Steel Appliances Example

A
  • One current factory in Denver
  • Need a second factory in eastern US
  • Minimizes transportation to/from supply sources & markets
  • Used a Gravity Model approach
21
Q

Heuristic Methods

A
  • Provide good feasible solutions fast
  • Not guaranteed optimal
  • Often greedy or iterative
22
Q

Capacity & Demand Constraints

A
  • Supply constraints ensure feasible capacity usage
  • Demand constraints ensure all demands are met
23
Q

Inventory Costs

A
  • Vary by location and quantity
  • Key factor in total supply chain cost
24
Q

Transportation Costs

A
  • Depend on distance and volume shipped
  • Influence whether to centralize or decentralize facilities

P SSCM V2 (9 decks)

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