Lecture 04_Packaging Logistics Flashcards
Packaging Tasks
1. Package design
* Volume, weight, bulkiness, fragility
* Legal conditions
* Packaging type, packaging material
**2. Packaging process **
- Automation
**3. Closed-loop economy processes **
− Returns
− Disposal
Packaging Functions
product function
* Providing the quantitative amount of factors
* Collecting the output
marketing function
- advertising medium, information medium
usage function
- usage for other purposes at the customer
logistics function
- protective function
- storage function
- transport function
- manipulation function
- information function
4 Problems
- Cutting Stock Problem
- Knapsack Problem
- Bin Packaging Problem
- Block Heuristic
**Cutting Stock Problem **
Decision Variables
Constraints
Objective Function
Decision Variables
- # of rolls x(i) cut according to pattern i
- Rest y1 and y2 in inventory
Constraints:
* Order fulfillment
* Storage restriction [ y(1) + y(2) <=160
* Non-negativity
Objective function:
* Minimze Scrap /Waste
Z1 = 21x(1) + 3x(2) + 12x(3) + 21x(4) + 3x(5)
- Used rolls
Z2 = x1 + x2 + x3 + x4 + x5
Knapsack Problem
General
which objects x(i) with capacity requirement a(i) to select and add to limited capacity W
Knapsack Problem
Max (i=1)∑ c(i)*x(i)
maximize value of selected objects
Constraints
Resource capacity
(i=1)∑ a(i) * x(i) <= W
Binary Decision Variables
x(i) ∈ {0,1} i = 1,2,…,n
Bin Packaging
General
- allocation of N objects to M bins
- Binary optimization problem
- Minimize # of required bins
Bin Problem
Formulate Optimization Problem
Decision Variables
- y(i) Usage of Bin (binary 0 or 1)
- x(ij) Allocation of object j to container i (binary, 0 or 1)
Objective Function
Min (i=1) ∑ y(i)
Constraints
- Bin Capacity
(j=1) ∑ a(j) * x(ij) <= y(i) * K
with i= 1,…,n
- Allocation of all objects
i=1∑ x(ij) = 1
with j = 1,…n
Binary variables
y(i), x(ij) ∈ {0,1]
i = 1,2,…,m
j = 1,2,…,n
Priority Rules for Bin Packaging
3 Methods
First Fit Heuristic
- assign object to first bin that has sufficient capacity
- use new bin if no sufficient capacity is available
Best Fit Heuristic
− assign object to bin with residual capacity closest to object weight/size (minimize total residual capacity)
− use new bin if no sufficient capacity is available
Presorting starting with highest
- can drastically improve performance of heuristics
Block Heuristic
Creating Layer Plans
1. Create blocks and orientation
- block length and width based on # of packages in vertical n(i) and horizontal m(i) direction, both integer
2. create possible partitions with
𝐴1≤𝐴 →𝑛1⋅𝑏≤𝐴
𝐴2+𝐴3≤𝐴→𝑛2⋅𝑏+𝑛3⋅𝑎≤𝐴
𝐵 +𝐵 ≤𝐵→𝑚 ⋅𝑎+𝑚 ⋅𝑎≤𝐵
𝐵 +𝐵 ≤𝐵→𝑚 ⋅𝑎+𝑚 ⋅𝑏≤𝐵
-
Create all possible combinations of patterns
- Layer plan (A1), (A2,A3), (B1,B2), (B1,B3)
- number of packages (n1 * m1 + n2 * m2 + n3 * m3) -
Check
- For (B1,B2) and (B1,B3)
- B1 have to be the same
Worst-Fit Decreasing
Heuristic
Bin Problem
- presort Products with highest to lowest
- When residual space add next product to the container that will have the highest residual space
