Topic #2: Warehousing Decisions Introduction Warehouse Design (Strategic Decisions) – Facility Sizing – Facility Configuration (length, width, and height of the building) – Locating and sizing of receiving, shipping and storage zones – Selecting storage media and storage/retrieval mechanism

Tactical Decision – Stock Allocation

Operational Decisions: Batch formation, Order picker routing, Packing problems (p. 165-195)

Flows of Items (e.g., CDC)

Probably in full pallets or full cartons. (p. 158)

Flows of Items (e.g., RDC)

Order fulfilling tasks

(p. 158)

Common Warehouse Cost

(p. 159)

Storage and Handling â€“ Example I

(p. 161)

Storage and Handling â€“ Example II

(p. 162)

Storage and Handling â€“ Example III

(p. 162)

Stock Allocation Strategy Example

(Ballou, p.532)

Stock Allocation Problem What is the cost of assigning item j to space k, cjk?

(p. 176)

Space Requirement and Retrievals pjr j

(p. 177)

mj

Distance b/w Spaces and I/Os trk (for r=1)

(p. 177)

Distance b/w Spaces and I/Os trk (for r=2)

Assignment cost = (p. 177)

Stock Allocation Model Generalized Assignment Problem (GAP)

for each product

Really necessary?

(p. 176)

for each space

A Simplified Example by EXCEL Objective

Cost, ckj Location k \ Product j 1 2 3 4 5 6 7 8 9 10

645.00

Product j mj

1 5 5.00

2 4 4.00

3 1 1.00

10

1.00 1.00 0.00 1.00 0.00 1.00 1.00 0.00 0.00 0.00

0.00 0.00 1.00 0.00 1.00 0.00 0.00 1.00 1.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

Assign, xkj 1

2 36 42 43 36 40 39 41 48 46 43

3 97 102 90 87 86 106 102 100 101 97

87 77 75 71 71 96 92 88 84 74

1 1 1 1 1 1 1 1 1 1

Batch Formation Problem Strict order picking vs. Batch picking What is the decision (# of orders in a batch) d about? â€“ Balance between picking and sorting

(p. 183)

Batch Formation Model o: average number of orders per day u: average number of items per order t1: time for a path cover all locations t2: time to shipping zone Minimize

o t1 + uo(Îąd )t 2 d

s.t. d â‰Ľ 0, integer

(p. 182-3)

A parameter to be estimated

t1 d= Îąut 2

Batch Formation Example 3.5m wide 15 aisles 1.05x1.05 palette

25m long

300 items/order t2 = 1.5 min. Îą = 0.1

d* = 3 (speed)

(p. 183)

Packing Problem Objective: â€œminimize the number of bins (or containers)â€? Simplest Version: one-dimensional packing problem or bin packing problem Weights of items: pi (i=1 to n); Capacity of a bin: q.

Lower Bound of bin packing

(p. 187)

Bin Packing Model

pi: weight of i

q: capacity of a bin

Assignment of item i to bin j.

(p. 188)

Whether or not a bin is needed?

Bin Packing Heuristics First Fit (FF) Algorithm, with the knowledge of items (the on-line version)

Any possible way to improve? (p. 188- 189)

Best Fit (BF) Algorithm

How to deal with the off-line situation? Sort the items by non-increasing weights!

(p. 188- 189)

Other Operational Decisions

Two-dimensional (Bin) Packing Problem (p. 184 and 191)

Traveling Salesman Problem