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)

(p. 158)

Common Warehouse Cost

(p. 159)

Storage and Handling â&#x20AC;&#x201C; Example I

(p. 161)

Storage and Handling â&#x20AC;&#x201C; Example II

(p. 162)

Storage and Handling â&#x20AC;&#x201C; 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&#x20AC;&#x201C; 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&#x2030;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&#x20AC;&#x153;minimize the number of bins (or containers)â&#x20AC;? 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

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