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# Dynamic Lot Sizing Models

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## Luis Jesús Pérez Rivera

on 3 November 2014

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#### Transcript of Dynamic Lot Sizing Models

M Sc. Luis Jesús Pérez Rivera
MSc.ljperez@gmail.com
Dynamic Lot Sizing Models
uniform demand
lumpy demand
Refers to experience-based techniques for problem solving, learning, and discovery that
give a solution which is not guaranteed to be optimal.
Where the exhaustive search is impractical, heuristic methods
are used to speed up the process of finding a satisfactory solution
via mental shortcuts to ease the cognitive load of making a decision.
Heuristic:
Considers ordering for a number of periods ahead, say
m
. Tries to achieve the minimum average cost per period.
Silver-Meal heuristic
Al the heuristics that will be covered, under different approaches,
try to minimize the sum of the ordering (or setup) cost and the holding cost
.
Heuristic Assumptions
1. Inventory holding cost occurs at the end of the period.

2. Quantity needed for the period is used at the beginning of the period.

3. Orders are placed at the beginning of the period.

4. Replenishment is instantaneous.
future demand for the next
n
periods is given by
Let
Compute
stop when
then
order issued at the beginning of period
i
that covers
m
periods into the future.
The process repeats trough the planning horizon.
James, the manager of a computer store, estimates the demand of mice for the next 5 months to be: 100,100,50,50 and 210. To place and order cost James \$50 and he estimates that holding a mouse over a month will cost him \$0.50. Estimate the lot sizing for each month using the SM heuristic.
Similar to the Silver-Meal heuristic, the difference is that the decision is based on the
average variable cost per unit rather than per period.
Least unit cost (LUC)
Compute
stop when
then
order issued at the beginning of period
i
that covers
m
periods into the future.
The process repeats trough the planning horizon.
The limitation of both SM and LUC heuristics is that they consider 1 lot a time and the cost per period (or unit) can vary widely from period to period.
The
Part period balancing
heuristic
(
PPB
) attempts to minimize the variable cost for all lots.
the intersection of holding and ordering cost is true for uniform demand but not necessarily true for lumpy demand.

However, this consideration may provide reasonable solutions.
Part period balancing (PPB)
Part period: 1 unit of the item carried in inventory for 1 period.
Compute
stop when
then
order issued at the beginning of period
i
that covers
m
periods into the future.
Wagner-Whitin algorithm (WW)

It has the same objective as the heuristic approaches: minimizing the variable inventory cost.
The difference is that it actually yields the optimum solution!
Full transcript