Reading Assignment For next class: Case 8: Lot Sizing at Altametal (pg. 111)

MGTSC 352 Lecture 13: Aggregate Planning WestPlast Case H ow to deal with multiple objectives How to use binary variables

WestPlast (based on a true story) Plastic pellets Continuous chemical process –Product switching results in waste Capacity < Demand –Cap: 335,000 tonnes (est.) (could be as high as 425,000 tonnes) Contractual obligations and forecasts

Active Learning Pairs, 1 min. How does Westplast evaluate the “goodness” of a production plan? What do you think of their approach?

WestPlast Criteria Maximize Revenue Maximize Plant Capability Index (PCI) 1.plant output rate 2.quality compared to industry standards 3.raw material quality needed 4.overhead burden 5.process aggravation each subcriteria has a “weight ” (10% - 30%)

PCI Example 1.plant output rate –Product X: 100 –Product Y: 70 (slower) 2.quality compared to industry standards –Product G: 100 (excellent quality) –Product H: 80 (slightly lower quality) 3.raw material quality needed –Product Q: 100 (least expensive raw material) –Product W: 60 (more expensive raw material) 4.overhead burden (low OH = 100) 5.process aggravation (low aggravation = 100)

PCI Example continued Product Score Card.20 (output score) +.10 (quality score) +.30 (raw mat. score) +.15 (overhead score) +.25 (aggravation score) The result is a score between 0 and 100 with more desirable products scoring closer to 100.

Questions Is their plan (pg. 80, column G) a good plan? Can we find a better plan? How? What is ‘better’? Excel Pgs

Questions Our “better plan” produces 9 products. Suppose that, on the average, adding a product takes machine time equivalent to 10,000 lbs of output per product. Does WestPlast want to make more than 9 products? Less than 9 products? How can we find out? Pgs

Using Binary Variables to Limit # of Products Add binary decision variable for each product (1 = produce, 0 = don’t produce) Add binary constraints Want: –If binary variable = 0 then amt. produced = 0 –If binary variable = 1 then amt. produced ≤ demand IF() formulas would make the problem nonlinear Instead: –Add constraint amt. produced ≤ (binary variable)  demand Pgs

WestPlast wants to: Maximize Revenue Maximize PCI = Plant Capability Index By changing product mix Subject to: –Contractual obligations –Don’t produce more than forecast demand How can we optimize two criteria at the same time?