Today’s Presentation It’s a day like all days – filled with those events which alter and change the course of history.

The Production Planning Problem – Homework #3 Cost per hour to operate line Hours available per month Fixed cost each month to reconfigure line for Product A Fixed cost each month to reconfigure line for Product B Factory 1 Line 1 $ Factory 1 Line 2 $ Factory 2 Line 1 $ Factory 2 Line 2 $

More data Available labor hours per month Labor rate ($/hour) Factory Burden factor Available units of raw material per month Factory 12960$ Factory 24400$ Unit selling price Production line hours per unit Units raw material per unit of product Raw material cost per unit of raw material Labor hours per unit Minimum production per month Product A$ $ Product B$ $ Determine how many units should be produced each month on each production line in order to maximize monthly profits.

Compute Unit Profit factory 1 factory 2 line 1 line 2 line 1 line 2 product Aproduct Bproduct Aproduct Bproduct Aproduct Bproduct Aproduct B XA11XB11XA12XB12XA21XB21XA22XB22 selling price line cost/hr line hr/unit line unit cost raw mat unit cost raw mat unit/prod raw mat cost/unit labor hr/unit labor rate $/hr48 45 labor unit cost factory burden rate burden unit cost total unit cost unit profit fixed cost

The Answer Product AProduct B Factory 1 Line Factory 1 Line Factory 2 Line Factory 2 Line Maximum monthly profit ___$11,609.78

The Formulation Let X ijk = units produced product i (i = A,B) in factory j (j = 1,2) on line k (k = 1,2) Max 76XA XB11+92XA XB12+62XA XB21+46XA XB ZA ZA12-900ZA ZA ZB ZB ZB ZB22

Some of the constraints !Min production levels XA11+XA12+XA21+XA22>120 XB11+XB12+XB21+XB22>85 !Available labor hours 30XA11+30XA12+43XB11+43XB12< XA21+30XA22+43XB21+43XB22<4400 !Available raw material 10XA11+10XA12+13XB11+13XB12< XA21+10XA22+13XB21+13XB22<1500

More of the constraints !Production line hours 8XA11+12XB11<480 8XA12+12XB12<600 8XA21+12XB21<1000 8XA22+12XB22<680 ! !Fixed cost XA ZA11<0 XA ZA12<0 XA ZA21<0 XA ZA22<0 XB ZB11<0 XB ZB12<0 XB ZB21<0 XB ZB22<0

Inetger Solutions Best Integer Solution - OBJECTIVE FUNCTION VALUE = 11, VARIABLE VALUE XA XA XA XA XB XB XB XB

Continued Part Period Balancing (PPB) 10 Inventory holding cost = h (PP m ) Find m so that K h(PP m ) or PP m K / h We in the business call K / h “the economic part period factor” Order quantity = Q = D 1 + D 2 + … + D m

An Old Favorite 11 Wk1Wk2Wk3Wk4Wk5Wk6Wk7Wk8Wk9 Wk PP m  K/h = 132 /.6 = 220 pp1 = 0 pp2 = 42 Pp3 = 42 + (2) 32 = 106 pp4 = pp3 + 3(12) = 142 pp5 = pp4 + 4(26) = 246 Q 1 = = 154 pp1 = 0 pp2 = 45 pp3 = 45 + (2) 14 = 73 pp4 = (76) = 301 Q 6 = = 247 Q 10 = 38 cost =3 x x.60 = $ Wk1Wk2Wk3Wk4Wk5Wk6Wk7Wk8Wk9 Wk

12 No Fixed Cost I believe this problem can be solved as a transportation problem.

13 The Transportation Problem x tj = number of units produced in month t to satisfy month j demands I’m going to need an example of this.

14 The Example h = $2 per unit per month

15 What can we conclude from all of this? Most heuristics outperform EOQ the Silver-Meal heuristic incurs an average cost penalty relative to Wagner-Whitin of less than 1 percent. Significant costs penalties using Silver-Meal will incur if demand pattern drops rapidly over several periods when there are a large number of periods having no demand

16 Can we have some really neat homework problems? Huh? Text: Chapter 7: problems 13, 14, 17, 18, 19, 22

17 Safety Stock When demand or lead-time is random (or both), then safety stock may be established as a “hedge” against uncertain demands. For the deterministic case: R = D L For the stochastic case: R = LTD avg + s where LTD = a random variable, the lead-time demand, LTD avg = average lead-time demand and s is the safety stock. Uncertain Lead-time Demands

18 Safety Stock based on Fill Rate Fill rate criterion: set s = z STD where STD = standard deviation of the lead-time demand distribution then R = LTD avg + z STD LTD LTD avg Shortage probability Pr{LTD > R) = p R s

19 Compute the variability coefficient, v = variance of demand per period square of average demand per period If V <.25, use EOQ with D avg else use a DLS method But that is only a “rule of thumb.” But I need to know when demands are lumpy, don’t I?