OMSAN LOJİSTİK

Top Management Program in Logistics & Supply Chain Management (TMPLSM) Production and Operations Management 5: Capacity

Calculating Capacity Simple, near perfect world 1 machine, no labor or material constraints Annual demand 1.2 million units Rated equipment capacity : 300 units per hour Assumptions Enough capacity?

Rated capacity (our “usual” definition) Potential output if the resource is always busy considering normal maintenance, downtime, yields, and hours of operation. Peak capacity For short bursts, output can exceed rated capacity (e.g., by using overtime, or forgoing maintenance). Utilizable capacity (in expectation) Output achievable given variability in arrival and service times. Typically 70-85% of rated capacity. Actual capacity (the realization) Actual realizable output may exceed or fall short of utilizable capacity because you don’t actually get what you expected in terms of breakdowns, variability, etc. Capacity definitions

Expectation You flip a fair coin two times, you EXPECT (your best guess is ) 1 head and 1 tail (you expect this 50% of the time, while you expect 2 heads 25% of the time, and 0 heads 25% of the time). Realization You flip a coin twice, your realization is that you actually got, say, 0 heads and 2 tails. The difference between an “expectation” and a “realization”

6 Demand Rated Capacity Utilizable Matching supply w/ demand in service Increase capacity Rated Capacity Utilizable Increase utilizable capacity Demand Rated Capacity Utilizable Increase demand (reduce capacity) Demand

7 Rated Utilizable Inventory and capacity are substitutes for goods (but not services) Rated Capacity Utilizable But inventory becomes obsolete Demand Rated Capacity Utilizable Demand Inventory

8 Capacity Issues When to Add Capacity? How Much Capacity to Add? Where to Add Capacity? What type of Capacity to Add? CAPACITY IS NOT A FIXED NUMBER CAPACITY IS NOT A FIXED NUMBER!

9 Capacity Alternatives Time Units Capacity Demand Capacity lags demand “Capital-Request” Driven Time Units Capacity Demand Capacity leads Demand Capability Driven

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11 How Large Should Zenith’s Factory Be? In 1996, Zenith needed to decide how big its TV factory should be. Yearly fixed costs associated with the capacity to build 1 TV set/year totaled $1.80 ($180 for capacity of 100 sets/yr, etc.). Zenith made a profit of $25.90 on each TV sold. Its demand was projected to be 1.7 million sets/year, with a standard deviation of 0.5 million sets/year. How big should Zenith build its factory?

12 P = the probability that you sell the x th unit. C u = cost of underage (the profit you get from selling the xth unit). C o = cost of overage (the loss you incur if you don’t sell the xth unit). Expected Marginal Profit (MP) = P (C u ) Expected Marginal Loss (ML) = (1 - P) (C o ) Stock the x th unit iff MP > ML, i.e., iff P (C u ) > (1 - P) (C o ), which equates to: Marginal Analysis for the x th unit P > (C U + C O ) COCO

13 For Zenith: P c is the probability of SELLING the x th unit. P c is the probability that demand is MORE than amount “x”. C o = cost of overage, c u = cost of underage P C = critical fractile ( ) = = P c = (C U + C O ) COCO Service Level = expected fraction of customers served. P C = 1  “optimal service level” (very roughly)

14 P c = probability demand is more than “x”. P c = area under curve = x = Units demanded (millions)

15 Find the “z” associated with P c (Using the Normal Curve Tail Area) z z = (1-P c ) = area under curve to left of z = P c = area under curve to right of z = 0.065

16 Convert Back from “z” to “x” (Zenith’s factory should be capable of building 2.5 million TVs/yr).  z = x -   1.51 = x –  x = 2.5 million x = Units demanded (millions)

17 Is Marketing “overly optimistic”? What if Management says “Estimate the demand, and build a factory of that size.” –If we build to the expected mean demand of 1.7 million sets/year, we under-build. –If we build to an INFLATED mean demand of 2.5 million sets per year, we build the optimal capacity. –But we will have “excess” capacity 93.5% of the time.

18 Insights From Newsvendor Model Optimal service level trades off marginal profit against marginal loss. When C U > C O, order MORE than the mean demand. When C O > C U, order LESS than the mean demand

19 Alternate Capacity Strategies Capacity Time Capacity addition (initially unused) Capacity Demand forecast When C u is high: Time Capacity addition (fills shortage) Demand forecast When C o is high:

20 El Impacto del Lote El Impacto del Setup

21 Inventory (Queue), Capacity, & Information are substitutes Inventory Information Capacity What is the right mix?

22 Relationship between Inventory (L), Capacity Utilization (  ), & Variability (c a 2 +c s 2 )/2 L = L q +  L = W q +  L = [1 /  [  / (1 –  )] (c a 2 +c s 2 ) / 2] +  L =  (1 + [  / (1 –  )] [(c a 2 +c s 2 ) / 2])

23 Where should the firm position itself? Utilization,  Inventory, L (b) (c)(a) (c a 2 +c s 2 )/2=

24 The Triangle Utilization,  Inventory, L Inventory Information Capacity (c a 2 +c s 2 )/2= (b) (c)(a)

25 Remember  The “Newsvendor Model” helps you decide how much (utilizable) capacity is optimal when the overall magnitude of demand is uncertain.  The “Triangle Model” helps you decide how you might change your utilizable Capacity by changing Inventories (or Queues) and Information