Aggregate Planning - University of Arizona

Aggregate Planning - University of Arizona

1 AGGREGATE PLANNING Chapter 11 MIS 373: Basic Operations Management LEARNING OBJECTIVES After this lecture, students will be able to 1. Explain what aggregate planning is and how it is useful. 2. Identify the variables decision makers have to work with in aggregate planning. 3. Describe some of the graphical and quantitative techniques planners use. 4. Prepare aggregate plans and compute their costs. 5. Discuss aggregate planning in services. MIS 373: Basic Operations Management 2 MOTIVATIONS McDonald's Do you need to know the demand for each burger to plan your labor force? THE PLANNING SEQUENCE Long-term planning Intermediate-term planning Short-term detailed planning MIS 373: Basic Operations Management 4 THE CONCEPT OF AGGREGATION Aggregate planning is essentially a big-picture approach to planning. avoid focusing on individual products or services focus on a group of similar products or services For purposes of aggregate planning, it is often convenient to think of capacity in terms of labor hours or machine hours per period, or output rates (barrels per period, units per period), without worrying about how much of a particular item will actually be involved. MIS 373: Basic Operations Management 5 AGGREGATE PLANNING The main idea behind aggregate planning: Aggregate planning translates business plans into rough labor schedules and production plans Issues to consider for aggregate planning

Production rate: aggregate units per worker per unit time Workforce level: available workforce in terms of hours Actual production: Production rate x Workforce level Inventory: Units carried over from previous periods Costs: production, changing workforce, inventory MIS 373: Basic Operations Management 6 AGGREGATE PLANNING What does aggregate planning do? Given an aggregate demand forecast , determine production levels, inventory levels, and workforce levels, in order to minimize total relevant costs over the planning horizon Why do organizations need to do aggregate planning? It takes time to implement plans (e.g. hiring). It is not possible to predict with accuracy the timing and volume of demand for individual items. Planning is connected to the budgeting process which is usually done annually on an aggregate (e.g., departmental) level. It can help synchronize flow throughout the supply chain; it affects costs, equipment utilization; employment levels; and customer satisfaction MIS 373: Basic Operations Management 7 MATCHING DEMAND AND SUPPLY Proactive Alter demand to match supply (capacity) Among other approaches, we can alter demand by simply changing the price. Reactive Alter supply (capacity) to match demand Through capacity planning and aggregate planning Mixed Some of each MIS 373: Basic Operations Management 8 DEMAND OPTIONS Pricing Used to shift demand from peak to off-peak periods Price elasticity is important Promotion Advertising and other forms of promotion Issue: response rate and response patterns. Less control over timing of demand (may worsen the problem by bringing demand at the wrong time). Back orders (delaying order filling) Orders are taken in one period and deliveries promised for a later period Possible loss of sales, increased record keeping, lowered customer service level New demand Offer different products/services during off-peak periods.

Yield (Revenue) Management Maximizing revenue by using a variable pricing strategy. Prices are set relative to capacity availability. MIS 373: Basic Operations Management 9 SUPPLY OPTIONS Hire and layoff workers May have upper or lower limit Unions/internal policies may prohibit layoffs Skill levels Associated costs (e.g., recruiting, training, severance-pay, morale) Overtime Overtime may result in lower productivity, poorer quality, more accidents, increased payroll costs Part-time workers Usually low-to-moderate job skills Independent-contractors Inventories Produce in one period and sell in another Costs: holding and carrying cost, money tied up in inventory, insurance, obsolescence, deterioration, spoilage, breakage etc. Subcontracting Less control over output. Quality problems. Higher costs MIS 373: Basic Operations Management 10 AGGREGATE PLANNING SUPPLY STRATEGIES Level capacity strategy: Maintaining a steady rate of regular-time output; variations in demand are met by using inventories or other options such as overtime, part-time workers, subcontracting, and backorders Chase demand strategy: Matching capacity to demand; the planned output for a period is set at the expected demand for that period. MIS 373: Basic Operations Management 11 LEVEL STRATEGY Capacities are kept constant over the planning horizon Advantages Stable output rates and workforce Disadvantages Greater inventory (or other) costs MIS 373: Basic Operations Management

12 CHASE STRATEGY Capacities are adjusted to match demand requirements over the planning horizon Advantages Investment in inventory is low Labor utilization in high Disadvantages The cost of adjusting output rates and/or workforce levels MIS 373: Basic Operations Management 13 CHOOSING A STRATEGY Important factors: Company policy Constraints on the available options e.g., discourage layoffs, no subcontracting to protects secrets, union policies regarding over time Flexibility Chase flexibility may not be present for companies designed for high steady output (e.g., refineries, auto assembly) Cost Alternatives are evaluated in term of cost (while matching demand within the constraints). MIS 373: Basic Operations Management 14 EXAMPLE #1: CHASE DEMAND Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $5/unit/period Hiring Cost: $200/worker Firing Cost: $100/worker Period Demand 1 2 3 4 5

40 30 20 50 60 MIS 373: Basic Operations Management 15 EXAMPLE #1: CHASE DEMAND Time Periods Beginning Inventory 0 Demand 1 2 3 4 5 Total 40 30 20 50 60 200 Production End Inventory # Hired # Fired # Hired in the beginning of a period # Fired in the beginning of a period MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $5/unit/period Hiring Cost: $200/worker 16 Firing Cost: $100/worker

EXAMPLE #1: CHASE DEMAND 0 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 30 20 50 60 200 End Inventory # Hired # Fired Recall the chase strategy: Capacities are adjusted to match demand requirements over the planning horizon MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $5/unit/period Hiring Cost: $200/worker 17 Firing Cost: $100/worker EXAMPLE #1: CHASE DEMAND 0

1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 30 20 50 60 200 End Inventory 0 # Hired 0 # Fired 1 MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $5/unit/period Hiring Cost: $200/worker 18 Firing Cost: $100/worker

EXAMPLE #1: CHASE DEMAND 0 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 30 20 50 60 200 End Inventory 0 0 # Hired 0 0 # Fired 1 1 MIS 373: Basic Operations Management Beginning Inventory: 0 units

Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $5/unit/period Hiring Cost: $200/worker 19 Firing Cost: $100/worker EXAMPLE #1: CHASE DEMAND 0 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 30 20 50 60 200 End Inventory 0 0 0 # Hired 0 0

0 # Fired 1 1 1 MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $5/unit/period Hiring Cost: $200/worker 20 Firing Cost: $100/worker EXAMPLE #1: CHASE DEMAND 0 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 30 20 50 60 200

End Inventory 0 0 0 0 # Hired 0 0 0 3 # Fired 1 1 1 0 MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $5/unit/period Hiring Cost: $200/worker 21 Firing Cost: $100/worker EXAMPLE #1: CHASE DEMAND 0 1 2 3 4 5 Total Demand 40 30 20

50 60 200 Production 40 30 20 50 60 200 End Inventory 0 0 0 0 0 # Hired 0 0 0 3 1 # Fired 1 1 1 0 0 MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $5/unit/period Hiring Cost: $200/worker

22 Firing Cost: $100/worker EXAMPLE #1: CHASE DEMAND 0 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 30 20 50 60 200 End Inventory 0 0 0 0 0 0 # Hired 0

0 0 3 1 4 # Fired 1 1 1 0 0 3 MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $5/unit/period Hiring Cost: $200/worker 23 Firing Cost: $100/worker EXAMPLE #1: CHASE DEMAND 0 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production

40 30 20 50 60 200 End Inventory 0 0 0 0 0 0 # Hired 0 0 0 3 1 4 # Fired 1 1 1 0 0 3 One defining characteristics of the chase strategy is that we dont have end inventory. All we produced are/were sold. holding cost MIS No 373: Basic

Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $5/unit/period Hiring Cost: $200/worker 24 Firing Cost: $100/worker EXAMPLE #1: CHASE DEMAND 0 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 30 20 50 60 200 End Inventory 0 0 0 0

0 0 # Hired 0 0 0 3 1 4 # Fired 1 1 1 0 0 3 TC=Production + Holding + Hiring + Firing = 200*10 + 0 + 4*200 + 3*100 = $3,100 MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $5/unit/period Hiring Cost: $200/worker 25 Firing Cost: $100/worker EXERCISE PROBLEM Perform aggregate planning using the chase strategy: Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker

Period Demand 1 2 3 4 5 50 40 30 30 40 SOLUTION: CHASE STRATEGY Beginning Inventory 10 Demand 1 2 3 4 5 Total 50 40 30 30 40 190 Production End Inventory # Hired # Fired Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker

SOLUTION: CHASE STRATEGY Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 30 40 190 Production 40 40 30 30 40 180 End Inventory # Hired # Fired We only produce 40 units because there are 10 units beginning inventory that we can use. So, we can still meet the demand of 50 units. Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY

Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 30 40 190 Production 40 40 30 30 40 180 End Inventory 0 # Hired 0 # Fired 1 The beginning workforce is 5 workers. Since we only produce 40 units in this period and each worker can handle 10 units in a period, we only need 4 works here. We hence fire 1 at the beginning of this period. Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period

Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY 10 1 2 3 4 5 Total Demand 50 40 30 30 40 190 Production 40 40 30 30 40 180 End Inventory 0 0 # Hired 0 0 # Fired 1

0 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY 10 1 2 3 4 5 Total Demand 50 40 30 30 40 190 Production 40 40 30 30 40 180 End Inventory 0 0 0 # Hired 0

0 0 # Fired 1 0 1 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY 10 1 2 3 4 5 Total Demand 50 40 30 30 40 190 Production 40 40 30 30 40 180 End

Inventory 0 0 0 0 # Hired 0 0 0 0 # Fired 1 0 1 0 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY 10 1 2 3 4 5 Total Demand 50 40 30 30 40

190 Production 40 40 30 30 40 180 End Inventory 0 0 0 0 0 0 # Hired 0 0 0 0 1 1 # Fired 1 0 1 0 0 2 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker

Firing Cost: $200/worker SOLUTION: CHASE STRATEGY 10 1 2 3 4 5 Total Demand 50 40 30 30 40 190 Production 40 40 30 30 40 180 End Inventory 0 0 0 0 0 0 # Hired 0 0

0 0 1 1 # Fired 1 0 1 0 0 2 TC=Production + Holding + Hiring + Firing = 180*10 + 5*10 + 1*100 + 2*200 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker EXAMPLE #2: LEVEL CAPACITY 0 Demand 1 2 3 4 5 Total 40 30 20 50 60 200 Production

End Inventory # Hired # Fired MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Holding Costs: $5/unit/period Hiring Cost: $200/worker 35 Firing Cost: $100/worker EXAMPLE #2: LEVEL CAPACITY 0 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 40 40 40 40 200 End Inventory # Hired # Fired Recall the level strategy: Capacities are kept constant over the

planning horizon. So, Total demand=40+30+20+50+60=200 Production per period=200/5=40 MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Holding Costs: $5/unit/period Hiring Cost: $200/worker 36 Firing Cost: $100/worker EXAMPLE #2: LEVEL CAPACITY 0 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 40 40 40 40 200 End Inventory 0 # Hired 0

# Fired 1 MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Holding Costs: $5/unit/period Hiring Cost: $200/worker 37 Firing Cost: $100/worker EXAMPLE #2: LEVEL CAPACITY 0 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 40 40 40 40 200 End Inventory 0 # Hired

0 # Fired 1 Fire 1 worker in this period because 4 workers are sufficient to produce 40 units in a period. MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Holding Costs: $5/unit/period Hiring Cost: $200/worker 38 Firing Cost: $100/worker EXAMPLE #2: LEVEL CAPACITY 0 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 40 40 40 40 200

End Inventory 0 10 # Hired 0 0 # Fired 1 0 MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Holding Costs: $5/unit/period Hiring Cost: $200/worker 39 Firing Cost: $100/worker EXAMPLE #2: LEVEL CAPACITY 0 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 40

40 40 40 200 End Inventory 0 10 30 # Hired 0 0 0 # Fired 1 0 0 MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Holding Costs: $5/unit/period Hiring Cost: $200/worker 40 Firing Cost: $100/worker EXAMPLE #2: LEVEL CAPACITY 0 1 2 3 4 5 Total Demand 40 30

20 50 60 200 Production 40 40 40 40 40 200 End Inventory 0 10 30 20 # Hired 0 0 0 0 # Fired 1 0 0 0 MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Holding Costs: $5/unit/period Hiring Cost: $200/worker 41 Firing Cost: $100/worker EXAMPLE #2: LEVEL CAPACITY

0 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 40 40 40 40 200 End Inventory 0 10 30 20 0 # Hired 0 0 0 0

0 # Fired 1 0 0 0 0 MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Holding Costs: $5/unit/period Hiring Cost: $200/worker 42 Firing Cost: $100/worker EXAMPLE #2: LEVEL CAPACITY 0 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 40 40 40 40

200 End Inventory 0 10 30 20 0 60 # Hired 0 0 0 0 0 0 # Fired 1 0 0 0 0 1 MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Holding Costs: $5/unit/period Hiring Cost: $200/worker 43 Firing Cost: $100/worker EXAMPLE #2: LEVEL CAPACITY 0 1 2 3

4 5 Total Demand 40 30 20 50 60 200 Production 40 40 40 40 40 200 End Inventory 0 10 30 20 0 60 # Hired 0 0 0 0 0 0 # Fired

1 0 0 0 0 1 One defining characteristics of the level strategy is that we dont need to adjust capacity (here, labor force), except for the initial period. MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Holding Costs: $5/unit/period Hiring Cost: $200/worker 44 Firing Cost: $100/worker EXAMPLE #2: LEVEL CAPACITY 0 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 40 40

40 40 200 End Inventory 0 10 30 20 0 60 # Hired 0 0 0 0 0 0 # Fired 1 0 0 0 0 1 TC=Production + Holding + Hiring + Firing But, how to calculate the holding cost? Average inventory in a period MIS 373: Basic Operations Management Beginning Inventory: 0 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Holding Costs: $5/unit/period Hiring Cost: $200/worker 45 Firing Cost: $100/worker EXAMPLE #2: LEVEL CAPACITY

0 Regular Production Costs: $10/unit 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production 40 40 40 40 40 200 End Inventory 0 10 30 20 0 60 Hiring Cost: $200/worker Average Inventory

0 5 20 25 10 60 Firing Cost: $100/worker # Hired 0 # Fired 1 =(0+10)/2=(10+30)/2 0 0 0 0 0 0 0 0 0 1 Inventory Holding Costs: $5/unit/period We can estimate the holding cost by considering the average inventory in each period. MIS 373: Basic Operations Management 46 EXAMPLE #2: LEVEL CAPACITY 0 Regular Production Costs: $10/unit 1 2

3 4 5 Total Demand 40 30 20 50 60 200 Production 40 40 40 40 40 200 End Inventory 0 10 30 20 0 60 Hiring Cost: $200/worker Average Inventory 0 5 20 25

10 60 Firing Cost: $100/worker # Hired 0 # Fired 1 =(0+10)/2=(10+30)/2 0 0 0 0 0 0 0 0 0 1 Inventory Holding Costs: $5/unit/period TC=Production + Holding + Hiring + Firing TC= 200*10 + 60*5 + 0*200 + 1*100 = $2,400 MIS 373: Basic Operations Management 47 EXAMPLE #2: LEVEL CAPACITY 0 Regular Production Costs: $10/unit 1 2 3 4 5 Total

Demand 40 30 20 50 60 200 Production 40 40 40 40 40 200 End Inventory 0 10 30 20 0 60 Hiring Cost: $200/worker Average Inventory 0 5 20 25 10 60 Firing Cost: $100/worker

# Hired 0 # Fired 1 =(0+10)/2=(10+30)/2 0 0 0 0 0 0 0 0 0 1 Inventory Holding Costs: $5/unit/period TC=Production + Holding + Hiring + Firing TC= 200*10 + 60*5 + 0*200 + 1*100 = $2,400 MIS 373: Basic Operations Management 48 EXERCISE PROBLEM Perform aggregate planning using the level strategy: Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker Period Demand 1 2 3

4 5 50 40 30 30 40 Two additional assumptions: 1. Unmet demands in a period can be held and fulfilled in a future period. 2. There is no cost associated with unmet demands. SOLUTION: CHASE STRATEGY Beginning Inventory 10 Demand 1 2 3 4 5 Total 50 40 30 30 40 190 Production End Inventory Avg. Inventory # Hired # Fired Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY Beginning Inventory 10

1 2 3 4 5 Total Demand 50 40 30 30 40 190 Production 36 36 36 36 36 180 End Inventory Avg. Inventory # Hired # Fired Total demand=190 Total demand=190 10 = 180 Production per period=180/5=36 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY Beginning Inventory 10 1 2

3 4 5 Total Demand 50 40 30 30 40 190 Production 36 36 36 36 36 180 End Inventory -4 Avg. Inventory 3 # Hired 0 # Fired 1 By assumption #1, unmet demands in a period can be held and fulfilled in a future period. So, we keep track on the unmet demands, and try to fulfill them in a future period. Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker

SOLUTION: CHASE STRATEGY Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 30 40 190 Production 36 36 36 36 36 180 End Inventory -4 Avg. Inventory 3 # Hired 0 # Fired 1 Avg. inventory = [10 + (-4)]/2 = 3 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period

Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 30 40 190 Production 36 36 36 36 36 180 End Inventory -4 -8 Avg. Inventory 3 -6 # Hired 0

0 # Fired 1 0 -8 = (-4) + (-4) Unmet demand from period #1 and from period #2 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 30 40 190 Production 36 36 36 36 36 180 End Inventory

-4 -8 -2 Avg. Inventory 3 -6 -5 # Hired 0 0 0 # Fired 1 0 0 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 30 40

190 Production 36 36 36 36 36 180 End Inventory -4 -8 -2 4 Avg. Inventory 3 -6 -5 1 # Hired 0 0 0 0 # Fired 1 0 0 0 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker

SOLUTION: CHASE STRATEGY Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 30 40 190 Production 36 36 36 36 36 180 End Inventory -4 -8 -2 4 0 Avg. Inventory 3 -6 -5 1

2 # Hired 0 0 0 0 0 0 # Fired 1 0 0 0 0 1 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 30

40 190 Production 36 36 36 36 36 180 End Inventory -4 -8 -2 4 0 Avg. Inventory 3 -6 -5 1 2 # Hired 0 0 0 0 0 0 # Fired 1 0 0 0

0 1 By assumption #2, there is no cost associated with unmet demand (i.e., negative inventory has no costs). TC=Production + Holding + Hiring + Firing = 180*10 + 10*(3+1+2) + 0 + 1*200 = $2,030 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY 10 1 2 3 4 5 Total Demand 50 40 30 30 40 190 Production 36 36 36 36 36 180 End Inventory Avg. Inventory

# Hired # Fired Tim suggested another way to solve this problem.Beginning Inventory: 10 units Beginning Workforce: 5 workers Pushing unmet demands to its next period Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY 10 1 2 3 4 5 Total Demand 50 40 44 30 30 40 190 Production 36 36 36 36 36 180 End Inventory 0 Avg. Inventory 5 # Hired

0 # Fired 1 Tim suggested another way to solve this problem. Pushing unmet demands to its next period Instead of -4 end inventory, here we have 0. See that the demand for period #2 increase from 40 to 44. Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY 10 1 2 3 4 5 Total Demand 50 40 44 30 38 30 40 190 Production 36 36 36 36 36 180 End Inventory

0 0 Avg. Inventory 5 0 # Hired 0 0 # Fired 1 0 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY 10 1 2 3 4 5 Total Demand 50 40 44 30 38 30 32 40 190 Production 36 36

36 36 36 180 End Inventory 0 0 0 Avg. Inventory 5 0 0 # Hired 0 0 0 # Fired 1 0 0 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY 10 1 2 3 4 5 Total Demand

50 40 44 30 38 30 32 40 190 Production 36 36 36 36 36 180 End Inventory 0 0 0 4 Avg. Inventory 5 0 0 2 # Hired 0 0 0 0 # Fired 1 0 0

0 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY 10 1 2 3 4 5 Total Demand 50 40 44 30 38 30 32 40 190 Production 36 36 36 36 36 180 End Inventory 0 0 0 4 0

4 Avg. Inventory 5 0 0 2 2 9 # Hired 0 0 0 0 0 0 # Fired 1 0 0 0 0 1 Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker SOLUTION: CHASE STRATEGY 10 1 2 3 4 5

Total Demand 50 40 44 30 38 30 32 40 190 Production 36 36 36 36 36 180 End Inventory 0 0 0 4 0 4 Avg. Inventory 5 0 0 2 2 9 # Hired 0 0 0

0 0 0 # Fired 1 0 0 0 0 1 TC=Production + Holding + Hiring + Firing = 180*10 + 10*9 + 0 + 1*200 = $2,090 While the TC number is different, this approach seems more intuitive than the previous approach, especially on the parts about inventory. Beginning Inventory: 10 units Beginning Workforce: 5 workers Production Rate: 10 units/worker/period Regular Production Costs: $10/unit Inventory Costs: $10/unit/period Hiring Cost: $100/worker Firing Cost: $200/worker AGGREGATE PLANNING IN SERVICES The aggregate planning process is different for services in the following ways: Most services cannot be inventoried Demand for services is difficult to predict Capacity is also difficult to predict Service capacity must be provided at the appropriate place and time Labor is usually the most constraining resource for services MIS 373: Basic Operations Management 66 AGGREGATE PLANNING IN SERVICES Hospitals: allocate funds, staff, and supplies to meet the demands of patients for their medical services Restaurants: smoothing the service rate, determining workforce size, and managing demand to match a fixed capacity Perishable inventory

Airlines: complex due to the large number of factors involved (planes, flight & group personnel, multiple routes, airports etc.) Capacity decisions must also take into account the percentage of seats to be allocated to various fare classes in order to maximize profit or yield (Revenue Management) MIS 373: Basic Operations Management 67 KEY POINTS An aggregate plan is an intermediate-range plan for a collection of similar products or services that sets the stage for shorter-range plans. Two aggregate planning supply strategies are 1) chase demand strategy and 2) level capacity strategy. MIS 373: Basic Operations Management 68

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    Wagner's Theorem - 1937. G is planar if and only if there is no subgraph of G that is a minor of K 5 or K. 3,3. Published seven years following Kurtowski's theorem. Equivalent to Kuratowski's proof, since it is...
  • OAA Extended Response/Short Answer

    OAA Extended Response/Short Answer

    Arial Times New Roman Wingdings Beam OAA Extended Response/Short Answer Before Reading the Question Before Reading the Question As You Read the Question Types of Extended Response Questions 1. Four Keywords 2. Two Special Keywords for One Subject 3. One...