Aggregate Planning Chapter 11

Aggregate Planning Aggregate planning Intermediate-range capacity planning that typically covers a time horizon of 2 to 18 months. Useful for organizations that experience seasonal, or other variations in demand. “Big-picture” approach. Groups together similar products (services) and deals with them as though they were a single products (service). Goal: Achieve a production plan that will effectively utilize the organization’s resources to satisfy overall demand

Overview of Planning Levels Long-Range Plans Long-term capacity} 5 Location} 8 Layout} 6 Product design} 4 Work system design} 7 Intermediate Plans (This Chapter) General levels of: Employment Output Finished-goods inventories Subcontracting Backorders Short-Range Plans Detailed plans: Production lot size} 13 Order quantities} 13 Machine loading} 16 Job assignments} 16 Job sequencing} 16 Work schedules} 16 Overview of Planning Levels

The Planning Sequence Long-term planning Intermediate-term planning Short-term detailed planning

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

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). Aggregation 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

Aggregate Planning Strategies 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

Demand Options Pricing Promotion Back orders (delaying order filling) Used to shift demand from peak to off-peak periods. Airline: night/weekend Restaurants: happy hour/early bird Price elasticity is important Yield (Revenue) Management Maximizing revenue by using a variable pricing strategy. Prices are set relative to capacity availability. 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 Very uneven situation Offer different products/services during off-peak periods to make use of excess capacity: fastfood stores offer breakfast.

Supply Options Hire and layoff workers May have upper or lower limit Unions/internal policies may prohibit layoffs Skill levels, recruiting costs Associated costs (e.g., recruiting, training, severance-pay, morale) Overtime Maintain skilled workforce; Seasonal peaks Unions/Overtime may result in lower productivity, poorer quality, more accidents, increased payroll costs Part-time workers Usually low-to-moderate job skills; Seasonal 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New Demand Less control over output. Quality problems. Higher costs

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

MIS 373: Basic Operations Management 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

MIS 373: Basic Operations Management 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

Uneven Demand and Two Strategies: Demand = Supply Demand < Supply Demand > Supply Supply (output) level 11-14

MIS 373: Basic Operations Management 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

Trial-and-Error Techniques Trial-and-error approaches consist of developing simple table or graphs that enable planners to visually compare projected demand requirements with existing capacity Alternatives are compared based on their total costs Disadvantage: it does not necessarily result in an optimal aggregate plan

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 1 2 3 4 5 Demand 40 30 20 50 60 MIS 373: Basic Operations Management

Example #1: Chase demand Beginning Inventory Time Periods 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory # Hired # Fired # Hired in the beginning of a period 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 # Fired in the beginning of a period MIS 373: Basic Operations Management

Example #1: Chase demand 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory # Hired # Fired Recall the chase strategy: Capacities are adjusted to match demand requirements over the planning horizon 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 MIS 373: Basic Operations Management

Example #1: Chase demand 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory # Hired # Fired 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 MIS 373: Basic Operations Management

Example #1: Chase demand 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory # Hired # Fired 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 MIS 373: Basic Operations Management

Example #1: Chase demand 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory # Hired # Fired 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 MIS 373: Basic Operations Management

Example #1: Chase demand 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory # Hired # Fired 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 MIS 373: Basic Operations Management

Example #1: Chase demand 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory # Hired # Fired 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 MIS 373: Basic Operations Management

Example #1: Chase demand 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory # Hired # Fired 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 MIS 373: Basic Operations Management

Example #1: Chase demand 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory # Hired # Fired 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 One defining characteristics of the chase strategy is that we don’t have end inventory. All we produced are/were sold. No holding cost MIS 373: Basic Operations Management

Example #1: Chase demand 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory # Hired # Fired 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 TC=Production + Holding + Hiring + Firing = 200*10 + 0 + 4*200 + 3*100 = $3,100 MIS 373: Basic Operations Management

Exercise 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 1 2 3 4 5 Demand 50 40 30

Solution Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 190 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 Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 180 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 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.

Solution Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 180 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 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.

Solution 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 180 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 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 180 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 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 180 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 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 180 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 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 180 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 TC=Production + Holding + Hiring + Firing = 180*10 + 5*10 + 1*100 + 2*200

Example #2: Level Capacity 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory # Hired # Fired 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 Firing Cost: $100/worker MIS 373: Basic Operations Management

Example #2: Level Capacity 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory # Hired # Fired Recall the level strategy: Capacities are kept constant over the planning horizon. So, 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 Firing Cost: $100/worker Total demand=40+30+20+50+60=200 Production per period=200/5=40 MIS 373: Basic Operations Management

Example #2: Level Capacity 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory # Hired # Fired 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 Firing Cost: $100/worker MIS 373: Basic Operations Management

Example #2: Level Capacity 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory # Hired # Fired Fire 1 worker in this period because 4 workers are sufficient to produce 40 units in a period. 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 Firing Cost: $100/worker MIS 373: Basic Operations Management

Example #2: Level Capacity 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory 10 # Hired # Fired 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 Firing Cost: $100/worker MIS 373: Basic Operations Management

Example #2: Level Capacity 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory 10 # Hired # Fired 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 Firing Cost: $100/worker MIS 373: Basic Operations Management

Example #2: Level Capacity 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory 10 # Hired # Fired 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 Firing Cost: $100/worker MIS 373: Basic Operations Management

Example #2: Level Capacity 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory 10 # Hired # Fired 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 Firing Cost: $100/worker MIS 373: Basic Operations Management

Example #2: Level Capacity 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory 10 # Hired # Fired 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 Firing Cost: $100/worker MIS 373: Basic Operations Management

Example #2: Level Capacity 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory 10 # Hired # Fired One defining characteristics of the level strategy is that we don’t need to adjust capacity (here, labor force), except for the initial period. 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 Firing Cost: $100/worker MIS 373: Basic Operations Management

Example #2: Level Capacity 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory 10 # Hired # Fired TC=Production + Holding + Hiring + Firing But, how to calculate the holding cost?  Average inventory in a period 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 Firing Cost: $100/worker MIS 373: Basic Operations Management

Example #2: Level Capacity 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory 10 Average Inventory 25 # Hired # Fired Regular Production Costs: $10/unit Inventory Holding Costs: $5/unit/period Hiring Cost: $200/worker Firing Cost: $100/worker =(0+10)/2 =(10+30)/2 We can estimate the holding cost by considering the average inventory in each period. MIS 373: Basic Operations Management

Example #2: Level Capacity 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory 10 Average Inventory 25 # Hired # Fired Regular Production Costs: $10/unit Inventory Holding Costs: $5/unit/period Hiring Cost: $200/worker Firing Cost: $100/worker =(0+10)/2 =(10+30)/2 TC=Production + Holding + Hiring + Firing TC= 200*10 + 60*5 + 0*200 + 1*100 = $2,400 MIS 373: Basic Operations Management

Example #2: Level Capacity 1 2 3 4 5 Total Demand 40 30 20 50 60 200 Production End Inventory 10 Average Inventory 25 # Hired # Fired Regular Production Costs: $10/unit Inventory Holding Costs: $5/unit/period Hiring Cost: $200/worker Firing Cost: $100/worker =(0+10)/2 =(10+30)/2 TC=Production + Holding + Hiring + Firing TC= 200*10 + 60*5 + 0*200 + 1*100 = $2,400 MIS 373: Basic Operations Management

Exercise 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 1 2 3 4 5 Demand 50 40 30 Two additional assumptions: Unmet demands in a period can be held and fulfilled in a future period. There is no cost associated with unmet demands.

Solution Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 190 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 Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 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 Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 36 180 End Inventory -4 Avg. Inventory # Hired # Fired 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 Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 36 180 End Inventory -4 Avg. Inventory # Hired # Fired 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 Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 36 180 End Inventory -4 -8 Avg. Inventory -6 # Hired # Fired -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 Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 36 180 End Inventory -4 -8 -2 Avg. Inventory -6 -5 # 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 Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 36 180 End Inventory -4 -8 -2 Avg. Inventory -6 -5 # 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 Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 36 180 End Inventory -4 -8 -2 Avg. Inventory -6 -5 # 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 Beginning Inventory 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 36 180 End Inventory -4 -8 -2 Avg. Inventory -6 -5 # Hired # Fired Negative Inventory has no meaning! By assumption #2, there is no cost associated with unmet demand (i.e., negative inventory has no costs). 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 TC=Production + Holding + Hiring + Firing = 180*10 + 10*(3+1+2) + 0 + 1*200 = $2,030

Solution 10 1 2 3 4 5 Total Demand 50 40 30 190 Production 36 180 End Inventory Avg. Inventory # Hired # Fired Another way to solve this problem.  Pushing unmet demands to its next 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 10 1 2 3 4 5 Total Demand 50 40 44 30 40 190 Production 36 180 End Inventory Avg. Inventory # Hired # Fired 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 10 1 2 3 4 5 Total Demand 50 40 44 30 38 30 40 190 Production 36 180 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 10 1 2 3 4 5 Total Demand 50 40 44 30 38 30 32 40 190 Production 36 180 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 10 1 2 3 4 5 Total Demand 50 40 44 30 38 30 32 40 190 Production 36 180 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 10 1 2 3 4 5 Total Demand 50 40 44 30 38 30 32 40 190 Production 36 180 End Inventory Avg. Inventory 9 # 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 10 1 2 3 4 5 Total Demand 50 40 44 30 38 30 32 40 190 Production 36 180 End Inventory Avg. Inventory 9 # Hired # Fired 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

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