Strategies for Meeting Demand

If demand for a company's products or services are stable over time or its resources are unlimited, then aggregate planning is trivial. Demand forecasts are converted to resource requirements, the resources necessary to meet demand are acquired and maintained over the time horizon of the plan, and minor variations in demand are handled with overtime or undertime. Aggregate production planning becomes a challenge when demand fluctuates over the planning horizon. For example, seasonal demand patterns can be met by:

  1. Producing at a constant rate and using inventory to absorb fluctuations in demand (level production)
  2. Hiring and firing workers to match demand (chase demand)
  3. Maintaining resources for high-demand levels
  4. Increasing or decreasing working hours (overtime and undertime)
  5. Subcontracting work to other firms
  6. Using part-time workers
  7. Providing the service or product at a later time period (backordering)

When one of these is selected, a company is said to have a pure strategy for meeting demand. When two or more are selected, a company has a mixed strategy.

The level production strategy, shown in Figure 11.4(a), sets production at a fixed rate (usually to meet average demand) and uses inventory to absorb variations in demand. During periods of low demand, overproduction is stored as inventory, to be depleted in periods of high demand. The cost of this strategy is the cost of holding inventory, including the cost of obsolete or perishable items that may have to be discarded.

The chase demand strategy, shown in Figure 11.4(b), matches the production plan to the demand pattern and absorbs variations in demand by hiring and firing workers. During periods of low demand, production is cut back and workers are laid off. During periods of high demand, production is increased and additional workers are hired. The cost of this strategy is the cost of hiring and firing workers. This approach would not work for industries in which worker skills are scarce or competition for labor is intense, but it can be quite cost-effective during periods of high unemployment or for industries with low-skilled workers.

Maintaining resources for high-demand levels ensures high levels of customer service but can be very costly in terms of the investment in extra workers and machines that remain idle during low-demand periods. This strategy is used when superior customer service is important (such as Nordstrom's department store) or when customers are willing to pay extra for the availability of critical staff or equipment. Professional services trying to generate more demand may keep staff levels high, defense contractors may be paid to keep extra capacity "available," child-care facilities may elect to maintain staff levels for continuity when attendance is low, and full-service hospitals may invest in specialized equipment that is rarely used but is critical for the care of a small number of patients.


Overtime and undertime are common strategies when demand fluctuations are not extreme. A competent staff is maintained, hiring and firing costs are avoided, and demand is met temporarily without investing in permanent resources. Disadvantages include the premium paid for overtime work, a tired and potentially less efficient work force, and the possibility that overtime alone may be insufficient to meet peak demand periods.

Subcontracting or outsourcing is a feasible alternative if a supplier can reliably meet quality and time requirements. This is a common solution for component parts when demand exceeds expectations for the final product. The subcontracting decision requires maintaining strong ties with possible subcontractors and first-hand knowledge of their work. Disadvantages of subcontracting include reduced profits, loss of control over production, long lead times, and the potential that the subcontractor may become a future competitor.

Using part-time workers is feasible for unskilled jobs or in areas with large temporary labor pools (such as students, homemakers, or retirees). Part-time workers are less costly than full-time workers--no health-care or retirement benefits--and are more flexible--their hours usually vary considerably. Part-time workers have been the mainstay of retail, fast-food, and other services for some time and are becoming more accepted in manufacturing and government jobs. Japanese manufacturers traditionally use a large percentage of part-time or temporary workers. IBM staffs its entire third shift at Research Triangle Park, North Carolina, with temporary workers (college students). Part-time and temporary workers now account for about one third of our nation's work force. The temp agency Manpower, Inc. is the largest private employer in the world. Problems with part-time workers include high turnover, accelerated training requirements, less commitment, and scheduling difficulties.

THE COMPETITIVE EDGE
Meeting Peak Holiday Demand at Neiman Marcus

Neiman Marcus operates a 377,000-square-foot mail-order distribution center in Irving, Texas. Forty percent of its business is accounted for by the 2.8 million "Christmas Book" catalogs mailed out in mid-September. A flurry of orders is received immediately after the catalogs are mailed; then volume drops off and levels out until early November. The sales volume then begins a steep ascent that peaks early in December. September demand represents 52 percent of peak shipments, and October represents 91 percent of peak shipments. Demand in November and December is in excess of 100,000 shipments per week. The peak demand volume of 28,000 orders per day is more than double normal sales. Despite these numbers, Neiman Marcus ships 90 percent of holiday orders within 1 day and 99 percent within 2 days, with 99.4 percent accuracy. How does it achieve such performance levels?

The company plans in advance. Although it's hard to predict which items will be hot sellers each year, close relations with suppliers and an early analysis of September's demand pattern (within 10 days of the catalog mailing) can make back ordering large volumes feasible. Fast-moving items are moved to a prominent place in the warehouse, and work flow is prioritized so that customer back orders receive immediate attention. A new conveyor system sports color-coded conveyors that identify flow patterns from different sources to shipping (from apparel to shipping, for example, versus toys or small gifts). It also uses bar codes extensively to route cartons to special areas for gift wrapping, Federal Express shipment, or special attention. Customers are given options for when their order is shipped. They can order now for shipment at a later date or receive Federal Express second-day service on any item in the catalog at no extra cost.

Another key to success is dedicated people with a great attitude. Neiman Marcus hires 300 extra people in their distribution center during the holiday season. Twenty percent of these workers return each year. To allow sufficient time for training, the company begins hiring temporaries when the catalogs are mailed out in September and gradually builds up their numbers over the next two months. Permanent staff personnel train the new hires, and the system of work is purposely designed to be simple and easy to learn.

Incentive pay, based on productivity and quality and reinforced with prizes and awards, adds fun and excitement to the work environment. With Neiman Marcus, as with many other retailers, making people happy during the holiday season ensures that the year will be a profitable one.

Source: Based on Karen Auguston, "Neiman Marcus Plans Picking to Meet Peak Holiday Demands," Modern Material Handling (December 1992): 44-48.


Backordering is a viable alternative only if the customer is willing to wait for the product or service. For some restaurants you may be willing to wait an hour for a table; for others you may not.

One aggregate planning strategy is not always preferable to another. The most effective strategy depends on the demand distribution, competitive position, and cost structure of a firm or product line. Several quantitative techniques are available to help with the aggregate planning decision. We will discuss pure and mixed strategies using trial and error, the transportation method, and other quantitative techniques.

APP by Trial and Error

Using trial and error to solve aggregate production planning problems involves formulating several strategies for meeting demand, constructing production plans from those strategies, determining the cost and feasibility of each plan, and selecting the lowest cost plan from among the feasible alternatives. The effectiveness of trial and error is directly related to management's understanding of the cost variables involved and the reasonableness of the scenarios tested. Example 11.1 compares the cost of two pure strategies. Example 11.2 uses Excel to compare pure and mixed strategies for a more extensive problem.

EXAMPLE
11.1
Aggregate Production Planning Using Pure Strategies

The Good and Rich Candy Company makes a variety of candies in three factories worldwide. Its line of chocolate candies exhibits a highly seasonal demand pattern, with peaks during the winter months (for the holiday season and Valentine's Day) and valleys during the summer months (when chocolate tends to melt and customers are watching their weight). Given the following costs and quarterly sales forecasts, determine whether a level production or chase demand production strategy would more economically meet the demand for chocolate candies:

SOLUTION:

For the level production strategy, we first need to calculate average quarterly demand.

This becomes our planned production for each quarter. Since each worker can produce 1,000 pounds a quarter, 100 workers will be needed each quarter to meet the production requirements of 100,000 pounds. Production in excess of demand is stored in inventory, where it remains until it is used to meet demand in a later period. Demand in excess of production is met by using inventory from the previous quarter. The production plan and resulting inventory costs are given in Exhibit 11.1.

For the chase demand strategy, production each quarter matches demand. To accomplish this, workers are hired and fired at a cost of $100 for each one hired and $500 for each one fired. Since each worker can produce 1,000 pounds per quarter, we divide the quarterly sales forecast by 1,000 to determine the required workforce size each quarter. We begin with 100 workers and hire and fire as needed. The production plan and resulting hiring and firing costs are given in Exhibit 11.2.

Comparing the cost of level production with chase demand, chase demand is the best strategy for the Good and Rich line of chocolate candies.

Although chase demand is the better strategy for Good and Rich from an economic point of view, it may seem unduly harsh on the company's workforce. An example of a good "fit" between a company's chase demand strategy and the needs of the workforce is Hershey's, located in rural Pennsylvania, with a demand and cost structure much like that of Good and Rich. The location of the manufacturing facility is essential to the effectiveness of the company's production plan. During the winter, when demand for chocolate is high, the company hires farmers from surrounding areas, who are idle that time of year. The farmers are let go during the spring and summer, when they are anxious to return to their fields and the demand for chocolate falls. The plan is cost-effective, and the extra help is content with the sporadic hiring and firing practices of the company.

Probably the most common approach to production planning is trial and error using mixed strategies and spreadsheets to evaluate different options quickly. Mixed strategies can incorporate management policies, such as "no more than x percent of the workforce can be laid off in one quarter" or "inventory levels cannot exceed x dollars." They can also be adapted to the quirks of a company or industry. For example, many industries that experience a slowdown during part of the year may simply shut down manufacturing during the low-demand season and schedule everyone's vacation during that time. Furniture manufacturers typically close down for the month of July each year, and shipbuilders close down for the month of December.

For some industries, the production planning task revolves around the supply of raw materials, not the demand pattern. Consider Motts, the applesauce manufacturer whose raw material is available only 40 days during a year. The workforce size at its peak is 1,500 workers, but it normally consists of around 350 workers. Almost 10 percent of the company's payroll is made up of unemployment benefits--the price of doing business in that particular industry.

EXAMPLE
11.2
Aggregate Production Planning Using Pure and Mixed Strategies

Demand for Quantum Corporation's action toy series follows a seasonal pattern--growing through the fall months and culminating in December, with smaller peaks in January (for after-season markdowns, exchanges, and accessory purchases) and July (for Christmas-in-July specials).

Each worker can produce on average 100 cases of action toys each month. Overtime is limited to 300 cases, and subcontracting is unlimited. No action toys are currently in inventory. The wage rate is $10 per case for regular production, $15 for overtime production, and $25 for subcontracting. No stockouts are allowed. Holding cost is $1 per case per month. Increasing the workforce costs approximately $1,000 per worker. Decreasing the workforce costs $500 per worker.

Management wishes to test the following scenarios for planning production:

  1. Level production over the twelve months.
  2. Produce to meet demand each month.
  3. Increase or decrease the workforce in five-worker increments.

SOLUTION:

Excel was used to evaluate the three planning scenarios. The solution printouts are shown in Exhibit 11.3, Exhibit 11.4, and Exhibit 11.5, respectively. From the scenarios tested, step production yields the lowest cost.

General Linear Programming Model

Pure and mixed strategies for production planning are easy to evaluate, but they do not necessarily provide an optimum solution. Consider the Good and Rich Company of Example 11.1. The optimum production plan is probably some combination of inventory and workforce adjustment. We could simply try different combinations and compare the costs (i.e., the trial-and-error approach), or we could find the optimum solution by using linear programming.3 Example 11.3 develops an optimum aggregate production plan for Good and Rich chocolate candies using linear programming.

EXAMPLE
11.3
Aggregate Production Planning using Linear Programming

Formulate a linear programming model for Example 11.1 that will satisfy demand for Good and Rich chocolate candies at minimum cost. Solve the model with available linear programming software.

SOLUTION:

Model formulation:

  • Objective function: The objective function seeks to minimize the cost of hiring workers, firing workers, and holding inventory. Cost values are provided in the problem statement for Example 11.1. The number of workers hired and fired each quarter and the amount of inventory held are variables whose values are determined by solving the linear programming (LP) problem.
  • Demand constraints: The first set of constraints ensure that demand is met each quarter. Demand can be met from production in the current period and inventory from the previous period. Units produced in excess of demand remain in inventory at the end of the period. In general form, the demand equations are constructed as

where Dt is the demand in period t, as specified in the problem. Leaving demand on the right-hand side, we have

There are four demand constraints, one for each quarter. Since there is no beginning inventory, I0 = 0, and it can be dropped from the first demand constraint.
  • Production constraints: The four production constraints convert the workforce size to the number of units that can be produced. Each worker can produce 1,000 units a quarter, so the production each quarter is 1,000 times the number of workers employed, or

  • Workforce constraints: The workforce constraints limit the workforce size in each period to the previous period's workforce plus the number of workers hired in the current period minus the number of workers fired.

Notice the first workforce constraint appears slightly different. Since the beginning workforce size of 100 is known, it remains on the right-hand side of the equation.
  • Additional constraints: Additional constraints can be added to the LP formulation as needed to limit such options as subcontracting or overtime. The cost of those options is then added to the objective function.

The LP formulation is solved using Excel solver to yield the solution in Exhibit 11.7.4 The cost of the optimum solution is $32,000, an improvement of $3,000 over the chase demand strategy and $38,000 over the level production strategy.

  • Firing twenty workers in the first quarter: This brought the workforce size down from one hundred to eighty workers. The eighty workers produced 80,000 pounds of chocolate, which exactly met demand. In the second quarter, no workers were hired or fired, 80,000 pounds were produced, 50,000 pounds were used to meet demand, and 30,000 pounds were placed into inventory.
  • Hiring ten workers in the third quarter: The workforce rose to ninety workers, and 90,000 pounds of chocolate candies were produced. The 90,000 pounds produced plus the 30,000 pounds in inventory were sufficient to meet the demand of 120,000 pounds.
  • Hiring sixty workers in the fourth quarter: The resulting workforce of 150 workers produced 150,000 pounds of chocolate candies, which exactly met demand.

APP by the Transportation Method

For those cases in which the decision to change the size of the workforce has already been made or is prohibited, the transportation method of linear programming can be used to develop an aggregate production plan. The transportation method gathers all the cost information into one matrix and plans production based on the lowest-cost alternatives. Example 11.4 illustrates the procedure. Table 11.1 shows a blank transportation tableau for aggregate planning.

EXAMPLE
11.4
APP by the Transportation Method of Linear Programming

Burruss Manufacturing Company uses overtime, inventory, and subcontracting to absorb fluctuations in demand. An aggregate production plan is devised annually and updated quarterly. Cost data, expected demand, and available capacities in units for the next four quarters are given here. Demand must be satisfied in the period it occurs; that is, no backordering is allowed. Design a production plan that will satisfy demand at minimum cost.

Regular production cost per unit $20
Overtime production cost per unit $25
Subcontracting cost per unit $28
Inventory holding cost per unit per period $3
Beginning inventory 300 units

SOLUTION:

The problem is solved using the transportation tableau shown in Table 11.2. The tableau is a worksheet that is completed as follows:

  • To set up the tableau, demand requirements for each quarter are listed on the bottom row and capacity constraints for each type of production (i.e., regular, overtime, or subcontracting) are placed in the far right column.
  • Next, cost figures are entered into the small square at the corner of each cell. Reading across the first row, inventory on hand in period 1 that is used in period 1 incurs zero cost. Inventory on hand in period 1 that is not used until period 2 incurs $3 holding cost. If the inventory is held until period 3, the cost is $3 more, or $6. Similarly, if the inventory is held until period 4, the cost is an additional $3, or $9.
  • Interpreting the cost entries in the second row, if a unit is produced under regular production in period 1 and used in period 1, it costs $20. If a unit is produced under regular production in period 1 but is not used until period 2, it incurs a production cost of $20 plus an inventory cost of $3, or $23. If the unit is held until period 3, it will cost $3 more, or $26. If it is held until period 4, it will cost $29. The cost calculations continue in a similar fashion for overtime and subcontracting, beginning with production costs of $25 and $28, respectively.
  • The costs for production in periods 2, 3, and 4 are determined in a similar fashion, with one exception. Half of the remaining transportation tableau is blocked out as infeasible. This occurs because no backordering is allowed for this problem, and production cannot take place in one period to satisfy demand that occurs in previous periods.
  • Now that the tableau is set up, we can begin to allocate units to the cells and develop our production plan. The procedure is to assign units to the lowest-cost cells in a column so that demand requirements for the column are met, yet capacity constraints of each row are not exceeded. Beginning with the first demand column for period 1, we have 300 units of beginning inventory available to us at no cost. If we use all 300 units in period 1, there is no inventory left for use in later periods. We indicate this fact by putting a dash in the remaining cells of the beginning inventory row. We can satisfy the remaining 600 units of demand for period 1 with regular production at a cost of $20 per unit.
  • In period 2, the lowest-cost alternative is regular production in period 2. We assign 1,200 units to that cell and, in the process, use up all the capacity for that row. Dashes are placed in the remaining cells of the row to indicate that they are no longer feasible choices. The remaining units needed to meet demand in period 2 are taken from regular production in period 1 that is inventoried until period 2, at a cost of $23 per unit. We assign 300 units to that cell.
  • Continuing to the third period's demand of 1,600 units, we fully utilize the 1,300 units available from regular production in the same period and 200 units of overtime production. The remaining 100 units are produced with regular production in period 1 and held until period 3, at a cost of $26 per unit. As noted by the dashed line, period 1's regular production has reached its capacity and is no longer an alternative source of production.
  • Of the fourth period's demand of 3,000 units, 1,300 come from regular production, 200 from overtime, and 500 from subcontracting in the same period. 150 more units can be provided at a cost of $31 per unit from overtime production in period 2 and 500 from subcontracting in period 3. The next-lowest alternative is $34 from overtime in period 1 or subcontracting in period 2. At this point, we can make a judgment call as to whether our workers want overtime or whether it would be easier to subcontract out the entire amount. As shown in Table 11.2, we decide to use overtime to its full capacity of 100 units and fill the remaining demand of 250 from subcontracting.
  • The unused capacity column is filled in last. In period 2, 250 units of subcontracting capacity are available but unused. This information is valuable because it tells us the flexibility the company has to accept additional orders.

The optimum production plan, derived from the transportation tableau, is given in Table 11.3.5 The values in the production plan are taken from the transportation tableau one row at a time. For example, the 1,000 units of a regular production for period 1 is the sum of 600 + 300 + 100 from the second row of the transportation tableau. Ending inventory is calculated by summing beginning inventory and all forms of production for that period and then subtracting demand. For example, the ending inventory for period 1 is

The cost of the production plan can be determined directly from the transportation tableau by multiplying the units in each cell times the cost in the corner of the cell and summing them. Alternatively, the cost can be determined from the production plan by multiplying the total units produced in each production category or held in inventory by their respective costs and summing them, as follows:

Although linear programming models will yield an optimum solution to the aggregate planning problem, there are some limitations. The relationships among variables must be linear, the model is deterministic, and only one objective is allowed (usually minimizing cost).

THE COMPETITIVE EDGE
What-if? Planning at John Deere & Co.

The WaterLoo, Iowa, tractor works of John Deere & Co. employs 5,000 workers in a 7.5 million-square-foot facility. More than 60,000 parts are consumed daily in the production of farm tractors. Deere uses an interactive advanced planning system analysis to level demand and fine-tune labor requirements, evaluate inventory requirements for varying customer response times, and adjust its production plan when crises occur. Through what-if? analysis Deere has:

  • Found a cost-saving balance between overtime and inventory for a period of gradually increasing demand;
  • Reduced the lead time required to restock its dealers from 12 weeks to 5 weeks; and
  • Kept production going, while shipping priority items on time, during a labor strike at a parts supplier.
Source: Based on "System Helps Deere & Co. Weather Market Fluctuations," Industrial Engineering (June 1992): 16-17.


Other Quantitative Techniques

The linear decision rule (LDR) is an optimizing technique originally developed for aggregate planning in a paint factory. It solves a set of four quadratic equations that describe the major capacity-related costs in the factory: payroll costs, hiring and firing, overtime and undertime, and inventory costs. The results yield the optimal workforce level and production rate.

The search decision rule (SDR) is a pattern search algorithm that tries to find the minimum cost combination of various workforce levels and production rates. Any type of cost function can be used. The search is performed by computer and may involve the evaluation of thousands of possible solutions, but an optimum solution is not guaranteed. The management coefficients model uses regression analysis to improve the consistency of planning decisions. Techniques like SDR and management coefficients are often embedded in commercial decision support systems or expert systems for aggregate planning.


11-7. Identify several industries that have highly variable demand patterns. Explore how they adjust capacity.

11-8. Discuss the advantages and disadvantages of the following strategies for meeting demand:

  1. Use part-time workers.
  2. Subcontract work.
  3. Build up and deplete inventory.

*11-9. Read about the size of the contingency workforce at Manpower's web site. What special problems do temporary workers bring to the work environment? What problems to they alleviate?

*These exercises require a direct link to a specific Web site. Click Internet Exercises for the list of internet links for these exercises.


3 Students unfamiliar with linear programming are referred to the chapter supplement for review.

4 Be careful not to confuse the cell addresses on the Excel spreadsheet with the letter variables used in the LP model formulation as shown in Exhibit 11.6.

5 For this example, our initial solution to the aggregate production problem happens to be optimal. In other cases, it may be necessary to iterate to additional transportation tableaux before an optimum solution is reached. Students unfamiliar with the transportation method should review the supplement to Chapter 9.