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Operations Research Models and Methods
Computation Section
Subunit P & G Game
 - Description

P & G Production Control Simulation
by William Lesso

In the early 1960’s Procter & Gamble developed a strategy for scheduling the number of units of soap used for household laundry to be produced each week. In the P&G plant in Dallas, Texas, at that time, there were half dozen or so lines that packaged boxes of soap. Tide and Cheer were the main brands and these were packaged in various sizes all the way from small boxes purchased in Laundromats to the 2-pound size for large families.

These boxes were packed into cartons that were then loaded onto pallets, either for immediate shipment or temporary storage in warehouses. The plant serviced distributors in a 5 state area. The demand for full pallets of the various soaps and sizes varied considerably.

P&G did an extensive study of the demand and how to schedule production so as to not have too much inventory or experience too many shortages. Shortages were considered very costly since a householder in need of soap and not finding the P&G brand would select a competitor’s brand and might not switch back.

The results of this study were published as a series of Harvard Business School case studies. To train their production managers in the strategy developed, P&G developed a simulation model to illustrate the effects of the varying demand and how the P&G strategy worked. At that time, the simulation was done manually. A group of managers were brought together in a class and explained the problem as presented below. They were then given worksheets to record the decisions and a ‘simulated’ demand. At each step of the simulation, the moderator would call out the demand for that week – like a BINGO game. The players would record this and decide whether to change production level or not. At the end or the 52 weeks of simulation, each player would total up the costs to see how well he or she did. In the instructor’s manual accompanying the simulation was a statement to the effect, ‘Experienced managers were known to break down and cry when they saw how poorly they had done.’

The Situation


The simulation deals with a single production line producing a single product. The demand for the product averages 100 units per week with a standard deviation of 30 units per week. While any given customer may buy soap on a fairly regular schedule, not all have the same usage. To the company, the demand appears random with large weekly fluctuations. This is what makes the simulation exciting and at times frustrating.

The initial production level for the line is 70 units per week. In each week the production level may remain the same or be changed. The production level may be changed either up or down by between 5 and 10 units. There is a fixed cost of $2500 for any change representing administrative expense and the labor and materials required. There is a two-week lag before the change goes into effect. This represents the time required to implement the change. The lag complicates the situation because of the highly varying demand. In the two weeks before the change goes into effect, the demand could be radically more or less than the expected amount. This is analogous to trying to steer a ship in heavy seas and varying currents when there is lag between a steering command and its implementation.

The company has its own warehouse with a capacity of 240 units. Holding costs are $350 per unit per year or about $7 per week. Any extra inventory can be stored in public warehouse with no limit at $1000 per unit per year or about three times as much. This cost reflects the cost of moving a unit in and out of the public warehouse and the cost charged for using the warehouse. The initial inventory is set at 270 units so that there is little probability of shortage during the first two weeks of operation.

When the inventory is insufficient to satisfy demand there is a shortage. The cost of a shortage is $100 per unit per WEEK! We assume that shortages are backordered and filled with the first available production.

The simulation runs for 52 weeks. In weeks 26 and 27 production is shut down for maintenance of the line. Because demand continues during the shut down, the production plan must prepare for the shutdown.

The player is to specify the production change in each week of the planning period. The goal is to minimize the total cost of production changes, inventories and shortages.

The P & G Game


The manual simulation was computerized in the 1970’s in interactive BASIC and with the advent of microcomputers became a viable tool in teaching Production Scheduling and Inventory Control. More recently, it has been converted by Paul Jensen to Visual Basic for Applications and implemented for Microsoft Excel. We call the simulation the P&G Game.

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Operations Research Models and Methods
by Paul A. Jensen
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