Professor Guillermo Gallego
9 October 2001
Aggregate Production Planning
Aggregate production planning is concerned with the determination of production, inventory, and work force levels to meet ﬂuctuating demand requirements over a planning horizon that ranges from six months to one year. Typically the planning horizon incorporate the next seasonal peak in demand. The planning horizon is often divided into periods. For example, a one year planning horizon may be composed of six one-month periods plus two three-month periods. Normally, the physical resources of the ﬁrm are assumed to be ﬁxed during the planning horizon of interest and the planning eﬀort is oriented toward the best utilization of those resources, given the external demand requirements.
Since it is usually impossible to consider every ﬁne detail associated with the production process while maintaining such a long planning horizon, it is mandatory to aggregate the information being processed. The aggregate production approach is predicated on the existence of an aggregate unit of production, such as the “average” item, or in terms of weight, volume, production time, or dollar value. Plans are then based on aggregate demand for one or more aggregate items. Once the aggregate production plan is generated, constraints are imposed on the detailed production scheduling process which decides the speciﬁc quantities to be produced of each individual item. The plan must take into account the various ways a ﬁrm can cope with demand ﬂuctuations as well as the cost associated with them. Typically a ﬁrm can cope with demand ﬂuctuations by: (a) Changing the size of the work force by hiring and ﬁring, thus allowing changes in the production rate. Excessive use of hiring and ﬁring may limited by union regulations and may create severe labor problems.
(b) Varying the production rate by introducing overtime and/or idle time or outside subcontracting. (c) Accumulating seasonal inventories. The tradeoﬀ between the cost incurred in changing production rates and holding seasonal inventories is the basic question to be resolved in most practical situations.
(d) Planning backorders.
These ways of absorbing demand ﬂuctuations can be combined to create a large number of alternative production planning options.
Costs relevant to aggregate production planning:
(a) Basic production costs: material costs, direct labor costs, and overhead costs. It is customary to divide these costs into variable and ﬁxed costs.
(b) Costs associated with changes in the production rate: costs involved in hiring, training, and laying oﬀ personnel, as well as overtime compensations.
(c) Inventory related costs.
Aggregate production planning models may be valuable as decision support systems and to evaluate proposals in union negotiations. Here we limit our study to linear cost models and to a brief discussion of models with quadratic costs. . Before presenting a model based on linear programming we will discuss two extreme aggregate production plans: The just-in-time production plan and the production-smoothing plan.
IEOR 4000: Production Management
Professor Guillermo Gallego
– The Just-in-time production plan, also known as the chase plan, consists in changing the production rate to exactly satisfy demand. The idea is consistent with the JIT production philosophy and results in low holding costs but may result in high cost of adjusting the production rate, i.e., high ﬁring and hiring costs or high idle times. As a consequence, the just-in-time plan is best suited to situations where the cost of changing the production rate is relatively inexpensive.
– The production-smoothing plan, also known as the stable plan, consists in keeping the production rate constant over time. This strategy minimizes the production cost when production costs are convex. A stable, make to stock, production strategy needs to build inventories to...