Goal ProgrammingApplications for ServicesReferences:‘Operations Research’byWinston‘Operations Research Models And Methods’byPaul A. JensenAndJonathanF. Bard
Introduction•Many service operations management decisions involve trying to make the most effective use of an organization's resources. •Resources typically include •labor, •money, •storage space/capacity, or •materials. •These resources may be used to produce services such as •schedules for shipping and production, •advertising policies, •investment decisions, or •hospital meal plans.•Linear programming (LP) and Goal programming (GP)are widely used mathematical techniques designed to help operations managers in planning and decision making relative to the tradeoffs necessary to allocate resources.
Overview of Linear ProgrammingAll LP problems have four properties in common.1.All problems seek to maximize or minimizesome quantity.2.The presence of restrictions, or constraints, limits the degree to which we can pursue our objective. 3.There must be alternative coursesof action to choose from. 4.The objective and constraints in linear programming problems must be expressed in terms of linearequations or inequalities.
Applications of Linear Programming•Ingredient Blending Applications: The diet problem•Shift Scheduling Problem•Workforce Planning Problem•Transportation Problem•Employee Scheduling Applications: An Assignment Problem•Labor Planning•Marketing Applications: Media Selection•…
Goal Programming•Linear programming models allow for only one objective, and all constraints must be met absolutely. •In real life, virtually all problems have several objectives in different units of measure. This makes construction of a consolidated single objective difficult. •For example, an emergency ambulance system could have the following objectives:1.Maintain an average response time of approximately 4 minutes.2.Ensure that 90 percent of all calls receive aid in less than 10 minutes.3.Try not to exceed a budget of $100,000 per year.4.Allocate calls to ambulance crews in an equitable manner.
Goal Programming•is a variation of LP that permits multiple and conflicting goals with different dimensions. •Multiple goals are rank-orderedand treated as preemptive priorities. •The solution approach:•higher-ranked goals are not sacrificed to achieve lower-ranked goals. •is equivalent to solving a series of nested LP problems in which higher-ranked goals become constraints on lower-ranked goals.•While LP optimizes a single objective, goal programming minimizes deviations from goals. •This solution approach is known as satisfying, because not all goals necessarily will be met. Instead, the goals will be achieved as closely as possible.
Goal ProgrammingGoal TypesThree possible types of goals:1.