Scheduling linear programming

Problem of approximation, 52 Product ensemble, 198 Production scheduling problem, 297 Profit maximization, 286 Programming, dynamic, 305 Programming, linear (see Linear programming)... 

The technique is useful where the problem is to decide the optimum utilisation of resources. Many oil companies use linear programming to determine the optimum schedule of products to be produced from the crude oils available. Algorithms have been developed for the efficient solution of linear programming problems and the SIMPLEX algorithm, Dantzig (1963), is the most commonly used. 

Both the mixing process and the approximation of the product profiles establish nonconvex nonlinearities. The inclusion of these nonlinearities in the model leads to a relatively precise determination of the product profiles but do not affect the feasibility of the production schedules. A linear representation of both equations will decrease the precision of the objective but it will also eliminate the nonlinearities yielding a mixed-integer linear programming model which is expected to be less expensive to solve. 

I. E. (1997) A mixed-integer linear programming model for shortterm scheduling of single-stage multiproduct batch plants with parallel lines. Ind. Eng. 

S. (2004a) Job-Shop Scheduling by Combining Reachability Analysis with Linear Programming. Proceedings of the IFAC... 

Linear programming Boiler/turbo generator system (11.4) Thermal cracker (14.1) >. i Planning and scheduling (16.1)... 

Reactor systems that can be described by a yield matrix are potential candidates for the application of linear programming. In these situations, each reactant is known to produce a certain distribution of products. When multiple reactants are employed, it is desirable to optimize the amounts of each reactant so that the products satisfy flow and demand constraints. Linear programming has become widely adopted in scheduling production in olefin units and catalytic crackers. In this example, we illustrate the use of linear programming to optimize the operation of a thermal cracker sketched in Figure E 14.1. 

Ku, H. M. and I. A. Karimi. Scheduling in Serial Multiproduct Batch Processes with Finite Interstate Storage A Mixed Integer Linear Program Formulation. Ind Eng Chem Res 27 10, 1840 (1988). 

Lee, H., Pinto, J.M., Grossmann, I.E., and Park, S. (1996) Mixed-integer linear programming model for refinery short-term scheduling of crude oil unloading with inventory management Industrial el Engineering Chemistry Research, 35, 1630. 

Linear programming is one of the most common optimization techniques applied. LPs are commonly used on production scheduling and resourcing problems. A linear program is a class of optimization problems where the objective function and constraints are linear. The objective function and constraints of a linear program are convex therefore, a local optimum is the global optimum. In addition, LPs demonstrate the characteristic wherein the optimum solutions of LPs lie on a constraint... 

The use of linear programming to optimize the flow of process streams through a petroleum refinery began in the mid-1950 s (Symonds, 1955 Manne, 1956). Now, almost twenty-five years later, it is safe to say that one half of U.S. refining capacity is represented by linear programming or LP models which are routinely optimized to schedule operations, evaluate feedstocks, and study new process configurations. 

The remainder of this paper is organized as follows. In Section 2, we formulate the planning problem as a mixed-integer linear program. In Section 3, we present our schedule-generation scheme for the scheduling problem. In Section 4, we report the results of an experimental performance analysis that is based on a sample production process presented in Maravelias and Grossmann (2004). 

Scheduling of refinery processes environmental impact. e-constraint method along with a MILP method Scheduling of refinery processes was modeled as a mixed-integer linear programming (MILP) model. Song et al. (2002)... 

In the experimental work discussed in this article only linear heating schedules have been employed and we shall therefore confine ourselves to the linear programming. The reciprocal heating schedule offers greater mathematical simplicity in some cases so that its use may sometimes be preferred. 

Many scheduling problems can be formulated as linear programs or other forms of mathematical programs. 

Scheduling problems that allow preemptions are often easier than problems that do not tillow preemptions. The problems that allow preemptions can often be solved in polynomial time. Consider, for example, the problem Pm prmp C. Job j may be processed on any one of the m machines it may be preempted and may continue its processing on another machine at another time. A schedule that minimizes the makespan can be obtained by first solving the following linear program (LP) ... 

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