We consider the planning and scheduling of production in a multitask/multistage batch manufacturing process typical of industries such as chemical manufacturing, food processing, and oil refining. We allow instances in which multiple sequences of tasks may be used to produce end products. We formulate the problem as a mixed-integer linear program and show that the linear programming relaxation ...

We consider the planning and scheduling of production in a multi-task/multi-stage batch manufacturing process typical of industries such as chemical manufacturing, food processing, and oil refining. We allow instances in which multiple sequences of tasks may be used to produce end products. We formulate the problem as a mixed integer linear program and show that the linear programming relaxatio...

this paper studies the multi-stage supply chain system (msscm) controlled by the kanban mechanism. in the kanban system, decision making is based on the number of kanbans as well as batch sizes. a kanban mechanism is employed to assist in linking different production processes in a supply chain system in order to implement the scope of just-in-time (jit) philosophy. for a msscm, a mixed-integer...

this paper addresses the mixed integer reliability redundancy allocation problems to determine simultaneous allocation of optimal reliability and redundancy level of components based on three objective goals. system engineering principles suggest that the best design is the design that maximizes the system operational effectiveness and at the same time minimizes the total cost of ownership (tco...

The lift-gas allocation problem with pressure-drop constraints and well-separator routing is a mixed-integer nonlinear program considerably hard to solve. To this end, a mixed-integer linear programming formulation was developed by multidimensional piecewiselinearization of pressure drop functions using standard (CC) and logarithmic (Log) aggregated models. These models were compared by means o...

In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer formulation, we derive its linear counterparts and show that they could be stronger than existing linear formulations. We also develop a variant of Jensen’s inequa...

To mitigate the effects of a corrosive operating environment, the Coast Guard has planned an extensive preventative maintenance program for its Sikorsky HH60J helicopters based on helicopter flight time. We construct a mixed integer linear program that schedules the weeks during which each helicopter undergoes maintenance, as well as the weeks during which a helicopter conducts operations eithe...

We survey the techniques used for presolving Mixed-integer linear programs (MILPs). Presolving is an important component of all modern MILP solvers. It is used for simplifying a given instance, for detecting any obvious problems or errors, and for identifying structures and characteristics that are useful for solving an instance.

Suppose that we have a linear program max{cx : Ax ≤ b, x ≥ 0} (P) where A is an m × n matrix, c an n-dimensional row vector, b an m-dimensional column vector, and x an n-dimensional column vector of variables. Now, we add in the restriction that some of the variables in (P) must take integer values. If some but not all variables are integer, we have a Mixed Integer Program (MIP), written as max...