Avaneesh Gupta

A novel MILP formulation for short-term scheduling of multi-stage multi-product batch plants with sequence-dependent constraints

Abstract This paper presents a continuous-time mixed-integer linear programming (MILP) model for short-term scheduling of multi-stage multi-product batch plants. The model determines the optimal sequencing and the allocation of customer orders to non-identical processing units by minimizing the earliness and tardiness of order completion. This is a highly combinatorial problem, especially when sequence-dependent relations are considered such as the setup time between consecutive orders. A common approach to this scheduling problem relies on the application of tetra-index binary variables, i.e. (order, order, stage, unit) to represent all the combinations of order sequences and assignments to units in the various stages. This generates a huge number of binary variables and, as a consequence, much time is required for solutions. This paper proposes a novel formulation that replaces the tetra-index binary variables by one set of tri-index binary variables (order, order, stage) without losing the models generality. By the elimination of the unit index, the new formulation requires considerably fewer binary variables, thus significantly shortening the solution time.

A novel MILP formulation for short-term scheduling of multistage multi-product batch plants

Abstract This study presents a continuous-time mixed-integer linear programming model for short-term scheduling of multistage multi-product batch plants. The model determines the optimal sequencing and the allocation of customer orders to non-identical processing units by minimizing the earliness and tardiness of order completion. This is a highly combinatorial problem, especially when sequence-dependent relations considered to be are such as the setup time between consecutive orders. A common approach to this scheduling problem relies on the application of tetra-index binary variables, i.e. (order, order, stage unit) to represent all the combinations of order sequences and assignments to units in the various stages. This generates a huge number of binary variables and, as a consequence, much time is required for solutions. This study proposes a novel formulation that replaces the tetra-index binary variables by one set of tri-index binary variables (order, order, stage) without losing the models generality. By the elimination of the unit index, the new formulation requires considerably fewer binary variables, thus significantly shortening the solution time.

A Bi-index continuous time MILP model for short-term scheduling of single-stage multi-product batch plants with parallel units

Abstract This paper presents a mixed integer linear programming formulation for the short-term scheduling of single-stage multi-product batch plants with parallel non-identical production units. This scheduling problem is highly combinatorial in nature especially because of the sequence-dependent changeover constraints. To formulate this type of problem, tri-index discrete decision variables, i.e. (order, order, unit), are commonly applied to represent the order assignments. This approach requires a large number of discrete decision variables that consequently make the model very time consuming to solve. To overcome this problem, the proposed formulation instead applies bi-index discrete variables (order, order). This greatly reduces the overall number of discrete decision variables while still keeping the generality of the model. For handling large-scale problems, pre-ordering heuristics were imposed to further reduce the solution time. Examples with various numbers of units and orders illustrate the effectiveness of the formulation both with and without the pre-ordering constraints.

An approach of capability representation for improving capacity planning

With the growing interest in dealing with the volatile demand fluctuations, there is a renewed interest to enhance responsiveness in capacity planning and, in particular, to address the dynamic changes in product mix. However, with traditional MRP-II and ERP systems, capacity planning assumes that all machines in the work system are either the same or completely different. Similarities among products and resources (such as production equipment) are not a part of the consideration. As a result, inherent flexibility of the system is lost in the planning process. In this paper, we propose a new representation for the capability by characterizing critical capability drivers and their range. With a more refined representation, overlapping and non-overlapping capability regions can be identified, and their inter-relationships with respect to capacity can then be applied for improving the match between the capacity and production orders. Thus, better planning and capacity utilization can be achieved. An example is presented to demonstrate the proposed approach and to compare it with traditional MRP-II planning.

A Linear Programming Model for Workstation Adequacy

Workstation design can have a profound effect on an individuals health. Most product designs are based on a 5th percentile “reach” and a 95th percentile “clearance”. These designs quite often fail to match a persons body measurements since the dimensions of each body link are not exactly the same xth percentile. Even with an adjustable workstation, the user has a dilemma as to what adjustment to make for each adjustable parameter as each adjustment depends on the previous adjustment and the potential number of adjustments is somewhat infinite. This paper focuses on a methodology to achieve a postural fit for a given workstation with an adjustable table, chair, and footrest. The least stressful and somewhat comfortable postures were first determined from the literature. Thereafter, a Linear Programming model was developed to capture these mappings as mathematical constraints and solved. The model was validated with an adjustable workstation and a few participants.