Combined MILP-constraint programming approach for the optimal scheduling of multistage batch processes

Supply chain network design and operation: Systematic decision-making for centralized, distributed, and mobile biofuel production using mixed integer linear programming (MILP) under uncertainty

For many emerging mobile broadband services and applications, the source and destination are located in the same local region. Consequently, it is very important to design access networks to facilitate efficient local data exchange. In the past few years, most existing studies focus on either the wired or wireless domains. In this paper, we aim to exploit both the wired and wireless domains. Specifically, we consider a fiber-wireless access network in which a passive optical network (PON), consisting of one optical line terminal and multiple optical network units (ONUs), connects densely deployed base stations. In such a scenario, we propose two novel access schemes to utilize both network coding and device association in the following two cases: each device can be associated with one ONU for uploading and downloading its data packets; and each device can be associated with two different ONUs for uploading and downloading its data packets, which are referred to as, the network coding design and symmetric device association (NCsDA) problem and the network coding design and asymmetric device association (NCaDA) problem, respectively. To understand the potentials of NCsDA, we first formulate a mixed integer nonlinear programming to minimize the weighted number of packet transmissions (WNT), which is related to both the energy consumption and system capacity. We then theoretically analyze the tight upper bounds of the minimal WNT in the PON, which helps us to approximate the NCsDA problem by mixed integer linear programming . We also give theoretical analysis on the NCaDA problem and formulate it as a mixed integer linear programming. Next, we develop efficient algorithms based on linear programming relaxation and give network coding designs to solve the NCsDA problem and the NCaDA problem. To validate our design, we conduct extensive simulations, which demonstrate the impact of important network parameters and the promising potentials of the proposed NCsDA and NCaDA schemes.

BackgroundFlux Balance Analysis (FBA) is a genome-scale computational technique for modeling the steady-state fluxes of an organism’s reaction network. When the organism’s reaction network needs to be completed to obtain growth using FBA, without relying on the genome, the completion process is called reaction gap-filling. Currently, computational techniques used to gap-fill a reaction network compute the minimum set of reactions using Mixed-Integer Linear Programming (MILP). Depending on the number of candidate reactions used to complete the model, MILP can be computationally demanding.ResultsWe present a computational technique, called FastGapFilling, that efficiently completes a reaction network by using only Linear Programming, not MILP. FastGapFilling creates a linear program with all candidate reactions, an objective function based on their weighted fluxes, and a variable weight on the biomass reaction: no integer variable is used. A binary search is performed by modifying the weight applied to the flux of the biomass reaction, and solving each corresponding linear program, to try reducing the number of candidate reactions to add to the network to generate a working model. We show that this method has proved effective on a series of incomplete E. coli and yeast models with, in some cases, a three orders of magnitude execution speedup compared with MILP. We have implemented FastGapFilling in MetaFlux as part of Pathway Tools (version 17.5), which is freely available to academic users, and for a fee to commercial users. Download from: biocyc.org/download.shtml.ConclusionsThe computational technique presented is very efficient allowing interactive completion of reaction networks of FBA models. Computational techniques based on MILP cannot offer such fast and interactive completion.

A computational comparison of cargo prioritization and terminal allocation problem models

This work presents an approach for scheduling of operational activities in a large real-world pipeline network, where oil derivatives and ethanol are transported and distributed among refineries, terminals, depots, and final clients. The hierarchical decomposition approaches to solve the pipeline-scheduling problem presented by Boschetto et al. [Ind. Eng. Chem. Res. 2010, 49, 5661] and Magatao et al. [Ind. Eng. Chem. Res. 2012, 51, 4591], which are based on the integration of mixed integer linear programming (MILP) models and a set of heuristic modules, are merged and compounding blocks are also improved. Thus, a novel decomposition approach for scheduling product distribution through a pipeline network is proposed. In addition, this work presents a new MILP approach for the last hierarchical level: the timing block (timing model). This paper expands and improves the former MILP model, which was the timing block core. A series of operational constraints were considered within a continuous time representat...

Faster integer-feasibility in mixed-integer linear programs by branching to force change

As several mixed-integer linear programming (MILP) optimization models have been developed in the past few years for design, planning, and scheduling of chemical processes, questions arise about their sensitivity to uncertainties in the problem data and modeling assumptions. We present a study of the effects of time horizon discretization and inaccurate data on the quality of the MILP solution. The results provide information on how detailed discretizations and how accurate forecasts are required in order to obtain good-quality solutions with the MILP model. The studies indicate that the LP relaxation gap of the MILP reduces as the number of time periods of the planning model is increased. Another interesting finding is that, for all the problems solved, uncertainty in prices and demands does not seem to have any major impact on the quality of the solution of the MILP model as long as plan revision is allowed through adjustment of production levels and amounts of purchases and sales. We also develop an efficient solution method for the planning problem and demonstrate its superiority to a popular MILP package

Optimal scheduling of cyclic batch processes for heat integration—I. Basic formulation

This article presents a planning problem in a distribution network incorporating two levels of inventory management. Perishable products are routed with lot-sizing, multi-sourcing and limited transport capacity using a homogeneous fleet of vehicles. A mixed integer linear programming (MILP) and a greedy heuristic have been developed to solve this real planning problem. There are some instances for which the solver cannot give a good lower bound within the limited time and for other instances it takes a lot of time to solve MILP. The greedy heuristic is an alternative to the mixed integer linear program, used to quickly solve some large instances taking into account original and difficult constraints. For some instances the gap between the solution provided by the solver (MILP) and the heuristic becomes quite significant. An iterated local search (ILS) using the variable neighborhood descent (VND) method has been implemented to improve the quality of heuristic solutions. We have included the ILS method in an APS (Advanced Planning System) and have compared it with an exact resolution of the MILP. Two types of instances are tested: models derived from actual data and models built using a random generator of instances that have wider diversity for computational evaluation. The ILS procedure significantly improves the quality of solutions and average computational time is much shorter than MILP resolution.

Distribution systems (DS) are a focal connection point for existing and new renewable energy sources. DS have increasing sizes; they connect increasing numbers of renewable energy sources and have a mandate to operate as financial entities seeking to maximize their profits in an electricity market. To achieve these goals, DS require highly efficient planning tools. In this paper, we propose a successive fuzzy mixed integer linear programming (MILP) method for optimally placing and sizing capacitors in a DS that explicitly models induction run wind electric generators (WEGs). The optimization problem is linearized, transformed into a fuzzy MILP model and is solved successively while updating the solution vector. The fuzzy MILP method employs fuzzy models of voltage constraints that are often violated in a planned system that lacks reactive power support. The use of fuzzy constraints makes the proposed solution method very robust by avoiding infeasibility and reducing the need for user expertise. Further, the fuzzy MILP method represents the dual objectives of capacitor cost and annual energy loss minimization as fuzzy sets with individual satisfaction functions. The method maximizes the minimum of these satisfaction functions during optimization. Tests on 69-bus and 2002-bus DS show that the method performs well and is robust.

Draw management is a critical part of the successful recovery of mineral reserves by cave mining. This thesis presents a draw control model that indirectly increases resource value by controlling production based on geotechnical constraints. The mixed integer linear programming (MILP) model is formulated as a goal programming model that includes seven general constraint types. These constraints model the mining system and drive the operation towards the dual strategic targets of total monthly production tonnage and cave shape. This approach increases value by ensuring that reserves are not lost due to poor draw practice. The model also allows any number of processing plants to feed from multiple sources (caves, stockpiles, and dumps). The ability to blend material allows the model to be included in strategic level studies that target corporate objectives while emphasising production control within each cave. There are three main production control constraints in the MILP. The first of these, the draw maturity rules, is designed to balance drawpoint production with cave propagation rates. The maturity rules are modelled using disjunctive constraints. The constraint regulates production based on drawpoint depletion. Drawpoint production increases from 100 mm/d to 404 mm/d once the drawpoint reaches 6.5% depletion. Draw can continue at this maximum rate until drawpoint ramp-down begins as 93.5% depletion. The maximum draw rate decreases to 100 mm/d at drawpoint closure in the three maturity rule systems included in the thesis. The maturity rule constraints combine with the minimum draw rate constraint to limit production based on the difference between the actual and ideal drawpoint depletion. Drawpoints which lag behind their ideal depletion are restricted by the maturity rules while those that exceeded the ideal depletion were forced to mine at their minimum rate to ensure that cave porosity was maintained. The third production control constraint, relative draw rate (RDR), prohibits isolated draw by ensuring that extraction is uniform across the cave. It does this by controlling the relative draw difference between adjacent drawpoints. It is apparent in this thesis that production from a drawpoint can have an indirect effect on remote drawpoints because the relative draw rate constraints pass from one neighbour to the next within the cave. Tightening the RDR constraint increases production variation during cave ramp-up. This variation occurs because the maturity rules dictate that new drawpoints must produce at a lower draw rate than mature drawpoints. As a result, newly opened drawpoints limit production from the mature drawpoints within their region of the cave (not just their immediate neighbours). The MILP is also used to quantify production changes caused by varying geotechnical constraints, limiting haulage capacity, and reversing mining direction. It has been shown that tightening the RDR constraint decreases total cave production. The ramp-up duration also increased by eighteen months compared to the control RDR scenario. Tighter relative draw also made it difficult to maintain cave shape during ramp-up. However, once ramp-up was complete, the tighter control produced a better depletion surface. The trial with limited haulage capacity identified bottlenecks in the materials handling system. The main bottlenecks occur in the production drives with the greatest tonnage associated with their drawpoints. There also appears to be an average haulage capacity threshold for the extraction drives of 2000 tonnes per drawpoint. Only one drive with a capacity below this threshold achieves its target production in each period. Reversing the cave advance to initiate in the South-East shows the greatest potential for achieving total production and cave shape targets. The greater number of drawpoints available early in the schedule provides more production capacity. This ability to distribute production over a greater number of drawpoints reduces the total production lag during ramp-up. In addition to its role in feasibility studies, the MILP is well suited for use as a production guidance tool. It has been shown in three case studies that the model can be used to evaluate production performance and to establish long term production targets. The first of the studies shows the analysis of historical production data by comparison to the MILP optimised schedule. The second shows that the model produces an optimised production plan irrespective of the current cave state. The final case study emulates the draw control cycle used by the Premier Diamond Mine. The series of optimised production schedules mirror that of the life-of-mine schedule generated at the start of the iterative process. The results illustrate how the MILP can be used by a draw control engineer to analyse production data and to develop long term production targets both before and after a cave is brought into full production.

The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered in this paper have the characteristic that only a subset of the binary variables have non-zero objective function coefficients if modeled as an MILP. This class of problems is formulated as a hybrid MILP/CP model that involves some of the MILP constraints, a reduced set of the CP constraints, and equivalence relations between the MILP and the CP variables. An MILP/CP based decomposition method and an LP/CP-based branch-and-bound algorithm are proposed to solve these hybrid models. Both these algorithms rely on the same relaxed MILP and feasibility CP problems. An application example is considered in which the least-cost schedule has to be derived for processing a set of orders with release and due dates using a set of dissimilar parallel machines. It is shown that this problem can be modeled as an MILP, a CP, a combined MILP-CP OPL model (Van Hentenryck 1999), and a hybrid MILP/CP model. The computational performance of these models for several sets shows that the hybrid MILP/CP model can achieve two to three orders of magnitude reduction in CPU time.

Two new continuous-time MILP (Mixed Integer Linear Programming) models are developed for resource constrained project scheduling problems in which activities can be conducted in different (multi) modes. There are efficient and flexible MILP models for this problem in which time is represented by a number of discrete time intervals. However, they require to use large numbers of binary variables as the number of activities increases and time horizon stretches. Hence efforts have been made to formulate MILP models based on continuous-time representation and therefore to speed up the solution process. We propose two novel MILP models based on the event and resource flow concepts. The models are verified by solving benchmark problems in the literature.

Purpose – This paper aims to address the problem of optimal allocation of demand of items among candidate suppliers to maximize the purchase value of items. The purchase value of the items directly relates to cost and quality of raw materials purchased from the supplier. In an increasingly competitive environment, firms are paying more attention to selecting the right suppliers for procurement of raw materials and component parts for their products. The present research work focuses on this issue of supply chain management. Design/methodology/approach – This present research work devises a hybrid algorithm for multi-period demand allocation among the suppliers. The customer demand is allocated by using a hybrid algorithm based on the technique for order preference by similarity to ideal solution (TOPSIS), fuzzy set theory and the mixed linear integer programming (MILP) approaches. Findings – The supply chain network is witnessing a changing business environment due to government policies aimed at promoting new small manufacturing enterprises (small and medium-sized enterprises) for intermediate parts and components. Hence, the managers have an option to select a new group of suppliers and allocate the optimal multi-period demand among the new group of suppliers to maximize their purchase value. In this context, the proposed hybrid model would be beneficial for the managers to operate their supply chain effectively and efficiently. The present research work will be helpful for the managers who are interested to reconfigure their supply chain under the failure of any supply chain partner or in a changing business environment. The model provides flexibility to the managers for evaluation of the different available alternatives to take a decision of optimal demand allocation among the suppliers. The proposed hybrid (fuzzy, TOPSIS and MILP) model provides more objective information for supplier evaluation and demand allocation among suppliers in a supply chain. The managers can use the proposed model to the analysis of other management decision-making problems. Originality/value – This present research work devises a hybrid algorithm for multi-period demand allocation among the suppliers. This hybrid algorithm prioritizes the suppliers and then allocates the multi-period demand among the suppliers. The customer demand is allocated by using a hybrid algorithm based on the technique for order preference by similarity to ideal solution (TOPSIS), fuzzy set theory and the mixed linear integer programming (MILP) approaches.

Power gating is a very effective technique to reduce the subthreshold leakage by using sleep transistors to turn off the functional blocks or cells when they are not used. When the sleep transistors are turned on, the power grid may experience a huge current surge which may violate the integrity of the power grid. This paper addresses this problem by formulating the wakeup scheduling of sleep transistors as an exact mixed integer linear program (MILP). Since the resulting MILP is hard, we propose a very efficient yet near optimal algorithm by successively relaxing the MILP to a sequence of linear program (LP) problems. The results obtained on the ISCAS benchmarks indicate that our proposed algorithm obtains a near optimal solution with a speedup of 15× on average compared to the MILP. The proposed algorithm has a runtime complexity which is linear in practice.