One-dimensional cutting stock problems are traditionally formulated by using Mixed Integer Non-Linear Programming (MINLP). The nonlinearity is normally resolved by treating a complete list of cutting pattern vectors as known, leading to a **MILP** **model**. However, this approach can be computation- ally inefficient due to a large solution space. Many papers proposed different MIP models without pre-specified cutting patterns. For example, Johnston et al. [1] proposed an exact integer **model**. Kasimbeyli et al. [2] proposed a two-objective integer linear **model** related to the minimization of the total trim loss and the total number of different lengths of stock rolls in inventory. Schilling and Georgiadis [3] applied a MIP **model** to industrial cases with the objective of maximizing

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The **model** includes the most relevant issues of long term staff planning at public universities (since public universities are usually more flexible). Furthermore, the **model** gives optimal or near-optimal solutions in reasonable times and the quality of the solutions is good. The optimization **model** is a useful tool that permits to determine the optimum size and composition of the workforce in a long term horizon and has enough flexibility to give good solutions even if more constraints are added (e.g., allowing or not dismissals in KC or prioritizing or not internal promotions). Also, the optimization **model** permits to easily deﬁne various computational scenarios as a strategic planning tool, from which evaluate the impact of strategic policies before implementing them into the organization. The main applications of this planning tool are: to update the plan for workforce and the assessment of the impact that different strategies may have on the personnel costs and the structure of a university; i.e. the accomplishment of a preferable staff composition, adding/eliminating new courses or studies; increasing/reducing the number of students per group; changes in teaching capacity requirements; investment in training and research; changes in the proportion of people that can be promoted; allowing or not dismissals in non-tenure track staff; or prioritizing promotions over external hiring. The main conclusion of the paper is that personnel policies directly impact the economic optimization –and towards a preferable workforce composition– of the long term staff plan in universities. The development of adequate policies around personnel promotion can reduce the number of workers dismissed while proposing a transition towards a different preferable workforce structure based on the promotional ratios. The formalized procedure adopted in this paper (based on a **MILP** **model**) is adequate to address different aspects around the strategic staff plan.

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Due to the limitation of benchmark data of MMTSAL, five test problem of TSAL are used. Small size test problems, P12, P16 and P24 can be found in [4] and the large size test problem of P65 and P205 can be found in [3]. Number of tasks, number of station and number of **model** used are shown in Table 1. Since, the data for processing time in TSAL are only for one **model**, we added the processing time for mixed-**model** where the processing time is randomly generated between the values of 0 to 10. The data used in this paper need to be analyzed first in order to generate a new data set that satisfying the conditions in the **model**. All of these data are analyzed using C++ of MS Visual Studio 2017 before they can be used to solve the **MILP** **model**. Then, the **MILP** is solved using General Algebraic Modelling System (GAMS) with the solver CPLEX on PC Intel (R) Core (TM) i7-3770, 3.40 GHz processor and 8 GB memory.

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During the corresponding literature review, it was observed that **MILP** **model** was the most commonly used method among all mathematical programming techniques for the assessment of biomass supply chain. Still, unlike most researchers, Marufuzzaman and Ekşioğlu (2017), proposed the mixed integer non-linear programming **model** (MINLP) that eliminated the deadlock in biomass supply chain of lignocellulosic biomass due to seasonality by dynamic transportation routing and utilization of multi-mode facilities, while minimizing total cost. They solved a linear approach of their proposed **model** by using hybrid Benders-based rolling horizon algorithm. Rentizelas et al. (2009), developed a MINLP **model** that maximized the net present value (NPV) of the investment on bioenergy conversion systems for trigeneration (electricity, heating and cooling) that used agricultural waste as the raw material for biomass. They utilized genetic algorithm (GA) and quadratic programming (SQP) as their optimization methods. By using a simulation **model** for biomass supply chain, Zhang et al. (2012), developed a supply chain **model** by using Arena simulation software that determined potential plant locations based on GIS, and that took biomass raw material cost, energy consumption and greenhouse emissions into account. Windisch et al. (2013) predicted the time spent for each organizational and managerial activity regarding forest biomass supply chain of two different countries by using mutually exclusive event simulation. They utilized business process mapping methodology for the comparison of the business processes and shareholders that take place in each supply chain.

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A **MILP** **model** has been developed to solve this ceramic tactical production planning problem. The objective is to minimize the total cost (set-up and inventory) over the time periods of the planning horizon. Decisions will have to simultaneously deal with not only the allocation of product families to production lines and kilns with a limited capacity, but also with the determination of lot sizing and other decisions regard to set-up continuity modelling. For example those which allow to know the first and the last product family processed on each production line and kiln in a planning period, so that one changeover can be saved if the last one processed in t and the first one in t+1 are the same. Or those which allow processing the minimum lot size between two consecutive periods with no changeover. All of them are later explained.

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Keccak sponge function, in which the propagation of certain cube variables are controlled in the first few rounds if some conditions are satisfied. If the conditions involve the key information, such cube tester could be used to recover the key. Using conditional cube testers, key recovery attacks were obtained for various instances of Keccak-MAC and Keyak in [HWX + 17]. Later, the attacks on Keccak-MAC and Ketje attacks were improved with better con- ditional cubes found by an **MILP** **model** by Li et al. in [LBDW17]. Inspired by [LBDW17], Song et al. [SGSL17] provided a new **MILP** **model** for searching conditional cubes of Kec- cak that fully describes the first two rounds, and the application of the new **model** leads to a series of better attacks against KMAC [The16], Keyak , Ketje and Keccak -MAC.

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Future developments are lead to include new restrictions related with machine setups, route priorities in machines, and setup dependencies when performing carrying out a change over from one product to another. Moreover, it would be useful to include restrictions related with the materials requirement plan in order to sequence the final products, whose raw materials are available in the inventory. Finally, the proposed novel **MILP** **model** for multi-machine injection moulding sequencing will be implemented and validated in an enterprise, considering real data.

For the DP counterpart of an MDP, so without the uncertainty in transition of a system, we proposed an equivalent **MILP** **model** that can be solved exactly. For such models, no discretization is necessary in case of continuous state spaces as these are replaced by continuous decision variables. We explored how we could extend this equivalence to models where uncertainty is involved. This is not straightforward, since for this type of problems the standard **MILP** solution methods such as simplex and branch and bound do not work in general. We discussed a set of different approaches to MILPs with uncertainty in **model** parameters in Chapter 5. The majority of the models in literature, such as the expected value method, does not take risks associated with stochastic parameters into account, but simply ignores it.

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Cube attack on KMAC128 For KMAC128, the capacity is 256, which covers only four lanes. By placing the conditional cube variable at two bits in a column of a 4 , our **MILP** **model** could find large conditional cubes with 4 bit conditions which are least possible conditions. To make the attack clear, a toy cube of KMAC is introduced first, as shown in Table 6. This cube is selected from the CP-kernel and has dimension 16, and the conditional cube variable is placed at a[0][0][0], a[0][1][0]. The 4-bit conditions can be derived directly from the positions of the conditional cube variable since only the conditional cube variable contributes to bit conditions in this case. Note that, b = λ(a) and the relation between a[x][y][z] and b[x][y][z] is not expressed explicitly in the bit conditions. The remaining 15 ordinary cube variables can be extracted from A[x][y][z], 0 ≤ x, y < 5, 0 ≤ z < 64 which are represented as a 5 × 5 array of lanes and labeled as ‘Positions of cube variables’ in the table. In the remainder of the paper, the bit conditions are omitted if they come only from the conditional cube variable.

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This is called the H-Representation of a w × v S-box, in which α and β are constant. With the help of SageMath [1], hundreds of linear inequalities can be derived by the differential distribution table of a S-box. But the inequalities is redundant in general, for example, the number of inequalities of GIFT S- box given by SageMath is 237. Because the efficiency of the **MILP** optimizer is reduced radically when the amount of linear inequalities increase, adding all of the inequalities to the **MILP** **model** will make the **model** insolvable in practical time.

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Reza Ramezanian et al (8), have presented a paper on multi-period, multi-product and multi-machine systems with setup decisions. In this study, they developed a mixed integer linear programming (**MILP**) **model** for general two-phase aggregate production planning systems. Due to NP-hard class of APP, they implement a genetic algorithm and tabu search for solving this problem. The computational results show that these proposed algorithms obtain good quality solutions for APP and could be efficient for large scale problems.

In this paper we introduced a static vehicular fog framework considering the software matching problem in future intelligent transportation systems. The goal of this study is to minimize the power consumption through extending the processing to the network edge using the processing capabilities available in vehicles. We also investigate the software matching problem in VFog composed of vehicles in a parking lot. Optimizing the VFog through a **MILP** **model**, it was found that the total power consumption can be reduced by 27% when each vehicle has at least 4 software packages (out of a maximum of 10 software packages) installed compared to the situation when all tasks are processed by the central cloud. Meanwhile, the corresponding reduction in the central cloud workload is 44%. Future work includes considering different software packages popularities, different required processing power consumption for each software package, and the impact of processing delay for each loaded software.

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This section introduces the **MILP** **model** that has been devel- oped to minimize the power consumption due to both pro- cessing by virtual machines (hosting servers) and the traffic flow through the network. As mentioned in the previous section, the **MILP** **model** considers an optical-based archi- tecture with two types of VMs (BBUVM and CNVMs) that could be accommodated in ONU, OLT and/or IP over WDM as in Fig. 6. The maximum number of VM-hosting servers considered was 1, 5, and 20 in ONU, OLT, and IP over WDM nodes respectively, which is commensurate with the node size and its potential location and hence space limitations (together with the size of exemplar network considered in the **MILP**). All VM-hosting servers were considered as sleep- capable servers for the purpose of VM consolidation (bin packing).

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This paper examines the reduction in brown power consumption of transport networks and data centres achieved by caching Video-on-Demand (VoD) contents in solar-powered fog data centers with Energy Storage Devices (ESDs). A Mixed Integer Linear Programming (**MILP**) **model** was utilized to optimize the delivery from cloud or fog data centres. The results reveal that for brown-powered cloud and fog data centres with same Power Usage Effectiveness (PUE), a saving by up to 77% in transport network power consumption can be achieved by delivering VoD demands from fog data centres. With fully renewable-powered cloud data centres and partially solar-powered fog data centres, savings of up to 26% can be achieved when considering 250 m 2 solar cells.

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lateral trans-shipment and financial decisions in order to help an organization to decide economically whether establish a new agent. Consequently, a **MILP** **model** is proposed with the aim of maximizing net present income of the firm regarding purchasing income and its various costs. To solve the proposed **model** a new hybrid GA-PSO meta-heuristic algorithm is introduced. To demonstrate the usefulness of the proposed hybrid algorithm some randomly generated test problem was provided, the comparison between hybrid algorithm results and GAMS solutions indicated that the average gap is 2.88 percent and the hybrid gives totally reliable and good answers. The most notable upshot can be drawn out of the depicted result is that the proposed hybrid can be applied to real and big problems since GAMS cannot deal with such problems. Finally, a decision procedure with three phases is proposed to help an organization to find whether establishing a new agent has economic justification or not.

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Abstract: In this paper a new approach will be presented for solving one the complicated problems in power systems, known as the unit commitment. Indeed, in this paper, the proposed unit commitment is converted and formulated as the mixed-integer linear programming (**MILP**) **model** and solved by utilizing the Yalmip toolbox. Results demonstrates the high efficiency of the proposed method.

In this paper, we find Dinur et al.’s [11] cube-attack-like cryptanalysis technique could also be converted to and improved by a **MILP** **model**. In Dinur et al.’s attack, the key point is to select the public variables as the cube in such a way that the superpolys depend only on a (relatively) small number of key bits. In detail, at the first round of Keccak, the attacker finds a set of cube variables that are not multiplied with each other (we denoted it as linear-cube), meanwhile, these cube variables are not multiplied with some key bits. By taking advantage of the CP-kernel [2], Dinur et al. found 32/64-dimension linear-cube s that are not multiplied with 64 key bits in Keccak-MAC-128 (with capacity 256).

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1. Note that the ANF of the Modulo operation becomes more and more com- plicated with the increasing of modulus and directly using the ANF to con- struct **MILP** **model** is very hard, we consider an iterated expression of the Modulo operation. After introducing some auxiliary variables and allocating these variables according to the iterated expression, the Modulo **model** is con- structed by successively invoking Copy, AND, and XOR models. This linear inequality system can be absorbed into the original **MILP** **model** of bit-based division property to find integral distinguishers for some ARX-based block ciphers.

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A case study from Das et al. (12) is considered. An automotive cylinder head is to be manufactured. It has 12 Design features located on five different faces consisting of 38 machining operations in total. They are to be distributed amongst four machine groups. Twelve different types of cutting tools are required. The orientation change time matrix (in seconds) is presented in Table 2. The details of the operations are specified in Table 3. The tool change time is a random number in the range (1, 10). The value is zero for no change in cutting tool. As the complete data for tool change time is not available, new values are generated. The matrix for tool change time is included in Appendix D. The **MILP** **model** is coded using AMPL 27 and solved using CPLEX solver. The simulated annealing algorithm is coded and solved using C++ 28 in Microsoft Visual Studio Express. The test is conducted using an Intel i-3 processor @1.4 GHz with 4GB RAM.

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A more thorough integration among energy systems is expected to significantly contribute to reducing primary energy consumption, as well as global pollutant emissions and energy costs for final users. Integrated District Heating (DHN) networks and Combined Heat and Power (CHP) are of particular interest for the object of defining an efficient system for distributed energy generation and are widely discussed in Literature, i.e. in terms of role and opportunities in a country like Denmark [1] or United Kingdom [2], or considering a review of the different technology opportunities [3] and of the energy sources [4] also for Combined Heat, Cooling and Power systems (CHCP). The expected advantages of energy integration can, in fact, be obtained in real world applications only if the structure (synthesis) and the management of the whole system are carefully optimized. For instance, in [5] a computational framework is proposed to face the problem at city districts level, in [6] a Mixed Integer Linear Programming (**MILP**) **model** is used to determine the type, number and capacity of equipment in CHCP systems installed in a tertiary sector building, in [7] a modelling and optimization method is developed for planning and operating a CHP-DH system with a solar thermal plant and a thermal energy storage, in [8] a detailed optimization **model** is presented for planning the short-term operation of combined cooling, heat and power (CCHP) energy systems, for a single user in [9]an algorithm for the minimization of a suitable cost function is applied to optimize CHP commercial and domestic systems with variable heat demand.

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