The **MILP** **model** in Section III-B is used to solved industrial cases whose specifications of master rolls shown in Table III. The width of master roll is 96 inches and the length is 525,000 inches. Due to longitudinal trim loss, the company does not allow to use any patterns with the width lower than 89 inches. All cutting patterns generated from the heuristics already consider this requirement. Due to set up loss, the company does not allow to cut any patterns that are shorter than 10,000 inches in length. Additionally, the set up loss of 3,500 inches occurs once we start a new cutting pattern.

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.

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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an objective function under certain constraints. Mixed-integer Linear Program- ming (**MILP**) is the most widely studied technique to solve these optimization problems. One of the most successful applications of **MILP** is to search for d- ifferential and linear trails. Mouha et al. first applied **MILP** method to count active S-boxes of word-based block ciphers [12]. Then, at Asiacrypt 2014, Sun et al. extended this technique to search for differential and linear trails [20], whose main idea is to derive some linear inequalities through the H-Representation of the convex hull of all differential patterns and linear bias of S-box. Xiang et al. [21] introduced a **MILP** **model** to search for integral distinguisher, Sasaki et al. [16] and Cui et al. [7] gave the **MILP**-based impossible differential search mod- el independently. There are many **MILP**-based tools proposed already, such as **MILP**-based differential/linear search **model** for ARX ciphers [8], **MILP**-based conditional cube attacks [11] on Keccak [4], etc.

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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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Abstract Cube-attack-like cryptanalysis was proposed by Dinur et al. at EUROCRYPT 2015, which recovers the key of Keccak keyed modes in a divide-and-conquer manner. In their attack, one selects cube variables manually, which leads to more key bits involved in the key-recovery attack, so the complexity is too high unnecessarily. In this paper, we introduce a new **MILP** **model** and make the cube attacks better on the Keccak keyed modes. Using this new **MILP** tool, we find the optimal cube variables for Keccak-MAC, Keyak and Ketje, which makes that a minimum number of key bits are involved in the key-recovery attack. For example, when the capacity is 256, we find a new 32-dimension cube for Keccak-MAC that involves only 18 key bits instead of Dinur et al.’s 64 bits and the complexity of the 6-round attack is reduced to 2 42 from 2 66 . More impressively, using this new tool, we give the very first 7-round key-recovery attack

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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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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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We enjoy the **MILP** **model** to investigate the differential effect of these ciphers and provide a more accurate estimation for the differential proba- bility, as well. Our observations show that despite HIGHT, LEA exhibits a strong differential effect. The details of differential effects are reflected in a more compact manner using the newly defined notion of probability polynomial. The results gained by this method improve or extend the previous results as follows. For LEA block cipher, we found more effi- cient 12 and 13-round differentials whose probabilities are better than the best previous 12 and 13-round differentials for a factor of about 2 6

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With the aim of providing companies with practical tools for assigning orders to suppliers, in this paper we propose and test two **MILP** models to solve the problem of assigning orders to suppliers in the case of several manufacturing plants, any finite number of linear pieces of the concave increasing cost function, lower bounds for the orders for each manufacturer and finite capacity of each supplier. We include the possibility that each manufacturing plant receives a number of units greater than its demand for the period, since this may be unavoidable because of the existence of lower bounds on the order sizes. Compared with specific algorithms, whether they are heuristic or exact (such as that proposed in Yenipazarli et al., 2016), the use of a **MILP** **model**, with a modelling language and a solver (as CPLEX), allows avoiding programming tasks, thus having a very brief time to prepare the tool, and provides exact optimal solutions. Moreover, if additional constraints have to be fulfilled, as often happens in practice, they can easily be incorporated into the models, as it is shown in Section 3. Of course, as the main potential disadvantage of using mathematical programming instead of heuristic approaches is the possibility of computational time be prohibitive, appropriate experiments should be performed in order to guarantee that the time required to obtain optimal solutions in industrial settings is short enough.

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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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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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Along with the development of Internet of Things (IoT) and the rise of fog computing, more new joint technologies have been proposed. Vehicular Ad-hoc Networks (VANET) are one of the emergent technologies that come with a very promising role, where the spare processing capabilities of vehicles can be exploited. In this paper, we propose a fog architecture to provide services for end users based on a cluster of static vehicles in a parking lot referred to as a vehicular fog. The proposed vehicular fog architecture is connected to the central data center through an optical infrastructure. As the processing requests from users require specific software packages that may not be available in all vehicles, we study the software matching problem of task assignments in vehicular fog. The goal of this paper is to examine the effect of software packages variety in vehicles on the assignment decision and the overall power consumption. A mixed integer linear programming (**MILP**) **model** was utilized to optimize the power consumption of the overall architecture, considering different numbers of software packages in the vehicular fog. The results reveal a power saving of up to 27% when vehicles are uploaded with four or more different software packages out of a library of ten software packages in this example.

In determining specialist availability, each full-time doc- tor was counted as one doctor and each part-time doctor was counted as 0.5 doctors. Of all doctors included in the **model**, only doctors with physician engagement ≥ 70% were chosen. The objective function in Equation 1 is to minimize the travel expenses of all medical specialist allocation. Equation 2 represents the supply constraints, requiring the total number of medical specialists allocated to all needed sites to not be higher than that available at supplying hos- pital g. Equation 3 shows the demand constraints, requiring the total number of medical specialists from all supplying hospitals to be at least equal to that requested by hospital h. Equation 4 calculates the number of selected doctors from supplying hospital g who will be assigned to help hospital h. Finally, Equation 5 requires that each doctor’s skill or capability to treat difficult patients, represented by the CMI of each medical specialist, must be higher than the CMI of the needed hospital.

Table 5 provides the confusion matrix for the **MILP** (without external equivalence information) for comparison. Although the middle column still shows that the **MILP** predicts more ties than humans annotators, we find that a clear majority of all unique pairs are now correctly placed along the diagonal. This confirms that our **MILP** successfully infers new ordering decisions, although it uses the same input (corpus evidence) as the baseline. The remaining ties are mostly just the result of pairs for which there simply is no evidence at all in the input Web counts. Note that this problem could for instance be circum- vented by relying on a crowdsourcing approach: A few dispersed tie-breakers are enough to allow our **MILP** to correct many other predictions.

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Impossible differential attack is one of powerful methods for analyzing block ciphers. When designing block ciphers, it must be safe for impossible differential attacks. In case of impossible differential attack, the attack starts from finding the impossible differential characteristic. However, in the case of the ARX-based block cipher, these analyzes were difficult due to the addition of modulus. In this paper, we introduce 157 new six-round impossible differential characteristics of ARX-basef block cipher, SPECK64, using Mixed Integer Linear Programming (**MILP**) base impossible differential characteristic search proposed by Cui [3] etc.

network, and finally integrated forward/reverse logistics network [1]. A comprehensive review of reverse and integrated logistics can be found in (Fleischmann [2]; Pokharel and Mutha [6]; Govindan [8]). In this paper, we survey specific network design problems for reverse and integrated logistics network design problems. Some authors like Üster et al. [10], Amiri [11], Patia et al. [12], and Aras et al. [13] are those ones, who carried out investigations about the integrated logistics. Keyvanshokooh [1] presented a mixed-integer linear programming to consider dynamic pricing approach for used products, forward/reverse logistics network configuration and inventory. Kamali et al. [14] proposed a single product, multi-echelon, multi-period closed loop supply chain for high-tech products (which have continuous price decrease). Four heuristics-based methods including genetic algorithm (GA), particle swarm optimization (PSO), differential evolution (DE), and artificial bee colony (ABC) are proposed for solving their **model**. Sahraeian et al. [15] introduced a supply chain network design problem which contains environmental concerns in arcs and nodes of network and there are some routes such as road, rail and etc. in each pair of nodes. Demand uncertainty and uncertainty

We assume that the throughput (data rate) that can be achieved between a regular node and a mobile backbone node is a monotonically non increasing function of both the distance between the two nodes and the number of other regular nodes that are also communicating with that particular mobile backbone node and thus causing interference. While our results are valid for any throughput function that is monotonically non increasing in both distance and cluster size, it is useful to gain intuition by considering a particular example. Building upon this continuous throughput **model**, we develop the mobile backbone network optimization problem as follows: given a set of N regular nodes distributed in a plane, our goal is to place K mobile backbone nodes, which can occupy thearbitrary locations in the plane, while simultaneously assigning the regular nodes to the mobile backbone nodes, such that the effectiveness of the resulting network is maximized. In this work, the effectiveness of the resulting network is measured by the number of regular nodes that achieve throughput at least _min, although other formulations (such as that which maximizes the aggregate throughput achieved by all regular nodes) are possible. Thus, our objective is to maximize the number of regular nodes that achieve throughput at least _min. ). We also assume that there is no need for the mobile backbone nodes to be ―connected‖ to one another. Thus, our **model** represents a ―one-time‖ network design problem and is also suitable for cases in which mobile backbone nodes are deployable, but cant be move once they have been deployed.

Progress has been made over the past few years in the area of verification of multi-agent systems where a num- ber of methods based on **model** checking and theorem prov- ing have been put forward (Alechina et al. 2010; Lomuscio, Qu, and Raimondi 2017; Kouvaros, Lomuscio, and Pirovano 2018). Some of this work has been combined with safety analysis and abstraction thereby resulting in the assessment of designs such as autonomous underwater vehicles (Ezekiel et al. 2011).