## 1 Introduction  
In several industries, such as paper, steel, and textile, items of specified sizes are cut out from the raw material placed on a flat surface. Problems aimed at minimizing the cost of such cutting work are referred to as two-dimensional cutting stock problems (CSPs) and two-dimensional bin packing problems (BPP), on which several studies have been carried out so far. In particular, when positioning the items to be cut from raw material of fixed width \(W\) and variable height \(H\), if the purpose of the problem is to minimize the height \(H\), it is formulated as the strip packing problem (SPP), and various heuristic solutions have been proposed. [PERSON] et al. proposed the typical solution method, the first-fit decreasing height (FFDH) method and the next-fit decreasing height (NFDH) method [1] [PERSON] et al. arranged FJDH and proposed the best-fit decreasing height (BFDH) method [2]: [PERSON], et al., also arranged FJDH and proposed the floor-ceiling no rotation (FCNR) method [3]. [PERSON] et al., in addition to the FJDH method, proposed solutions including the bottom-left method [4], in which items are introduced from the upper right of a material and then stacked from the bottom left, and heuristic approaches such as the bottom-left fill method [5], which adds an algorithm for reducing the gap between items. There are also solutions proposed using a metaheuristic method, such as the hill-climbing method [6], which is a typical local search method; simulated annealing [7]; the genetic algorithm (GA) [8; 9; 10]; and the native evolution algorithm [11], which eliminates GA crossover and evolves only by mutation. The SPP and BPP pressure that all members have been arranged as a precondition; however, solutions [12] have been proposed using a knapsack problem approach when not all members have been arranged for selecting members that are given gain so that their sum is maximized, although many of these deal with materials as cost objects. These previous studies are aimed at maximizing the yield of raw materials as the cost target. However, it is not just the material cost that must be considered [13]. For example, at a manufacturing site where special sheet-like materials are cut, a setup change cost is incurred for each cutting, which significantly impacts the total cost. Hence, a technique that can facilitate a reduction of the setup change cost is desired. In this paper, we propose an allocation method aimed at minimizing the number of setup changes by applying conventional methods, such as the FFDH and binary tree methods, for manufacturing sites that cut special sheet-like material. This method has helped achieve a reduction in the number of setup changes while ensuring a high yield [14]. Because a two-dimensional CSP is considered \(\mathcal{NP}\)-hard, combinatorial explosion occurs when the complexity of the problem and, in turn, the scale of the solutions increases, leading to an exponential increase in the calculation time. In contrast, the actual problem represented by the two-dimensional CSP has a short lead time and requires a high-speed solution. Quantum computers are next-generation computers that use quantum mechanics and are implemented through two types of methods: the quantum annealing and quantum gate methods. The quantum annealer is considered to be suitable for solving combinatorial optimization problems. Therefore, various combinatorial optimization problems have been studied using quantum annealing. In a previous study on the BPP, [PERSON] et al. (2018) performed Ising modeling using sequence pairs for maximizing the yield of the rectangular packing problem [15]. Furthermore, [PERSON] et al. (2000) performed Ising modeling with a formulation based on the NFDH method for the glass processing industry; they compared the performances of the quantum annealer and the classical bifurcation machine [16]. However, Ising models aimed at reducing setup change cost (= number of cuts) in the two-dimensional CSP have not yet been created.