In this paper, we treat a lexicographic bi-criteria combinatorial optimization model of mixture packaging of two types of items, which arises in actual food packing systems, so-called multi-head weighers. The primary objective is to minimize the total weight of chosen items for a package, and the second objective is to maximize the total priority of them. The constraints are that the total weight must be no less than a given target weight, and that the weight sum of chosen items of each type must also be no less than a given necessity minimum. The weight of an item of each type is bounded by the necessity minimum from the above. We show that a greedy heuristic solution with the total weight at most twice the minimum attains the total priority at least the conditionally maximum, which is an improved performance guarantee of greedy heuristic solutions for the lexicographic bi-criteria mixture packaging problem of two types of items.
In a convenience store, new items like lunch boxes and dairy products are delivered several times in one day. In addition, old unsold items must be disposed because of their expiration dates. The order is made once in a day, and the retailer has to decide the number of items ordered based on the current remaining items in the store and the demand distribution. This paper considers an optimal ordering problem with short lifetime products, where each order is made once in one day whereas delivery of ordered products and disposal of out-of-date products are twice in one day. The objective is to find the optimal numbers of items which are delivered twice in the next day, which minimize the total expected discounted cost over an infinite horizon. The model is formulated as a Markov decision process. To overcome curse of dimensionality, the appropriate set of basic functions are investigated to approximate the optimal value function of the Markov decision process. The derived approximate optimal ordering policy for the large-size problems is an unbalanced ordering policy under which more items are ordered in one delivery of one day than in another delivery of the same day even when the demand distribution is time-independent. In addition, it is shown through numerical examples that as the probability is larger that an old item is selected by a customer when both old and new items are in the store, the sub-optimal policy is more unbalanced and gains more profit.
We are given a sequence of m machines and an ordered set of n jobs. The n jobs are served by the m-machine system in their indexing order. We are also given a collection of pj machine subsets for each job j ∈ N, where N denotes the set of jobs. We are primarily asked to choose a machine subset from the pj options for each job j ∈ N so that the similarity sum over a series of chosen n machine subsets is maximized, where a degree of similarity of two machine subsets is defined to be the number of common machines between the two machine subsets. The series of chosen n machine subsets also induces a subsequence of machines for serving the n jobs. We call the length of an induced machine subsequence its stretch. We are secondarily asked to choose a machine subset from the pj options for each job j ∈ N so that the stretch of the induced machine subsequence is minimized. The lexicographic machine subset selection problem is motivated by a musical issue of selecting inversions in a chord progression with the triad. In this paper, we propose a polynomial time exact algorithm for the lexicographic machine subset selection problem. We also demonstrate the solutions on three examples of chord progressions with the triad, and on randomly generated instances.
In this paper, we analyze the complexity of the gear placement problem (GPP). In the GPP, we are given a rectangular plane, called a gearbox, on which a torque generator source and a set of gears, called target gears, are placed. The task is to find a placement of a set of gears called sub-gears, to connect every target gear to the torque generator source so that every target gear rotates in a given direction. The objective is to minimize the number of sub-gears to be used. We prove that the GPP is NP-hard by giving a reduction from the Hamiltonian path problem on 3-regular planar graphs, which is known to be NP-complete, to the GPP. We also present an upper bound for the number of sub-gears to be placed.
Many researchers have focused on the comparison between the JIT model and the EOQ model. However, few of them studied this problem from an evolutionary perspective. In this paper, a JIT purchasing with the single-setup-multi-delivery model is introduced to compare the total costs of the JIT model and the EOQ model. Also, we extend the classical JIT-EOQ models to a two-echelon supply chain which consists of one manufacturer and one supplier. Considering the bounded rationality of players and the quickly changing market, an evolutionary game model is proposed to discuss how these factors impact the strategy selection of the companies. And the evolutionarily stable strategy of the proposed model is analyzed. Based on the analysis, we derive the conditions when the supply chain system will choose the JIT strategy and propose a contract method to ensure that the system converges to the JIT strategy. Several numerical experiments are provided to observe the JIT and EOQ purchasing strategy selection of the manufacturer and the supplier. The results suggest that, in most situations, the JIT strategy is preferred. However, the EOQ strategy remains competitive when the supplier’s inventory cost level is high or the demand is low. Supply chain members can choose the EOQ strategy even when the JIT strategy is more profitable. In some situations, strategy selection also depends on the market situation. The JIT policy with low investment costs and high supply chain performance is preferred for the companies.
In this paper, we develop a stochastic model for an imperfect production-inventory system that faces random quality disruption and has limited time for production. In each time planning horizon, the inventory level is affected by product quality disruption. When the production system switches to the ‘out-of-control’ state from the ‘in-control’ state, it starts producing some defective products along with defect-free products, and this switching time is stochastic. The process of the inventory levels at the start of the time horizon is expressed by using a finite and continuous state continuous-time Markov process. We construct mathematical expressions of the transition probability, the steady-state probability, and the long-run average cost. Through a numerical experiment, the near-optimal solution is achieved. The outcome shows that under the situation of production time constraint, the integration of safety stock in an interruption prone production–inventory system, assists in improving the average cost function. The results also show that the optimal safety stock is large when the defect percentage, or the production switching rate, or the shortage cost is very high. Conversely, the small safety stock is desirable when the inventory holding cost or the rework cost is high.
In recent years, customer needs have diversified and companies have been forced to deliver products quickly to their customers. Distribution warehouses play an important role in improving the efficiency of the entire supply chain, and improving the efficiency of the order preparation operation, otherwise known as order picking, is therefore essential. This research models an order picking operation in which two or more pickers are operating simultaneously, and the optimal design for operation efficiency is analyzed. Here, the picker targets multi-picking, which entails the collection of multiple products in one tour, and the picker always selects the shortest route for collecting the products. In this research, the behavior of the pickers is modeled using a multi-agent system, such that multiple pickers pass one another in the warehouse and a conflict due to excessive congestion is reproduced. The effect prompted by changes to both the layout and the storage assignment using the aforementioned model was clarified. The simulation results show that an optimal warehouse design based on warehouse characteristics (picking area size and differences in the demand frequency of each product) and the number of pickers operating simultaneously significantly affects the efficiency of the order picking operation. Furthermore, it is possible to reduce picker travel time by using the class storage method. The greater the difference in the demand frequency of each product, the greater the effect.
The periodic vehicle routing problem (PVRP) is a generalization of the vehicle routing problem (VRP) to a planning period of more than one day. A fleet of vehicles needs to deliver goods periodically to each customer so that the delivery dates meet the request of the customer. This paper introduces a new model of PVRP, the periodic vehicle routing problem with flexible delivery dates, which covers a wider range of applications and is able to answer more diverse customer requirements. We propose an algorithm based on iterated local search (ILS), which is a metaheuristic approach that involves an iterative application of a local search algorithm and the use of perturbation as a diversification mechanism. Computational results show that our proposed method performed competitively in solving the standard PVRP. Moreover, we confirm that our new model can reduce the cost for more general instances.
We address the selective pickup and delivery problem with time-window constraints, which is a problem of finding vehicle routes that pick up commodities at stores and deliver them to customers so as to minimize the total distance of the routes under capacity and time-window constraints. In this paper, to design a local search method for this problem, we consider the following: Given the order of customers in a route, we determine the pickup stores and optimal times of visiting at customers so that the total distance is minimized. This is called the optimal pickup point problem and is a subproblem of the selective pickup and delivery problem with time-window constraints. We show that the optimal pickup point problem is NP-hard in general, and then we propose dynamic programmingmethods, which can obtain upper and lower bounds in linear time, and optimal solution in pseudo-polynomial time.
Various modes of transportation are available when people travel within cities, and trips can be classified into two types depending on whether some type of vehicle is used. Compared to vehicular travel, trips conducted only by walking have the advantages of lower environmental impact and less space required for road networks. By assuming that the proportion of walking-only trips decreases exponentially with the distance traveled, we explore the problem of finding a city shape with a fixed land area that maximizes the number of walking-only trips based on Manhattan distance. For many-to-one travel with the city center as the destination, we show that the optimal city shape is a diamond. For many-to-many travel, a method is presented that expresses the number of walking-only trips as a double integral, originally formulated as a four-dimensional integral. Using this, an optimization problem is formulated whose variables are the vertex coordinates of a polygon, and approximate solutions for the optimal city shape under several different settings are obtained numerically. For many-to-many travel, it is shown that a large number of walking-only trips occur when the city shape is close to being circular, although the exact shape varies with the distance deterrence coefficient.
In an effort to tackle environmental problems, sustainable policies that have a low environmental impact on the local community are being implemented in many countries, including Japan. One approach is the smart community, which is a policy to evaluate the cost of the entire community, considering each interaction while dividing society into seven fields: power, gas, water, railway, industry, business, and home models. In this study, we evaluate and optimize the home model. We develop an optimization model for the operation plan of energy storage equipment in a residential building as part of a smart community. The purpose of this model is to improve electricity costs from the demand profile and provide stable power supply from the supply profile. Therefore, this model controls the operation of energy storage equipment and also performs load leveling. It is intended to reduce the total power consumption during peak hours by operating the energy storage equipment at night, when the usage of other electrical appliances is low. A stochastic programming model is formulated using scenarios that represent the uncertainty of power and heat demand. This formulation assumes continuous operation in a residential building. We demonstrate the usefulness of the stochastic programming model by comparing it with the deterministic model. As an economic assessment, we compare the daily beneficial expense of the existing model with our new model of daily operations by following the improvement factors. Our model not only lowers peak total power consumption but also achieves load leveling. The total operating time of energy storage equipment is also reduced.
Demand for nursing care facilities such as senior daycares has increased in Japan because of an aging population. In these facilities, multiple staff members offer nursing care services to the elderly such as physical therapy and exercise using machines, according to a staff schedule planned manually. These staff members face some issues regarding heavy workloads, limited human resources, etc. Therefore, it is necessary to plan the staff schedules by distributing the workloads among all the staff members. Additionally, it is observed that staff members are stressed because of physical as well as mental stress when providing services since they also need to vigilant to prevent user accidents. A previous study proposed a scheduling model considering the feeling of physical and mental workloads separately. Thus, the differences for either of the workloads may become very large in planned schedules. This study proposes a scheduling model considering both physical and mental workloads, and produces a balancing schedule considering both types of workloads simultaneously. Additionally, the impact of a movement constraint that is added to the model to reduce the inefficient movement of staff is also discussed. Lastly, to analyze actual cases of the surveyed facility, we conducted numerical experiments with practical scenarios such as increasing the number of staff members, and changing the staff role according to actual staff shifts in the facility.