Data Envelopment Analysis (DEA) is a mathematical programming approach to assess relative efficiencies with a group of decision making units (DMUs) such as production systems. There have been some useful models for their successful applications in many fields. In this paper, we first point out the defect of the first DEA model CCR (Charnes, Cooper and Rhodes, 1978) in measuring the efficiencies of the production system with k independent subsystems and propose a new model YMK (Yang, Ma and Koike) by improving CCR model. Some properties and the relationship between CCR and YMK models are also discussed. It is conduded that the overall efficiency (YMK) of each DMU has a great deal to do with the efficiencies of its subsystems under CCR model. In fact, the overall efliciency value (YMK) of each DMU is equal to the maximum among the efficiency values of all its subsystems under CCR model. The examples given demonstrate the effectiveness of YMK model in measuring efficiencies of the production system with k independent subsystems.

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In this we consider a model in which a customer chooses one of two retailers with a choice probability depending on the distance from the customer's position to the retailer's position over a line segment market. We study an optimal strategy for two retailers in a competitive inventory model by using an equilibrium point in the context of the game theory. We find an equilibrium point concerned with the optimal ordering quantity to minimize the total cost.

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This paper proposes an improvement of the algorithm by Ikegami and Niwa (1998) for 2-shift nurse scheduling. In their algorithm, we prepare before hand a set of all the schedules for each nurse which specify which days she or he is feasibly assigned to the nighttime shift with an extra information that the nurse can or cannot work for the remaining days. Also we define the objective function to measure the degree of violations of the nighttime-related constraints which are caused by a solution. Then we set out to compare all the prepared solutions for each nurse in terms of the value of the objective function given that the other nurses' schedules are fixed as specified by the current trial solution. Finally we choose the best solution from these individual best ones. This solution in turn will be used as the next trial solution to define a new optimization problem to be solved and so on. This creates an iterative process once the first trial solution is given. For it we use a solution that assigns nobody to the nighttime shift on any day. Also we keep that specific schedule which produced the current trial solution out of the comparison process to avoid a creation of a loop. The iteration is continued until we have a schedule whose value is zero, i.e. a schedule which satisfies the nighttime constraints. Starting from this schedule, we go to the second phase of satisfying the daytime constrains through the same process after we prepare a set of schedules for each nurse which satisfy the daytime constraints like in the first phase. We again use as the initial solution a schedule which assigns nobody to the daytime shift on any day. This algorithm obtains a good solution, but is often slow as it basically checks all the alternative schedules for each nurse. The main contribution of this paper is to reduce the time taken in solving the subproblem by curtailing the number of alternative schedules to be looked at in each iteration. The observation of a sequence of the trial solutions in the first phase of the algorithm to satisfy the nighttime constraints shows the following. The two adjacent trial solutions have a small difference where the difference is defined to be the number of days when the night shift is assigned in one solution while not in the other: The difference is 0 to 3. This leads us to the modified algorithm which focuses only on the schedules that have a little difference from the current solution to be examined and results in a remarkable improvement.

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This paper proposes an integrated analytical/simulation approach for designing an automated guided vehicle system (AGVS) which consists of AGVs, machines with input buffers and a dispatching station in a just-in-time (JIT) environment. The objective is to determine the number of AGVs, the input buffer capacities and locations of the machines that minimize a cost function under the constraint that the planned utilization of each machine is achieved. The integrated analytical/simulation approach employs a simulation model to evaluate the performance of the AGVS and an analytical approach to reduce the repetition number of simulations in searching an optimal solution. The analytical approach leads to an efficient iterative procedure based on monotonicity properties of the cost function and the machine utilization in each design factor, and lower bounds of the number of AGVs and the input buffer capacities. Moreover, initial locations of the machines are derived from the HLP inequality. Computational results are given to demonstrate the efficiency of the proposed procedure. It is observed that the lower bounds and the initial locations are the optimal solution in case of deterministic processing times at machines.

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Let R(z) be a matrix function. We propose modified Newton's method to calculate zero points of det R(z). By the modified method, we can obtain accurate zero points by simple iterations. We also extend this problem to a multivariable case. Applications to the spectral analysis of M/G/1 type Markov chains are discussed. Important characteristics of these chains, e.g., the boundary vector and the matrix G, can be derived from zero points of a matrix function and corresponding null vectors. Numerical results are shown.

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We consider a generalized optimum requirement spanning tree problem (GORST problem) which is an extension of the problem studied by Hu. In the GORST problem, the degrees of vertices are restricted and the objective function is generalized. We will show that a particular tree T^*, which is obtained by a sort of greedy algorithm but is explicitly definable, is a solution to the GORST problem when a condition similar to the Monge property is satisfied. Also, we will define a problem of finding a tree network which minimizes the probability that a request of communication is not realized when the network has k failures (called a "k-failure problem"), and show that T^* is an explicit solution to the k-failure problem for any k when the maximum degree constraint is imposed and the Monge-like property is satisfied.

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