Aggregation effects in maximum covering models

The level of aggregation is critical in discrete location analyses as it affects the level of data collection required, computation times and the usefulness of the analyses. We examine the effects of three alternative nodal aggregation schemes on (i) the model's solution times, (ii) the locational decisions indicated by the maximum covering model, (iii) the coverage provided by the aggregate solutions compared with the optimal solutions, and (iv) the coverage predicted by the aggregate model compared with the coverage that results from using the aggregate model's facility sites and the disaggregate demands. The results suggest that considerable aggregation can be tolerated without incurring large errors in total coverage, but that location errors are introduced at moderate levels of aggregation. The magnitude of these errors is significantly affected by the aggregation scheme employed.     

The stochastic interdiction median problem with disruption intensity levels

In this paper we introduce a stochastic interdiction problem for median systems in which the operational state of the system??s disrupted elements in the aftermath of the disruption is uncertain as it is based on the intensity of the disruption. We assume that a disruption disables a facility with a given probability and this probability depends on the intensity of the disruption. The objective of this problem is to identify which disruption scenario entails a maximum overall traveling distance in serving all customers. We show that the initial two stage stochastic formulation can be reformulated into a deterministic counterpart whose size is polynomial in the number of facilities and intensity levels. Then, our ensuing efforts to solve the problem efficiently focus on studying alternative deterministic formulations that allow the solution of realistic size instances of the model. We observe that the most efficient of the deterministic formulations provide great scalability with respect to variations in the input parameters and size of the instances solved. Finally, we analyze the robustness of the optimal solutions due to misestimations in the probability functions that relate disruption intensity levels with the probabilities of facility survivability.     

Dynamic fleet scheduling with uncertain demand and customer flexibility

We develop a dynamic fleet scheduling model that demonstrates how a carrier can improve fleet utilization. The fleet scheduling model presented by Lee et?al. (Eur J Oper Res 218(1):261–269, 2012) minimizes (1) a carrier’s fleet size and (2) the penalty associated with the alternative delivery times selected. The model is static since requests are collected over time and processed together. In this paper we present a stochastic, dynamic version of the fleet reduction model. As demand is revealed throughout an order horizon, decisions are made in stages by sampling anticipated demand to avoid recourse penalties in later stages. Based on computational experiments we find the following:

1. Modeling stochasticity improves the quality of solutions relative to the analogous model that does not include stochasticity. Counter-intuitively, an order lead-time distribution in which most loads are requested early can negatively impact optimal solution costs.
2. The stochastic model produces good results without requiring prohibitively large numbers of demand scenarios.
3. Consignees that place orders early in the order horizon are more often assigned their requested delivery times than those who place orders late.

     

A bibliography for some fundamental problem categories in discrete location science

Following a brief taxonomy of the broad field of facility location modeling, this paper provides an annotated bibliography of recent papers in two branches of discrete location theory and modeling. In particular, we review papers related to (1) the median and plant location models and (2) to center and covering models. We show how the contributions of the papers we review are embedded in the field. A summary and outlook conclude the paper.     

An Inventory-Location Model: Formulation, Solution Algorithm and Computational Results

We introduce a distribution center (DC) location model that incorporates working inventory and safety stock inventory costs at the distribution centers. In addition, the model incorporates transport costs from the suppliers to the DCs that explicitly reflect economies of scale through the use of a fixed cost term. The model is formulated as a non-linear integer-programming problem. Model properties are outlined. A Lagrangian relaxation solution algorithm is proposed. By exploiting the structure of the problem we can find a low-order polynomial algorithm for the non-linear integer programming problem that must be solved in solving the Lagrangian relaxation subproblems. A number of heuristics are outlined for finding good feasible solutions. In addition, we describe two variable forcing rules that prove to be very effective at forcing candidate sites into and out of the solution. The algorithms are tested on problems with 88 and 150 retailers. Computation times are consistently below one minute and compare favorably with those of an earlier proposed set partitioning approach for this model (Shen, 2000; Shen, Coullard and Daskin, 2000). Finally, we discuss the sensitivity of the results to changes in key parameters including the fixed cost of placing orders. Significant reductions in these costs might be expected from e-commerce technologies. The model suggests that as these costs decrease it is optimal to locate additional facilities.     

Decomposition of unitary matrices for finding quantum circuits: application to molecular Hamiltonians

Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and quantum computation. Evolution of quantum circuits faces two major challenges: complex and huge search space and the high costs of simulating quantum circuits on classical computers. Here, we use the group leaders optimization algorithm to decompose a given unitary matrix into a proper-minimum cost quantum gate sequence. We test the method on the known decompositions of Toffoli gate, the amplification step of the Grover search algorithm, the quantum Fourier transform, and the sender part of the quantum teleportation. Using this procedure, we present the circuit designs for the simulation of the unitary propagators of the Hamiltonians for the hydrogen and the water molecules. The approach is general and can be applied to generate the sequence of quantum gates for larger molecular systems.     

Group leaders optimization algorithm

We present a new global optimization algorithm in which the influence of the leaders in social groups is used as an inspiration for the evolutionary technique which is designed into a group architecture. To demonstrate the efficiency of the method, a standard suite of single and multi-dimensional optimization functions along with the energies and the geometric structures of Lennard-Jones clusters are given as well as the application of the algorithm on quantum circuit design problems. We show that as an improvement over previous methods, the algorithm scales as N ^2.5 for the Lennard-Jones clusters of N-particles. In addition, an efficient circuit design is shown for a two-qubit Grover search algorithm which is a quantum algorithm providing quadratic speedup over the classical counterpart.     

The effect of lifetime buys on warranty repair operations

Lifetime buys are a common practice in the electronics and telecommunication industries. Under this practice, manufacturers procure their repair parts inventory in one order to support the spare part needs of a product for the duration of its warranty repair period. In this paper, we consider a repair operation in which defective items under warranty are returned to a manufacturer who either repairs these items using its spare parts inventory or replaces each defective unit with a new product. We show how fixed repair capability costs, variable repair costs, inventory holding costs, and replacement costs affect a firm's optimal repair and replacement decisions. The model is used to gain insights for products from a major mobile device manufacturer in the United States.     

The stochastic location model with risk pooling

In this paper, we present a stochastic version of the location model with risk pooling (LMRP) that optimizes location, inventory, and allocation decisions under random parameters described by discrete scenarios. The goal of our model (called the stochastic LMRP, or SLMRP) is to find solutions that minimize the expected total cost (including location, transportation, and inventory costs) of the system across all scenarios. The location model explicitly handles the economies of scale and risk-pooling effects that result from consolidating inventory sites. The SLMRP framework can also be used to solve multi-commodity and multi-period problems.