On statistical bounds of heuristic solutions to location problems

Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region. 

Evaluation of a PVT Air Collector

Hybrid Photovoltaic Thermal (PVT) collectors are an emerging technology that combines PV and solar thermal systems in a single solar collector producing heat and electricity simultaneously. The focus of this thesis work is to evaluate the performance of unglazed open loop PVT air system integrated on a garage roof in Borlänge. As it is thought to have a significant potential for preheating ventilation of the building and improving the PV modules electrical efficiency. The performance evaluation is important to optimize the cooling strategy of the collector in order to enhance its electrical efficiency and maximize the production of thermal energy. The evaluation process involves monitoring the electrical and thermal energies for a certain period of time and investigating the cooling effect on the performance through controlling the air mass flow provided by a variable speed fan connected to the collector by an air distribution duct. The distribution duct transfers the heated outlet air from the collector to inside the building. The PVT air collector consists of 34 Solibro CIGS type PV modules (115 Wp for each module) which are roof integrated and have replaced the traditional roof material. The collector is oriented toward the south-west with a tilt of 29 ᵒ. The collector consists of 17 parallel air ducts formed between the PV modules and the insulated roof surface. Each air duct has a depth of 0.05 m, length of 2.38 m and width of 2.38 m. The air ducts are connected to each other through holes. The monitoring system is based on using T-type thermocouples to measure the relevant temperatures, air sensor to measure the air mass flow. These parameters are needed to calculate the thermal energy. The monitoring system contains also voltage dividers to measure the PV modules voltage and shunt resistance to measure the PV current, and AC energy meters which are needed to calculate the produced electrical energy. All signals recorded from the thermocouples, voltage dividers and shunt resistances are connected to data loggers. The strategy of cooling in this work was based on switching the fan on, only when the difference between the air duct temperature (under the middle of top of PV column) and the room temperature becomes higher than 5 °C. This strategy was effective in term of avoiding high electrical consumption by the fan, and it is recommended for further development. The temperature difference of 5 °C is the minimum value to compensate the heat losses in the collecting duct and distribution duct. The PVT air collector has an area of (Ac=32 m2), and air mass flow of 0.002 kg/s m2. The nominal output power of the collector is 4 kWppv (34 CIGS modules with 115 Wppvfor each module). The collector produces thermal output energy of 6.88 kWth/day (0.21 kWth/m2 day) and an electrical output energy of 13.46 kWhel/day (0.42 kWhel/m2 day) with cooling case. The PVT air collector has a daily thermal energy yield of 1.72 kWhth/kWppv, and a daily PV electrical energy yield of 3.36 kWhel /kWppv. The fan energy requirement in this case was 0.18 kWh/day which is very small compared to the electrical energy generated by the PV collector. The obtained thermal efficiency was 8 % which is small compared to the results reported in literature for PVT air collectors. The small thermal efficiency was due to small operating air mass flow. Therefore, the study suggests increasing the air mass flow by a factor of 25. The electrical efficiency was fluctuating around 14 %, which is higher than the theoretical efficiency of the PV modules, and this discrepancy was due to the poor method of recording the solar irradiance in the location. Due to shading effect, it was better to use more than one pyranometer.

Modeling and illustrating requirement prioritization in public e-service development from a value-based perspective

A major problem in e-service development is the prioritization of the requirements of different stakeholders. The main stakeholders are governments and their citizens, all of whom have different and sometimes conflicting requirements. In this paper, the prioritization problem is addressed by combining a value-based approach with an illustration technique. This paper examines the following research question: How can multiple stakeholder requirements be illustrated from a value-based perspective in order to be prioritizable? We used an e-service development case taken from a Swedish municipality to elaborate on our approach. Our contributions are: 1) a model of the relevant domains for requirement prioritization for government, citizens, technology, finances and laws and regulations; and 2) a requirement fulfillment analysis tool (RFA) that consists of a requirement-goal-value matrix (RGV), and a calculation and illustration module (CIM). The model reduces cognitive load, helps developers to focus on value fulfillment in e-service development and supports them in the formulation of requirements. It also offers an input to public policy makers, should they aim to target values in the design of e-services.