105 An approximate procedure for determining the number, capacities and locations of solid waste transfer-stations in an urban region S.C. WIRASINGHE Depurtment of Civil Engineering, Univemity of Calgq~~. Calga?. Alberta. Canada T2N IN4 N.M. WATERS Department of Geography, Unioerslty of Calgary, Calgary, Al- berta, Canada T2N IN4 Received July 198 1 Revised March 1982 Many location problems may be separated into a series of interrelated macro, meso and micro decision-making states. The macro scale decision determines the type, capacity and number of facilities, the meso scale decision determines the , location and allocation of facilities and the micro scale decision determines such considerations as routing and scheduling of service vehicles. This paper concerns the first two levels of decision-making. The present paper demonstrates the use of two models: (i) an analytical model that uses continuum approximations and methods of calculus to determine the number of facilities, the capacity and the approximate location of each that minimizes the sum of the transportation and facility costs for a slowly varying demand rate, and (ii) a traditional location-allocation model that determines more exactly the resulting locations and allocations. These two approaches have specific requirements in terms of data input, cost of data collection and cost of solution This problem, in its analytical form, was originally posed in 1974 to SC. Wirasinghe by Professor V.F. Hurdle. While accepting the responsibility for any errors in this paper, we wish to share any credit for the analytical model with Professor Hurdle. Thanks are also due to Mr. R. Anderson of the City of Calgary and Mr. R.G. Neehall of the City of Edmonton for providing valuable data at short notice and to the referees for providing some good suggestions. ‘This research was supported in part by the Natural Saencea and Environmental Research Cound of Canada under grant no. A4711. North-Holland Publishing Company European Journal of Operational Research 12 (1983) 105-I 11 and, consequently, yield unique insights and benefits for prac- tising planners. The strengths and weaknesses of the two mod- els are complementary. This thesis is developed with an analy- sis of the Calgary, 4lherta refuse collection and disposal sys- tem. 1. Introduction There are basically two systems for transporting urban refuse (solid waste) from the origins (households, business, etc.) to the final destina- tions. The system used currently in Calgary, Al- berta, Canada is essentially as follows. The city is divided into collection-areas. Refuse is collected weekly from residential areas and daily from busi- ness areas. A truck and crew are assigned several areas from which the refuse is collected over a week, compacted in the truck, and transported directly to the nearest sanitary landfill site. In the other system, which is currently in use in Edmon- ton, Alberta, Canada, the refuse is taken to a local transfer-station, shredded or compacted, and transferred to high capacity tractor-trailers which haul it to a sanitary landfill site. Similar proce- dures are used in most other cities though some details may vary. For example, the frequency of collection may be 2 or 3 times a week, the refuse may not be compacted in the truck, and the final destination may be an incinerator instead of a landfill site. A main advantage of the Calgary system is its minimal impact on the neighbourhoods since the sanitary landfill sites are located in the outskirts of the city. On the other hand, the vehicle and labour zests related to transporting the refuse from the collection areas are high. Further. the vehicle oper- ating costs are expected to rise sharply when gaso- line price controls are gradually lifted in Canada. The Calgary system has been described in detail by Jones [3] who presented procedues for optimiz- ing the routing system. 0377-2217/83/0000-0000/$03.00 0 1983 North-Holland