Smith B. M., Wren A., A Bus Crew Scheduling System Using a Set Covering Formulation, Transportation Research, 22A, 97-108, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....used in this experiment is freely available at http: www idss.cs.put.poznan.pl jaszkiewicz moscp. Set covering problem is an NP complete combinatorial optimization problem [6] often used to test single objective metaheuristics. It finds many practical applications especially in crew scheduling [24]. In practice, solutions of set covering problem often cannot be evaluated with a single objective only. For example, in the case of crew scheduling it may be necessary to take into account both the cost and the quality of work. Other objectives important in the case of crew scheduling are ....

Smith B. M., Wren A., A Bus Crew Scheduling System Using a Set Covering Formulation, Transportation Research, 22A, 97-108, 1988.

....of public transport [5, 6, 7, 8, 9, 10] this chapter will concentrate on those published more recently and any others which relate to current work. Willers [14] presents a fuller review of the material in the proceedings. Complete scheduling packages which are in most common use are : IMPACS [15, 16, 17, 18], HASTUS [19, 20, 21, 22, 23, 24] HOT II [25, 26, 27] UMA(Trapeze) and Teleride Sage. Other systems are in use such as TransTec EDP in Germany, and a system called BERTA [28] is being developed in Berlin to provide automatic bus and driver schedules for an underground, bus and tram system, but ....

....its mathematical programming component which produces a schedule from a set of previously generated valid duties. Chapter 4 The TRACS II Scheduling System 4. 1 Introduction This chapter describes a computerised scheduling system which was developed at the University of Leeds by Smith and Wren [15, 16, 17]. The IMPACS (Integer Mathematical Programming for Automatic Crew Scheduling) system was installed by the University in London Transport (now London Buses Ltd. in 1984 and Greater Manchester Transport in 1985. It has been maintained and altered for commercial use within the BUSMAN system [73] ....

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B. M. Smith and A. Wren. A Bus Crew Scheduling System Using a Set Covering Formulation. Transportation Research, 22A:97 -- 108, 1988.

.... are commercially available and some details of these and other investigations have been published as a result of seven international workshops (see, e.g. 1, 2] One such package which uses a mathematical programming approach is TRACS II which was originally developed from the IMPACS system [3] and is now used within both the UK bus and train industries. This paper concentrates on the mathematical programming component of the TRACS II system, describing the algorithm and recent developments. Results on a selection of real world bus and train problems are reported. 2 THE DRIVER ....

....number of workpiece constraints of 13 50 and in the number of shifts of 50 90 . 5. 5 Branch and Bound The branch and bound method has been developed with an emphasis on finding a good integer solution quickly and uses a specialised hierarchy of branching strategies developed by Smith and Wren [3]. The schedule is found by developing a branch and bound tree, in which the lower bound on the objective cost is given by the optimal continuous solution. Once an integer solution has been found the nodes of the tree are fathomed if their cost is greater than or equal to a scheduler specified ....

B. M. Smith and A. Wren, A Bus Crew Scheduling System Using a Set Covering Formulation, Transportation Research, 22A, pp 97-108, 1988.

.... A bus scheduling system which became known as VAMPIRES was developed in the early 1970s [15] installed for Greater Manchester Transport in 1975, and further developed within the BUSMAN commercial package [17] A major bus driver scheduling system, IMPACS, was installed in London Transport in 1984 [12], and is still used by London successor companies; it was subsequently incorporated in BUSMAN. Various methods for constructing rotating rosters of bus drivers have been developed for individual users, with a generic version included in BUSMAN. Throughout the 1980s the team had worked in ....

B.M. Smith and A. Wren, `A bus crew scheduling system using a set covering formulation', Transpn.Res. 22A, 97-108 (1988).

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Smith, B.M. and Wren, A. A bus crew scheduling system using a set covering formulation. Transportation Research, 1988, 22A, 97-108.

....and the decision as to which shift is employed to drive the vehicle is left to the scheduler (it may alternatively be decided by a simple heuristic) This is then a set covering problem. The driver scheduling problem was formulated as an integer linear programming (ILP) model by Smith and Wren [23]: Let c j be the cost of potential shift j and let x j be the number of times shift j is chosen (either 0 or 1, because it is either chosen or not) n Minimize S c j x j (1) j=1 Every piece of vehicle work, i, has at least one shift assigned to it: S x j . 1, i = 1, 2, 3, m ....

Smith, B.M. and Wren, A., A bus crew scheduling system using a set covering formulation. Transportation Research, vol.22A, pp. 97-108, 1988.

....of work has to be covered in the solution by exactly one shift. Wren and Smith [4 7] and Desrochers et al. [5 7] allow several shifts to cover any piece of work in the solution, relying on the optimisation to keep the amount of overcover to a minimum. Blais and Rousseau [4 12] and Eusebio et al. [4 10] first relax the problem to obtain a set of idealised shifts which ensure that there are enough shifts in the solution to cover the number of buses running in any time period. Patrikalakis and Xerocostas [5 8] have adopted an alternative approach in which drivers shifts are formed first by ....

....all the m possible pieces of bus work and determines whether two consecutive pieces on the same block can be combined without sacrificing a useful possibility of changing drivers at the relief opportunity between the pieces. The original version of this routine is described by Smith and Wren [10], although enhancements have been made since. Essentially, relief opportunities are eliminated where their use would require the block to be broken more often than necessary, or where no sensible shift could be formed using the relief. Some of these opportunities are restored where further ....

Smith, B.M. and Wren, A. A bus crew scheduling system using a set covering formulation. Transportation Research, vol. 22A, pp.97-108, 1988.

....(1999) but tend to favour approaches which schedule vehicles in advance (see e.g. Caprara et al. 1999) Rousseau (1995) TRACS II, developed at the University of Leeds, is a mathematical programming based bus and train driver scheduling system. The system is based upon the IMPACS system (see Smith and Wren (1988); Wren and Smith (1988) which first generates valid shifts, and then selects a subset which covers all of the vehicle work and minimises an objective function. The main enhancements made to the Integer Linear Programming (ILP) component relate to the implementation of a choice of solution ....

....which schedule vehicles in advance (see e.g. Caprara et al. 1999) Rousseau (1995) TRACS II, developed at the University of Leeds, is a mathematical programming based bus and train driver scheduling system. The system is based upon the IMPACS system (see Smith and Wren (1988) Wren and Smith (1988)) which first generates valid shifts, and then selects a subset which covers all of the vehicle work and minimises an objective function. The main enhancements made to the Integer Linear Programming (ILP) component relate to the implementation of a choice of solution methods, and to improvements ....

Smith, B. M., A. Wren (1988). A Bus Crew Scheduling System Using a Set Covering Formulation Transportation Research(22A), pp. 97--108.

....practice, there may be billions of possible shifts and it would not be practical to generate them all, let al..one solve the resulting set partitioning problem. Viable scheduling systems have user de ned parameters to limit the generation of shifts, for example eliminating apparently inecient shifts [15]. The problem is thus di erent from the air crew scheduling problem, where normally all possible combinations of ight legs (equivalent to pieces of work in our problem) are generated as rotations (shifts) and set partitioning formulations [8, 14] have been successful. The other di erence between ....

.... such as time necessary to travel between relief points; An intelligent sieving process eliminates potential shifts which, by comparison with others, are unlikely to be useful; An Integer Linear Programming model is solved by column generation and branch and bound processes developed in [6, 15, 19] Over cover is removed by interactive editing. TRACS II has been proved in many tests [10] to produce schedules considerably better than those produced manually. For example, Reading Buses have recorded annual savings of about 135k in a eet of about 200 buses [19] TRACS II has also ....

B.M. Smith and A. Wren. A bus crew scheduling system using set covering formulation. Transpn.Res., (22A):97-108, 1988.

....x j = 1 if j is in the partition 0 otherwise 2 a ij = 1 if i 2 S j 0 otherwise Often in commercial driver scheduling packages a set covering formulation is used and solved by heuristic reductions with a mathematical programming solver. An example of such a system is IMPACS TRACS II [13, 9] developed by two of the authors of this paper. The IMPACS system was first implemented for London Transport in 1984 and is still in use by many organisations. The new system, TRACS II, has been used to form schedules for several different bus and train companies and is part of a commercial ....

B.M. Smith and A. Wren. A bus crew scheduling system using set covering formulation. Transpn.Res., (22A):97--108, 1988.

....Programming (ILP) system, is responsible for reducing the set of shifts into a good schedule containing the minimum number of shifts. For small and large problems TRACS II is capable of producing very good quality solutions in a reasonable time. It is a replacement for the earlier IMPACS system [4]. In this paper, our system uses the TRACS II BUILD process to generate a large number of potential shifts, which our system then reduces into a good solution. Thus it effectively replaces the SCHEDULE component by emulating its abilities to reduce the total number of shifts. 1.2.2 Use of Ant ....

B.M. Smith and A.Wren. A bus crew scheduling system using a set covering formulation. Transportation Research, (22A):pp.97--108, 1988.

....BUSPLAN and CREWPLAN components of the BUSMAN system [2] were used for steps (2) and (3) of the above process. As we no longer had access to the code of CREWPLAN we could not take account precisely of all the rules, but made some assumptions which may have been over generous; 2. The IMPACS suite [3] was used for step (3) applied to the BUSPLAN vehicle schedule. Although CREWPLAN had been derived from IMPACS around 1985, the systems had since diverged, and IMPACS had been upgraded to take account of more recent research. IMPACS was also more adaptable, and was adjusted to take account of the ....

B.M. Smith and A. Wren (1988) A bus crew scheduling system using a set covering formulation. Transportation Research,vol.22A, pp.97-108.

....international workshops (see, e.g. 1, 2] With improvements in technology, mathematical programming solution methods are increasingly more successful. One of the driver scheduling systems using a mathematical programming approach is TRACS II which was originally developed from the IMPACS system [3, 4] and which uses a set covering formulation to ensure that all vehicle work is covered. This paper outlines several improvements incorporated into the mathematical programming component of the TRACS II system. Results on a selection of bus and train problems are reported. 3 THE DRIVER SCHEDULING ....

....Thus mathematical programming is frequently combined with heuristic approaches to provide a viable solution method. 4 THE TRACS II SYSTEM TRACS II is the driver scheduling system which was developed at the University of Leeds, and which originates from the commercially available IMPACS system [3, 4]. TRACS II has since been altered to incorporate features required in order to schedule train crews, 5, 6] and many of the algorithms contained in the individual components have been improved. In principle though, the TRACS II system exhibits a similar overall solution method to the IMPACS ....

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B. M. Smith and A. Wren, A Bus Crew Scheduling System Using a Set Covering Formulation, Transportation Research, 22A, pp 97-108, 1988.

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