A. N. Elshafei, "Hospital Layout as a Quadratic Assignment Problem," Operations Research Quarterly, vol. 28, pp. 167--179, 1977.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the vertices are the facilities and the weight of the edge between facilities i and j is m ij . Architectural floor planning graph theoretic and not has traditionally been used in the design of industrial plants [DFF85, F92, FR78, Mu94] but also in the design of airports [BFP95] hospitals [E77], universities [DH72] and libraries [FT86] Often m ij is the number of people expected to travel from facility i to facility j. Another important application of maximum weight planar subgraph is circuit layout [Ma78, Mu94] The goal is to lay out a circuit on a one layer board to maximize the ....

A.N. Elshafei, "Hospital Layout as a Quadratic Assignment Problem," Operational Research Quarterly 28 (1977), 167--179. 19

....and C kn are now reduced in size by 1 and added (by simple matrix addition) to the new linear cost matrix. An interesting consequence of this second level of partial assignment is that the element C ikjn is necessarily involved in the assignment. In solving the Nugent 15 [22] and the Elshafei 19 [10] problems, many of the partial assignments at the second level are eliminated by the DP. In the Nugent 20, fewer partial assignments are eliminated at this level, though a large percentage of those partial assignments within the submatrices containing the optimum assignment are nonetheless ....

Elshafei, A. : "Hospital Layout as a Quadratic Assignment Problem, Operations Research Quarterly, vol. 28, no. 1 (1977): 167-179.

....rate for the schedule, which affected algorithm speed as well as the bound achieved. The performance of the algorithm, however, was not very sensitive to this rate. The results of those improvements are shown in Table II for three Nugent problems and a hospital facilities problem of Elshafei [12]. Table II Comparison of Bounds for Larger Problems Problem BKV DP LB1 MCCR EVB3 TDB Dual Ascent Nugent 12 578 523 493 495 n a 513 Nugent 15 1150 1039 963 989 1083 1010 Nugent 20 2570 2179 2057 2229 2394 2145 Elshafei 19 17,212,548 16,771,926 n a n a n a n a n a = not available Here, we see that ....

Elshafei, A, "Hospital Layout as a Quadratic Assignment Problem," Operations Research Quarterly, vol. 28, no. 1 (1977): 167-179.

....and Gonzalez (1976) have shown that the QAP is NP hard and that even finding an approximate solution within some constant factor from the optimal solution cannot be done in polynomial time unless P = NP. There are numerous applications of the QAP in di#erent fields, for example, hospital layout (Elshafei, 1977), ranking of archaeological data (Krarup and Pruzan, 1978) ranking of a team in a relay race (He#ey, 1977) scheduling parallel production lines (Geo#rion and Graves, 1976) and analyzing chemical reactions for organic compounds (Ugi et al. 1979) Li et al. 1994) presented a GRASP for the QAP ....

A. N. Elshafei. Hospital layout as a quadratic assignment problem. Operations Research Quarterly, 28:167--179, 1977.

....Heuristics, Iterated Local Search, Quadratic Assignment Problem, Run time Distributions, Search Space Analysis 1 Introduction The quadratic assignment problem (QAP) is an important problem in theory and practice. Many practical problems like backboard wiring [47] campus and hospital layout [11, 13], typewriter keyboard design [7] scheduling [16] and many others [12, 25] can be formulated as QAPs. The QAP can best be described as the problem of assigning a set of facilities to a set of locations with given distances between the locations and given flows between the facilities. The goal then ....

....8 in case n 1 = n 2 ) due to the definition of the distance matrices [54] iii) Real life instances Instances from this class are real life instances from practical applications of the QAP. Among those are the instances of Steinberg [47] instances ste36x) a layout problem for a hospital [13, 24] (instances kra30x) instances corresponding to the layout of typewriter keyboards [7] instances bur26x) Real life problems have in common that the flow matrices have many zero entries and the remaining entries are clearly not uniformly distributed. The matrix entries exhibit a clear structure ....

A.N. Elshafei. Hospital Layout as a Quadratic Assignment Problem. Operations Research Quarterly, 28:167--179, 1977.

....the vertices are the facilities and the weight of the edge between facilities i and j is m ij . Architectural floor planning graph theoretic and not has traditionally been used in the design of industrial plants [DFF85, F92, FR78, Mu94] but also in the design of airports [BFP95] hospitals [E77], universities [DH72] and libraries [FT86] Often m ij is the number of people expected to travel from facility i to facility j. Another important application of MAXIMUM WEIGHT PLANAR SUBGRAPH is circuit layout [Ma78, Mu94] The goal is to lay out a circuit on a one layer board to maximize the ....

A. N. Elshafei, "Hospital Layout as a Quadratic Assignment Problem," Operational Research Quarterly 28 (1977), 167-179.

....and Computer Science, University of Siegen, H olderlinstra e 3, D 57068 Siegen, Germany. E Mail: fpmerz,freislebg informatik.uni siegen.de) of typewriter keyboards and control panels [13] 49] Furthermore, it has been used in facility location problems, in particular hospital planning [43] [23] and in nding locations for new buildings of a campus [18] Besides other domains of engineering and design [32] a new application of the QAP in biology has recently been discovered in the context of indirect gradient analysis (reconstruction of the intensity of some latent environmental factors ....

A. N. Elshafei, \Hospital Layout as a Quadratic Assignment Problem," Operations Research Quarterly, vol. 28, pp. 167-179, 1977.

....One of our major goals in designing and implementing a parallel B B algorithm for QAP has been to enable fast solution of large QAP problems. In Table 6 we report on the solution of the problems of size 15 to 20 from the Nugent test set as well as the solution of the size 19 problem by Elshafei [10] and the size 20 problem by Armour and Buffa [1, 19] Nugent17 and Nugent18 have been obtained from Nugent20 by removing the last 3 resp. 2 facilities and locations. For comparison we give the results obtained by Mautor and Roucairol, which to our knowledge are the best hitherto reported. The ....

A. Elshafei, Hospital Lay-out as a quadratic assignment problem, Oper. Res. Quaterly 28 (1977) p. 167 - 179.

....and a statistical lower bound from Derigs [28, pg. 1037] Derig s bound, based on the method by Golden [29] is lower than the true global minimum with nearly 100 confidence. More specifically, Pr[c c lower ] exp( 50) Problem # Source Size (n) c upper c lower 1 Elshafei [30] 19 17212548 12143024 2 Nugent et al. 26] 30 6124 6057 3 Steinberg [31] 36 9526 8920 Table 2. The Test Problems. In an effort to improve the c upper bounds, we applied the simulated annealing algorithm from previous work [32] to each problem 10 times. Simulated annealing matched the ....

A. Elshafei, 1977. Hospital Layout as a Quadratic Assignment Problem, Operations Research Quarterly 28, 167-179.

....point of the next department on the routing specification. For a given facility, generally a subset of material will visit a department and the routings for each product or batch will be different. Such problems occur in many organizations, including manufacturing cell design [3] hospital design [10], land use planning [6] and construction site management [28] For U.S. manufacturers, between 20 to 50 of total operating expenses are spent on material handling and an appropriate facilities design can reduce these costs by at least 10 to 30 [18] Dr. James A. Tompkins, one of the seminal ....

Elshafei, A. N., "Hospital layout as a quadratic assignment problem." Operational Research Quarterly, 1977 28, 167-179.

.... between location i and location j, and b kl represents the flow of materials from facility k to facility l, the goal is to minimize the quantity C( n X i=1 n X j=1 a ij b (i) j) 2 Pi(n) 1) Many practical problems from such areas like location science [49] architectural design [12, 21], and hardware chip design [45, 21] can be formulated as instances of the QAP; other well known combinatorial optimization problems, such as the traveling salesman problem and the graph partitioning problem, are special cases of the QAP [14] Since the QAP is a NP hard problem [20] exact solution ....

A. N. Elshafei, "Hospital Layout as a Quadratic Assignment Problem," Operations Research Quarterly, vol. 28, pp. 167--179, 1977.

....or flow matrix B = b kl ) describes the dependence or the interactions between plants k and l. The linear term can be interpreted as building or running costs for locating plant i at site k. There are many applications for this allocation problem with spatial interactions. For example, [9] used QAP for hospital planning while in [5] the QAP was applied for the design of typewriter keyboards for minimizing the expected time of typing a text. For other applications, the reader is referred to a recent overview article about QAP by Burkard [6] Many well known combinatorial ....

A. N. ELSHAFEI. Hospital lay-out as a quadratic assignment problem. Operational Research Quarterly, 28:167--179, 1977. 50

....B B algorithm solving the Quadratic Assignment Problem. The Quadratic Assignment Problem (QAP) is a combinatorial optimization problem introduced by Koopmans and Beckman, in 1957, 23] It has numerous and various applications, such as location problems, VLSI design [36] architecture design [14], The objective of QAP is to assign n units to n sites in order to minimize the quadratic cost of this assignment, which depends both on the distances between the sites and on the flows between the units. We use the algorithm of Mautor and Roucairol [32] Their algorithm uses the depth first ....

A. Elshafei. Hospital layout as a quadratic assignment problem. Operational Research Quarterly, 28:167--179, 1977.

....of N . One of the major applications of the QAP is in location theory where the matrix F = f ij ) is the flow matrix, i.e. f ij is the flow of materials from facility i to facility j, and D = d kl ) is the distance matrix, i.e. d kl represents the distance from location k to location l [2, 3, 5]. The contribution to the total cost of simultaneously assigning facility i to location k and facility j to location l is f ij Delta d kl . The objective is to find an assignment of all facilities to all locations (i.e. a permutation p 2 Pi N ) such that the total cost of the assignment is ....

A. Elshafei, Hospital layout as a quadratic assignment problem, Operations Research Quarterly, 28 (1977), pp. 167--179.

....a non deterministic hill climbing procedure, with many other well know heuristics (see [28] for more details) Experiments were run on IBM compatible PCs with a 80286 Intel processor, and were stopped after one hour time. The test problems used are those known as Nugent problems [29] Elshafei [15], and Krarup [25] As can be seen in Table V, the performance of AS was always very good [5] Ant system always found a result within 5 of the best known, while AS with local optimization always found, except for the Nugent 30 problem, the best known solution. This application is described in ....

Elshafei A.E., "Hospital Layout as a Quadratic Assignment Problem", Operational Research Quarterly, 28, 167--179, 1977.

....of N . One of the major applications of the QAP is in location theory where the matrix F = f ij ) is the flow matrix, i.e. f ij is the flow of materials from facility i to facility j, and D = d kl ) is the distance matrix, i.e. d kl represents the distance from location k to location l [9, 10, 21]. The cost of simultaneously assigning facility i to location k and facility j to location l is f ij d kl . The objective is to find an assignment of all facilities to all locations (i.e. a permutation p 2 Pi N ) such that the total cost of the assignment is minimized. Throughout this paper we ....

....Throughout the experiment we used the following parameters: ffl ff = 0:5 ffl fi = 0:1 ffl maxiter = 100; 000. By using the same parameter setting we also illustrate the robustness of this approach. We tested the GRASP implementationon most of the problem classes in QAPLIB: BUR [6] CHR [8] ELS [10], ESC [11] KRA [22] NUG [30] ROU [32] SCR [37] SKO [39] and STE [40] The only class left out was CAR [7] which has QAP instances with a nonzero linear part and cannot be handled by our current GRASP implementation. We also tested the GRASP on two new classes of QAP test problems, with known ....

A. Elshafei, Hospital layout as a quadratic assignment problem, Operations Research Quarterly, 28 (1977), pp. 167--179.

....the vertices are the facilities and the weight of the edge between facilities i and j is m ij . Architectural floor planning graph theoretic and not has traditionally been used in the design of industrial plants [DFF85, Fo92, FR78, Mu94] but also in the design of airports [BFP95] hospitals [E77], universities [DH72] and libraries [FT86] Often m ij is the number of people expected to travel from facility i to facility j. Another important application of MAXIMUM WEIGHT PLANAR SUBGRAPH is circuit layout. Ma78, Mu94] The goal is to lay out a circuit on a one layer board to maximize the ....

A. N. Elshafei, "Hospital Layout as a Quadratic Assignment Problem," Operational Research Quarterly 28 (1977), 167-179.

....of the AS with a local optimizing routine, with many other well know heuristics (see [28] for more details) Experiments were run on IBM compatible PCs with a 80286 Intel processor, and were stopped after one hour time. The test problems used are those known as Nugent problems [29] Elshafei [15], and Krarup [25] As can be seen in Table V, the performance of AS was always very good. Ant system always found a result within 5 of the best known, while AS with local optimization always found, except for the Nugent 30 problem, the best known solution. Table V. Comparison of the AS with other ....

Elshafei A.E., "Hospital Layout as a Quadratic Assignment Problem", Operational Research Quarterly, 28, 167--179, 1977.

.... Parallel Branch and Bound for QAP 1 Introduction The Quadratic Assignment Problem (QAP) is a combinatorial optimization problem introduced by Koopmans and Beckman, in 1957, 12] It has numerous and various applications, such as location problems, VLSI design [18] architecture design [9], The objective is to assign n units to n sites in order to minimize the quadratic cost of this assignment, which depends both on the distances between the sites and on the flows between the units. It can be formulated as follows. Given two (n Theta n) matrices, F = f ij ) where f ij is the ....

.... the computational results is as follows : ffl Nugent et al., 18] classical problems for QAP of sizes n = 12, n = 15, and n = 16 (the flow matrix is extracted from the problem of size 20 and the sites are located on a 4 Theta 4 square) ffl Elshafei : hospital layout problem of size 19 from [9], ffl Scriabin and Vergin : economic layout problem of size 20 [23] from Armour and Buffa [1] 5.1 Computational Results We compared the results obtained by our method with those obtained by one of the fastest sequential algorithms (Burkard and Derigs, 1980 [4] and by the two previously most ....

A. Elshafei. Hospital layout as a quadratic assignment problem. Operational Research Quarterly, 28:167--179, 1977.

....the vertices are the facilities and the weight of the edge between facilities i and j is m ij . Architectural oor planning graph theoretic and not has traditionally been used in the design of industrial plants [DFF85, F92, FR78, Mu94] but also in the design of airports [BFP95] hospitals [E77], universities [DH72] and libraries [FT86] Often m ij is the number of people expected to travel from facility i to facility j. Another important application of MAXIMUM WEIGHT PLANAR SUBGRAPH is circuit layout [Ma78, Mu94] The goal is to lay out a circuit on a one layer board to maximize the ....

A. N. Elshafei, \Hospital Layout as a Quadratic Assignment Problem," Operational Research Quarterly 28 (1977), 167-179.

....In particular, we show that the best choice of a local search procedure depends strongly on the instance type. 1 Introduction The Quadratic Assignment Problem (QAP) is an important problem in theory and practice. Many practical problems like backboard wiring [35] Campus and Hospital Layout [12, 17], Typewriter keyboard design [7] Scheduling [23] and many others [16, 26] can be formulated as QAPs. The QAP can best be described as the problem of assigning a set of facilities to a set of locations with given distances between the locations and given flows between the facilities. The goal then ....

....of the distance matrices [40] among those are instances nugxx and skoxx in Section 4.4) iii) Other instances contained in QAPLIB are real life instances from practical applications of the QAP. Among those are the instances of Steinberg [35] instances ste36x) layout problem for a hospital [17, 25] (instances kra30x) instances corresponding to the layout of typewriter keyboards [7] instances bur26x) and a new type of instances proposed in [40] The real life problems have in common that the flow matrices have many zero entries and the remaining entries are clearly not uniformly ....

A.N. Elshafei. Hospital Layout as a Quadratic Assignment Problem. Operations Research Quarterly, 28:167--179, 1977.

....12) Chr22b 22 6194 (OPT) p = 10; 19; 3; 1; 20; 2; 6; 4; 7; 8; 17; 12; 11; 15; 21; 13; 9; 5; 22; 14; 18; 16) Chr25a 25 3796 (OPT) p = 25; 12; 5; 3; 18; 4; 16; 8; 20; 10; 14; 6; 15; 23; 24; 19; 13; 1; 21; 11; 17; 2; 22; 7; 9) QAPLIB A Quadratic Assignment Problem Library 4 A.N. Elshafei [11] The data describe the distances of 19 different facilities of a hospital and the flow of patients between those locations. name n feas. solution permutation Els19 19 17212548 (OPT) 27] p = 9; 10; 7; 18; 14; 19; 13; 17; 6; 11; 4; 5; 12; 8; 15; 16; 1; 2; 3) B. Eschermann and H.J. Wunderlich ....

A.N. ELSHAFEI. Hospital layout as a quadratic assignment problem. Operations Research Quarterly, 28:167--179, 1977.

....[14] and is also used in Ant Colony System [15] the successor of Ant Q. The main effect of this selection rule is to yield a faster detection of high quality solutions by the algorithm. We apply the modified MMAS to the Traveling Salesman Problem [24, 31] and the Quadratic Assignment Problem [11, 23] that models many practical problems arising in Location Science. MMAS has been applied to TSP before in [34, 33] but the results presented here are significantly better, the application of MMAS to the QAP is new. Both problems are NP hard [17] but whereas very large Euclidean TSPs can be solved ....

A.N. Elshafei. Hospital Layout as a Quadratic Assignment Problem. Operations Research Quarterly, 28:167--179, 1977.

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A. N. Elshafei, "Hospital Layout as a Quadratic Assignment Problem," Operations Research Quarterly, vol. 28, pp. 167--179, 1977.

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A.E.Elshafei. Hospital Layout as a Quadratic Assignment Problem, Operations Research Quarterly, 28, 1977, 167--179.

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