Tiru S. Arthanari

On the abstraction method for the container relocation problem

The container relocation problem or the blocks relocation problem is a classic combinatorial optimisation problem that occurs in day-to-day operations for facilities that use block stacking systems. A typical place where this problem arises is a container terminal where containers can be stacked vertically in order to utilise the scarce resource of yard surface, thus at times resulting in the unproductive reshuffling moves for containers stacked above the target container for retrieval. Due to the problem class being NP-hard, a number of studies on this topic propose heuristic approaches to solve this problem. There are a few exact methods (search-based algorithms or mathematical programming) proposed for this problem but the feasible problem size of such methods is quite restricted, limiting their practical significance. In this paper, we propose a new insight into reducing the search space of this problem by the abstraction method. Our main contribution to the existing literature is two-fold: the reduction in the search space by the abstraction method and the bidirectional search using the pattern database. Our computational results confirm that our approach enables instances of a near-practical size to be solved optimally within a reasonable computation time. HighlightsThis work achieves a reduction of the search space via abstraction method for CRP.This work defines and uses pattern database in relation to CRP.Searching from both current and goal state results in bidirectional search for CRP.Abstraction method is a general framework to improve existing search algorithms.

Third-party purchase: an empirical study of Chinese third-party logistics users

Purpose – Third-party purchase (3PP) is a new value-added service offered by third-party logistics (3PL) providers. The purpose of this paper is to examine the perception of 3PP service from the perspective of 3PL users. Design/methodology/approach – The authors conducted a survey of Chinese 3PL users and received 242 usable responses. The authors then employed structural equation modeling to test the conceptual model. Findings – The authors found that the likelihood of 3PL users using a 3PP service is significantly associated with uncertainty, but not with asset specificity or frequency or transaction size. 3PP usage is significantly associated with value-to-client. Originality/value – This research is the first survey study of 3PP as a value-added service offered by 3PL providers, from the perspective of 3PL users. The findings suggest that 3PL users are very positive about the value of 3PP service. The 3PP market is still in its infancy but it has great potential, especially for commodity items that ha...

Outsourcing purchasing services by Third Party Logistics providers: a conceptual model

The international markets of third party logistics (3PL) are quite competitive. Most 3PL providers offer the basic services, but rarely perform value-added activities. The primary focus of this research is on third party purchase as value-added services that can be beneficially offered by 3PL providers. This paper mainly discusses transaction cost theory, third party logistics, and group purchasing organisation. A proposed framework for evaluating third party purchase offered by 3PL providers is given based on transaction cost theory.

An empirical study of third-party purchase: New Zealand users’ perspective

ABSTRACT This article investigates the potential for third-party purchase (3PP) services offered by third-party logistics (3PL) providers, from the perspective of 3PL users, based on transaction cost analysis. We conducted a survey of New Zealand 3PL users and received 163 usable responses. Structural equation modelling was used to test the conceptual model. We found that 3PL users are more likely to adopt 3PP service when there is greater uncertainty. Asset specificity, frequency and transaction size do not have a significant relationship with 3PP service adoption. However, 3PP service is significantly related to the value-to-client and benefit-to-3PL provider. This study is pioneering research on 3PP service as a value-added service offered by 3PL providers from the perspective of 3PL users. The findings suggest that offering 3PP service will provide mutual benefits and value for both 3PL users and their 3PL providers.

Comparisons of QP and LP Based Learning from Empirical Data

The quadratic programming (QP) and the linear programming (LP) based method are recently the most popular learning methods from empirical data. Support vector machines (SVMs) are the newest models based on QP algorithm in solving the nonlinear regression and classification problems. The LP based learning also controls both the number of basis functions in a neural network (i.e., support vector machine) and the accuracy of learning machine. Both methods result in a parsimonious network. This results in data compression. Two different methods are compared in terms of number of SVs (possible compression achieved) and in generalization capability (i.e., error on unseen data).

Developing third-party purchase (3PP) services: New Zealand third-party logistics providers’ perspectives

Purpose This paper aims to examine the opportunity for third-party logistics providers (3PLs) to develop further value-added services for their clients, focused on purchasing. The provider perspectives on third-party purchase (3PP) services are examined in conjunction with their business environment, with a survey informed by transaction cost economics. Design/methodology/approach New Zealand 3PL providers were surveyed, and 166 responses were received. Structural equation modeling was used to test the conceptual model. Findings From the perspective of 3PL providers, uncertainty, frequency and transaction size, but not asset specificity, are significantly associated with client value from a 3PP service. While asset specificity in investments is not required by 3PLs, they need a high frequency of orders, sufficient order size and low levels of uncertainty as supporting conditions for the development of 3PP services. Research limitations/implications The sample focuses on 3PL providers and therefore does not address the behavioral characteristics of users or customers of the services. Originality/value This study shows that 3PP services may be further developed by 3PL providers to improve the value offered to their clients.

Traveling Salesman Problem and Membership in Pedigree Polytope - A Numerical Illustration

Symmetric traveling salesman problem (STSP), a difficult combinatorial problem is formulated as a multistage insertion (MI) decision problem in Arthanari and Usha (2000). MI formulation is a compact 0-1 formulation for STSP. MI has given rise to the definition of a combinatorial object called pedigree. Arthanari (2008) contains a necessary condition for a MI-relaxation solution to be expressible as a convex combination of pedigrees. The existence of a multicommodity flow with the optimum value equal to unity over some layered network is checked for this purpose. This paper walks through an illustrative example to show the construction of such a network and the procedures involved in checking the necessary condition. Another important feature of this example is it brings out the need for discarding some arcs from the network called dummy arcs, for the correctness of the necessary condition for membership.

Study of the pedigree polytope and a sufficiency condition for nonadjacency in the tour polytope

The pedigree is a combinatorial object defined over the cartesian product of certain subsets of edges in a complete graph. There is a 1–1 correspondence between the pedigrees and Hamiltonian cycles (tours) in a complete graph. Linear optimization over Hamiltonian cycles, also known as the symmetric traveling salesman problem (STSP) has several 0–1 integer and mixed integer formulations. The Multistage Insertion formulation (MI-formulation) is one such 0–1 integer formulation of the STSP. Any solution to the MI-formulation is a pedigree and vice versa. However the polytope corresponding to the pedigrees has properties not shared by the STSP polytope. For instance, (i) the pedigree polytope is a combinatorial polytope, in the sense, given any two nonadjacent vertices of the polytope W1,W2, we can find two other nonadjacent vertices, W3,W4, such that W1+W2=W3+W4 and (ii) testing the nonadjacency of tours is an NP-complete problem, while the corresponding problem for the pedigrees is strongly polynomial. In this paper we demonstrate how the study of the nonadjacency structure is useful in understanding that of the tour polytope. We prove that a sufficiency condition for nonadjacency in the tour polytope is nonadjacency of the corresponding pedigrees in the pedigree polytope. This proof makes explicit use of properties of both the pedigree polytope and the MI-relaxation problem.

The multi-flow necessary condition for membership in the pedigree polytope is not sufficient- a counterexample

The multistage insertion formulation (MI) for the symmetric traveling salesman problem (STSP), gives rise to a combinatorial object called pedigree. Pedigrees are in one-to-one correspondence with Hamiltonian cycles. The convex hull of all the pedigrees of a problem instance is called the pedigree polytope. The MI polytope is as tight as the subtour elimination polytope when projected into its two-subscripted variable space. It is known that the complexity of solving a linear optimization problem over a polytope is polynomial if the membership problem of the polytope can be solved in polynomial time. Hence the study of membership problem of the pedigree polytope is important. A polynomially checkable necessary condition is given by Arthanari in [5]. This paper provides a counter example that shows the necessary condition is not sufficient.

On Pedigree Polytopes and Hamiltonian Cycles

Abstract Polyhedral combinatorics deals with solving combinatorial optimisation problems using the polytope whose vertices are the characteristic vectors of the combinatorial objects of interest. Given the complete graph with n vertices, Kn, with rational edge weights, the symmetric travelling salesman problem (STSP) is to find a Hamiltonian cycle such that the total edge weight of the Hamiltonian cycle is as small as possible. Polyhedral approach to solve STSP, starts with the standard tour poly-tope, Qn, whose vertices are the characteristic vectors of Hamiltonian cycles, and given a point from a polytope, P containing Qn, it tries to find a separating hyperplane that separates the point and Qn or shows that the point is in Qn. In this paper we define a combinatorial object called pedigree, and study an alternative polytope, called Pedigree polytope. Pedigrees are in one-to-one correspondence with the Hamiltonian cycles on Kn. Interestingly the pedigree polytope seems to differ from Qn with respect to the complexity of testing whether two given vertices of the polytope are non-adjacent. A polynomial time algorithm is given for non-adjacency testing in pedigree polytope, whereas the corresponding problem is known to be NP-complete for Qn. In this paper we discuss some properties of the pedigree polytope and illustrate with examples.