Solving a continuous periodic review inventory-location allocation problem in vendor-buyer supply chain under uncertainty
In this work, a mixed-integer binary non-linear two-echelon inventory problem is formulated for a vendor-buyer supply chain network in which lead times are constant and the demands of buyers follow a normal distribution. In this formulation, the problem is a combination of an (r, Q) and periodic review policies based on which an order of size Q is placed by a buyer in each fixed period once his/her on hand inventory reaches the reorder point r in that period. The constraints are the vendors’ warehouse spaces, production restrictions, and total budget. The aim is to find the optimal order quantities of the buyers placed for each vendor in each period alongside the optimal placement of the ve…
An Investigation of the Robustness in the Travelling Salesman Problem Routes Using Special Structured Matrices
In this study, the robustness of the Travelling Salesman Problem (TSP) routes is investigated by recognising the special combinatorial structures of Kalmanson matrices. A recognition algorithm encompassing three procedures based on combinatorial and linear programming (LP) is developed and executed on several randomly generated instances. These procedures produce three lower bounds which provide guarantees on the optimality of the solutions. Computational experiments show that the proposed LP-based procedure performs efficiently well across all problem dimensions and provides the best lower bounds to the TSP. This is supported by an average deviation of less than 7% between the TSP tour len…