Inventory Routing Investigations
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The elimination of distribution inefficiencies, occurring due to the timing of customers' orders is an important reason for companies to introduce vendor managed inventory programs. By managing their customers' inventories, suppliers may be able to reduce demand variability and therefore distribution costs. We develop technology to measure the effectiveness of distribution strategies. We develop a methodology that allows the computation of tight lower bounds on the total mileage required to satisfy customer demand over a period of time. As a result, companies will be able to gain insight into the effectiveness of their distribution strategy. This technology can also be used to suggest desirable delivery patterns and to analyze tactical and strategic decisions. Secondly, we study the inventory routing problem with continuous moves (IRP-CM). The typical inventory routing problem deals with the repeated distribution of a single product, from a single facility, with an unlimited supply, to a set of customers that can all be reached with out-and-back trips. Unfortunately, this is not always the reality. We introduce the IRP-CM to study two important real-life complexities: limited product availabilities at facilities and customers that cannot be served using out-and-back tours. We need to design delivery tours spanning several days, covering huge geographic areas, and involving product pickups at different facilities. We develop a heuristic and an optimization algorithm to construct distribution plans. The heuristic is an innovative randomized greedy algorithm, which includes linear programming based postprocessing technology. To solve the IRP-CM to optimality, we give a time-discretized integer programming model and develop a branch-and-cut algorithm. As instances of time-discretized models tend to be large we discuss several possibilities for reducing the problem size. We introduce a set of valid inequalities, called delivery cover inequalities, in order to tighten the bounds given by the LP relaxation of the time-discretized model. We also introduce branching schemes exploiting the underlying structure of the IRP-CM. An extensive computational study demonstrates the effectiveness of the optimization algorithm. Finally, we present an integrated approach using heuristics and optimization algorithms providing effective and efficient technology for solving inventory problems with continuous moves.