استفاده از کامیون-موجودی-هزینه برای به دست آوردن راه حل هایی برای مدلهای لجستیک چند دوره ای

The antithetic opposition between the cost of inventory and the fixed cost of transportation, which leads to multiple alternate near-optima, can be a primary contributor to the computational intractability of the mixed integer program for a two-echelon multi-period distribution system. To alleviate the computational intractability, we develop a heuristic procedure that determines the deployments of trucks to, and the consequent levels of inventory at, the second echelon thereby reducing the number of variables in the model. The reduced model is shown to identify near optimal solutions for the entire distribution system in negligible computation time.

The deployment of trucks to a demand point over time and their loading, which also determines inventory levels, is central to operational planning in a distribution system. Depending on the relative magnitudes of the cost of truck deployment and the cost of inventory, demand over time at a demand point is satisfied by shipments of product via trucks and/or by holding product in inventory. A truck may be any unit of transport that is used in an industry such as a trailer, container, or metric-ton. We consider the use of a mixed integer programming model to obtain shipment plans and inventory levels to meet demand at each demand point, in each time period, for a two-echelon multi-period distribution system. The model optimizes the total fixed cost of transporting product and the total cost of carrying inventory at both echelons. The inventory costs in the model take into account both the cost of the item held in inventory and the granularity of the time period over which the inventory is held. In multi-echelon, multi-period distribution models the cost of transportation is mitigated by carrying inventory—the precise motivation for extending the planning horizon to a multi-period one. The placement of trucks over time to demand points is impacted by the relationship between the fixed cost of deploying a truck and the cost of carrying inventory. The multitudes of alternative deployments to each demand point can lead to the computational intractability of such models. As such, much of the literature on multi-echelon, multi-period distribution models has focused on heuristic solution techniques. The heuristic procedure that is developed in this paper stems from the observation that the specific levels of demand at demand points dictate the most suitable deployment of trucks over time, which allows the decoupling of the second echelon from the earlier echelon of distribution. The heuristic explicitly addresses the tradeoff between the fixed cost of transportation and the cost of carrying inventory to determine deployments to each demand point, thereby reducing the number of variables in the model. This heuristic decomposition pre-determines the second echelon deployments which are then incorporated in the two-echelon distribution model to obtain a plan for the entire system with computational ease. In Section 2, we present a review of the related literature. In Section 3, we present the integer programming model for a two echelon multi-period logistics system, and explain how its computational intractability is due to the existence of alternative deployments for each demand point arising from the tradeoff between transportation and inventory costs. This tradeoff is explained by introducing the constructs of load and truck-inventory-cost. In Section 4, we present the heuristic and in Section 5, we report the findings of a computational study to validate the heuristic. Concluding remarks are made in Section 6.

Intrinsic relationships between cost contributors, which are not reflected in the constraints in a model, capture tradeoffs that can be used to identify partial solutions resulting in a variable reduction of the model. The heuristic variable reduction proposed in this paper rests on a separation of the structural components of the feasible region—the two echelons of the distribution system—and a heuristic logic that uses the relationship between cost contributors to determine a solution for the second echelon. An algorithm to determine the deployments of trucks in each time period to each demand point at the second echelon uses the construct of truck-inventory-cost to evaluate the tradeoff between the costs of transportation and inventory. The identified deployments lead to a variable reduction in the model, thereby producing near-optimal solutions to the model within a few seconds of computation time. The heuristic variable reduction of the model can be useful in an operational setting since near-optimal solutions can be identified in negligible computation time.