Integrating Pricing And Distribution Decisions In Multiple Markets

This paper deals with the simultaneous optimization of prices and shipment quantities in a supply network when the supplier has the market power to set prices, thereby influencing demand directly.  We focus on the distribution stage of the supply chain where the firm’s products are shipped from several  locations (plants, warehouses) to various independent markets, and address the following questions: (i) what is the best price at each market?, and (ii) what is the best distribution plan given these prices?   The combined problem can be modeled as a nonlinear optimization problem.  For its solution, we propose an iterative linear programming approach that utilizes shadow price information from a series of successive transportation problems.  To evaluate the heuristic’s effectiveness, we compare it with a “brute-force” enumeration using a grid-search.  The grid-search is implemented on a spreadsheet with a programming loop to facilitate repeated invocation of the transportation problem solver routine

A Production Planning Model For Reconfigurable Lines

A key indicator of the efficiency of a production line is cyclic idle time.  Manufacturers use heuristic line balancing techniques to determine the allocation of elemental tasks to workers so as to minimize labor costs.  The productive, i.e. non-idle, portion of each cycle then reflects the efficiency of the line.  Line balancing techniques determine the allocation of tasks based on a pre-specified throughput.  When demand changes however, the line may have to be reconfigured to reflect the new desired flow rate, resulting possibly in a lower efficiency and a higher per-unit labor cost.  This raises an interesting question: should one use a flow rate that corresponds to the higher efficiency, handling any mismatch with demand through the use of inventory or backordering, or should the aim be to match flow rate precisely with demand rate even though the resulting efficiency might be lower?  This paper proposes an answer to this question by embedding line balance and efficiency into the framework of a well-known production planning model.  A heuristic method for solving the extended model is developed, and its application demonstrated using numerical examples.