News at Smith

Integrated Scheduling of Production and Distribution Operations

May 01, 2005


Research by Zhi-long Chen

With increasing competition, companies in the computer industry normally deliver assembled and packaged computers to customers within two to three business days. The food catering industry works much the same way; since food needs to be kept fresh, food preparation can only take place after the orders have been placed. Completed orders are usually delivered within a few hours. Many companies driven by direct orders, such as those in the computer industry and food catering services, produce and deliver to customers directly without holding intermediate inventories. These companies are confronted with the difficult task of optimizing both their customer service level as well as total distribution cost.

Zhi-Long Chen, professor of decision and information technologies at the Smith School of Business, with George L. Vairaktarakis, professor of operations at the Weatherhead School of Management at Case Western Reserve University, examined an integrated scheduling model of production and distribution operations. They conclude that in many instances, companies can save on costs and improve customer service by implementing an integrated model instead of a sequential model where production and distribution operations are scheduled sequentially.

When production operations and distribution operations are linked together directly without any intermediate step customer service and cost become the chief concern of these companies. For the study, Chen and Vairaktarakis define customer service level as a function of the times when the jobs are delivered to the customers and the distribution cost as consisting of a fixed charge and a variable cost proportional to the total distance of the route taken by the shipment.

“Generally, the shorter the lead times, the higher the service level. However, to achieve shorter lead times, more delivery shipments may have to be used and this will inevitably result in higher distribution cost,” notes Chen. Thus, companies will be forced to decide on how best to optimize the tradeoff between the distribution cost and the customer service level when coordinating their production and distribution operations.

Chen’s research model aims to integrate production scheduling for job processing in the processing facility with distribution scheduling and routing for delivery of completed jobs from the processing facility to the customers. Little work has been done on the integration of production and distribution scheduling, although problems associated with these two operations have been extensively studied by other researchers. Past research has typically considered customer service as their objective without accounting for distribution costs or assumed that jobs can be delivered to their customers almost immediately without any transportation delay.

To empirically test their integrated scheduling model, Chen studied two classes of problems that are commonly used in practice: (1) customer service as measured by the average time when the jobs are delivered to the customers; and (2) customer service as measured by the maximum time when the jobs are delivered to the customers. Two machine configurations - single-machine and parallel machine – in the processing facility are considered.

Chen first modeled these two classes of problems as optimization models (or essentially mathematical problems), which comprise of an objective function to be optimized and several constraints such as production capacity and distribution capacity that need to be satisfied. Depending on how difficult the problems were, they proposed a set of algorithms that could enable them to find optimal solutions quickly for easy problems and utilized heuristics (i.e., algorithms which may not produce optimal solutions) for more difficult problems. For each heuristic, Chen analyzed theoretically how good the heuristic was by looking at its worst-case and asymptotic performance. He also conducted computational studies to evaluate the average performance of the heuristic.

In addition to studying these two classes of problems, Chen examined the potential benefits that could be derived from the proposed integrated model as compared with a standard, sequential model where production and distribution operations are scheduled sequentially and separately. Chen observes that most companies are still using sequential approaches in their supply chain management because they are reasonably easier to implement. On the other hand, using an integrated approach may require the companies to facilitate coordination among their various departments, which can be demanding in practice. This part of the study provides evidence that significant benefits such as cost-saving and customer service improvement can be achieved by integration in many cases.

Chen and Vairaktarakis’s work contributes to the current supply chain management literature by creating an integrated model that companies can use to achieve better customer service while reducing their supply chain costs. “I hope our work will be used by supply chain software providers such as SAP and Manugistics to enhance their business models and solution tools. In turn, companies who use supply chain decision support systems from these providers can benefit from the integrated approach,” says Chen.

Chen and Vairaktarakis’ work will appear in an article to be published in an upcoming issue of the Journal of Management Science. For further information, contact

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