Scheduling the Operations of an Integrated Production- Distribution Process Lei Lei Rutgers Business School, Rutgers University, Newark, NJ, USA, llei@andromeda.rutgers.edu Wanpracha Art Chaovalitwongse Department of Industrial and Systems Engineering, Rutgers University, Piscataway, NJ, USA, wchaoval@rci.rutgers.edu Selim Bora Center for Operations Research, Rutgers University, Piscataway, NJ, USA, sbora@eden.rutgers.edu We consider a variation of the integrated scheduling problem where the operations of a capacitated facility and a fleet of heterogeneous vessels must be sequenced to minimize the operating cost dur- ing a multi-period production and distribution process. We prove the NP-hardness of the problem, analyze the problem properties, and propose a partial linear-programming relaxation based heuris- tic approach. We also derive an error bound of this heuristic for a special case of the problem. Fi- nally, the empirical observations on the computational performance of the heuristic under general cases are reported. Keywords: Integrated production and distribution, heterogeneous vessels, berthing and discharg- ing time, multi-level capacities, heuristic, error bound, empirical performances. 1. Introduction The cost to produce and deliver gasoline products to the market consists of three major compo- nents: the cost of crude oil to refiners, the cost of refinery processing, and the cost of marketing and distribution [13]. As the U.S. retail gasoline prices continue to rapidly elevate, effectively co- ordinating the demand and supply of gasoline products has become ever more crucial to large oil companies [6]. Our study is focused on the demand-supply coordination problem motivated by operational is- sues faced by a major U.S. corporation in petrochemical industry. The company operates a number of capacitated oil refineries and uses its own and chartered vessels to distribute the gasoline prod- ucts to discharging/demand locations along the coastline of North America. Each refinery is capa- ble of producing a number of products for its commercial and industry users and carries invento- ries for those produced but not yet being distributed. These inventories also serve as reservoirs to supply the demands during peak seasons. However, none of the inventories can exceed its maxi- mum holding capacity as which would halt the production. Each discharging location carries its own inventories and serves as a depot of distribution for the local market. Since vessels are expen- sive in both variable and fixed costs, any inefficiency in the supply process could result in a sub- stantial operating cost. The integrated production and distribution scheduling problem encountered in this process is very complicated due to the involvement of heterogeneous vessels (e.g., in terms of their loading capacities, discharging and berthing times, and operating costs) and the fact that each vessel has multi-level of loading capacities such that a load beyond the normal/base capacity will result in an extra overload cost. Practical issues faced by the company include how much should be produced in each time period (typically 2 weeks), which vessel should deliver to which depot in which time period, whether a particular vessel trip should carry an extra load and by how much, and what should be the ending inventory at a depot in a particular period, etc. Due to high distribution cost of gasoline products, an effectively integrated production and distribution sched- ule could help the company to further improve the profit of its supply chain and to strengthen its competitive advantage in the market place. 316 MISTA 2007