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Motivation
The study was motivated by the supply chain practices of the furniture industry (e.g., IKEA). In the furniture industry, companies purchase wood, veneers and components from contracted material suppliers overseas and then use direct containers or specialized pallets to ship these materials back to processing centers in North America where furniture is manufactured for wholesalers, or retailers to sell to customers in regional markets. Prior to the delivery to demand points, wood and semi-finished wood panels must be cut, glued, sized, sanded, assembled, labeled and packaged at the processing centers (PCs) according to customer specific requirements. The domestic trucks or rails are typically used to transport the finished goods from PCs to different regional markets. In regional markets there are many wholesalers and retailers who request the order quantity, a variety of products, and a delivery due date. It is understandable that customers expect wide selection, products that can be treated or customized on demand, and certainly fast, accurate delivery. The challenge facing furniture companies is providing this level of service cost effectively. Furniture manufacturers not only need to decide on the appropriate number of PCs to be opened, but the optimal assignment of demand points to PCs in order to achieve the best service at minimum cost. The delay in the delivery could lead to lost goodwill and customer dissatisfaction.
We consider a three-stage capacitated supply and distribution network. This network consists of a set of contracted material suppliers, a group of PCs, and many demand points in regional markets. Raw materials, components or semi-finished product needs to be shipped from lumber suppliers to PCs for their customization and final configuration. Then, each demand point receives the order shipped from the PC to which it is assigned. Each material-supplier has a limited production capacity and charges a shipping cost (via chartered vessels) proportional to the shipped quantities. Each PC has a limited processing capacity, processing time per unit, and holding cost. PCs start processing only after all the shipments from assigned material suppliers are received. Each demand point has uncertain demand, receives customized final furniture products from no more than one PC, and requests a due date. If the shipment cannot arrive at a demand point at the specified due date (due to the delay in shipping and/or the limitation of network capacity), a penalty cost proportional to the order size placed by that demand point is imposed. No partial delivery is acceptable. That is, if a demand point receives the furniture, then the order must be fully fulfilled. Both the shipping rate and the transit time between locations on the network are given. The objective is to determine the number of PCs to be opened, and the assignment of the demand points to PCs such that the total shipping and penalty cost is minimized.
Key Terms in this Chapter
Mixed Integer Nonlinear Programming: It refers to mathematical programming with continuous and discrete variables and nonlinearities in the objective function and constraints. The use of MINLP is a natural approach of formulating problems where it is necessary to simultaneously optimize the system structure (discrete) and parameters (continuous). MINLPs have been used in various applications, including the process industry and the financial, engineering, management science and operations research sectors.
Stochastic Programming: Stochastic programming is a framework for modeling optimization problems that involve uncertainty. Stochastic programming models are similar in style but take advantage of the fact that probability distributions governing the data are known or can be estimated. The goal here is to find some policy that is feasible for the possible data instances and maximizes the expectation of some function of the decisions and the random variables ( http://en.wikipedia.org/wiki/Stochastic_programming ).
Probabilistic Constrained Programming: The term probabilistic constrained programming means the same as chance constrained programming, i.e., optimization of a function subject to certain conditions where at least one is formulated so that a condition, involving random variables, should hold with a prescribed probability. The probability is usually not prescribed exactly but a lower bound is given instead which is in practice near certainty (nearly equal to 1). ( Andras Prekopa (1970) AU19: The in-text citation "Andras Prekopa (1970)" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. . On probabilistic constrained programming. Proceedings of the Princeton Symposium on Mathematical Programming. Princeton University Press, Princeton, NJ 1970 AU20: The in-text citation "University Press, Princeton, NJ 1970" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. . pp. 113-138.)
Facility Location Problem: Facility location, also known as location analysis or k center problem, is a branch of operations research and computational geometry concerning itself with mathematical modeling and solution of problems concerning optimal placement of facilities in order to minimize transportation costs, outperform competitors' facilities, etc. ( http://en.wikipedia.org/wiki/Facility_location ).
Make-To-Order Supply Chain: Make-to-order (MTO) is a manufacturing process in which manufacturing starts only after a customer's order is received. Forms of MTO vary, for example, an assembly process starts when demand actually occurs or manufacturing starts with development planning. Manufacturing after receiving customer's orders means to start a pull-type supply chain operation because manufacturing is performed when demand is confirmed, i.e. being pulled by demand ( http://www.lean-manufacturing-japan.com/scm-terminology/mto-make-to-order.html ).
Supply Chain Network Design: Supply Chain Network involves determining following process design: 1) Procurement: Where are your material suppliers and how will you procure raw materials and components; 2) Manufacturing: Where will you locate the factories for manufacturing/assembly and Manufacturing Methodology; 3) Finished goods: Where will you hold inventories, Number of Warehouses, Location of warehouses etc. and how will you distribute to markets - Transportation and Distribution logistics. All above decisions are influenced and driven by Key Driver which is the Customer Fulfillment.
Capacitated Supply and Distribution Network: It refers to the network where each of the material suppliers has their own supply capacities and PCs have their own processing capacities.