Facility location allocation

This chapter introduces the reader to elementary concepts of modeling, generic formulations for nonlinear and mixed integer optimization models, and provides some illustrative applications. Section 1.1 presents the definition and key elements of mathematical models and discusses the characteristics of optimization models. Section 1.2 outlines the mathematical structure of nonlinear and mixed integer optimization problems which represent the primary focus in this book. Section 1.3 illustrates applications of nonlinear and mixed integer optimization that arise in chemical process design of separation systems, batch process operations, and facility location/allocation problems of operations research. Finally, section 1.4 provides an outline of the three main parts of this book. 

Part 3 of this book presents a number of major developments and applications of MINLP approaches in the area of Process Synthesis. The illustrative examples for MINLP applications, presented next in this section, will focus on different aspects than those described in Part 3. In particular, we will consider the binary distillation design of a single column, the retrofit design of multiproduct batch plants, and the multicommodity facility location/allocation problem. 

The multicommodity capacity facility location-allocation problem is of primary importance in transportation of shipments from the original facilities to intermediate stations and then to the destinations. In this illustrative example we will consider such a problem which involves I plants, J distribution centers, K customers, and P products. The commodity flow of product p which is shipped from plant i, through distribution center j to customer k will be denoted by the continuous variable z tp. It is assumed that each customer k is served by only one distribution center j. Data are provided for the total demand by customer k for commodity p, Dkp, the supply of commodity p at plant i denoted as Sip, as well as the lower and upper bounds on the available throughput in a distribution center j denoted by V " and Vf7, respectively. 

Problem formulations [ 1-3 ] for designing lead-generation library under different constraints belong to a class of combinatorial resource allocation problems, which have been widely studied. They arise in many different applications such as minimum distortion problems in data compression (11), facility location problems (12), optimal quadrature rules and discretization of partial differential equations (13), locational optimization problems in control theory (9), pattern recognition (14), and neural networks... 

We will save the discussion of production planning models, however, for Chapter 5, based on the similarity of that problem to the facility location and location-allocation problems discussed in that chapter. Also in Chapter 5, we introduce the notion of risk pooling, which is a means of reducing the safety stock required to support a target service level by aggregating demands across multiple sources, for example across multiple customers or customer regions supported by a single facility. 

Each depot can be linked to a single hub, called single-allocation, or it can be linked to more than one hub, called multiple-allocation. Both situations occur in practice. As seen in Fig. 5.7, LTL trucking networks have each depot assigned to a single break bulk terminal (hub) for load consolidation. Passenger airline networks, on the other hand, have flights scheduled from many non-hub cities to a few hubs. Also note that capacity limitations at hubs may force multiple-allocation, as seen in many facility location problems. 

The concept of level r facility is introduced in Snyder and Daskin (2005) to handle sequential allocation of facilities to customers in an incapacitated facility location problem. In the model presented here, a level 1 supplier is responsible of supplying the products as long as there is no disruption and is named as a primary supplier. In case of a disruption, a backup supplier replaces the failed primary supplier. A buyer can have only one primary supplier for a given product. Remaining suppliers are then assigned as backups at the m levels, where m < m. Other parameters used in the sequential supplier assignment (SSA) model are given in Table 10.2. 

Use optimization for facility location and capacity allocation decisions. 

In this chapter, we start with the broad supply chain design discussed in Chapter 4 and focus on the fundamental questions of facility location, capacity allocation, and market allocation when designing a supply chain network. We identify and discuss the various factors that influence the facility location, capacity, and market allocation decisions. We then establish a framework and discuss various solution methodologies for network design decisions in a supply chain. 

In the next section, we discuss methodologies for making facility location and capacity allocation decisions during Phases II through IV. 

A manager s goal when locating facilities and allocating capacity should be to maximize the overall profitability of the resulting supply chain network while providing customers with the appropriate responsiveness. Revenues come from the sale of product, whereas costs arise from facilities, labor, transportation, material, and inventories. The profits of the firm are also affected by taxes and tariffs. Ideally, profits after tariffs and taxes should be maximized when designing a supply chain network. 

Use optimization for facility location and capacity allocation decisions. Gravity location models identify a location that minimizes inbound and outbound transportation costs. They are simple to implement but do not account for other important costs. Network optimization models can include contribution margins, taxes, tariffs, production, transportation, and inventory costs and are used to maximize profitability. These models are useful when locating facilities, allocating capacity to facilities, and allocating markets to facilities. 

The article reviews in detail the tectonic division of Georgian territory, geographic locations of the areas allocated for underground gas storage (UGS) facilities and their lithological and structural features and peculiarities... 

Sandia National Laboratories is situated south of Albuquerque, New Mexico, within the boundaries of KAFB, a U.S. Air Force (USAF) military reservation (Figure 1.3-1). SNL/NM facilities are located on DOE-ieased land allocated within KAFB. KAFB covers approximateiy 52,000 acres. 

---