Location-Distribution Problem

Let us now consider an integrated example, where both the location decisions and distribution decisions have to be made simultaneously. 

Assume that any two sites can supply all the demands but site 1 can supply customers 1,2, and 4 only site 3 can supply customers 2,3, and 4 while site 2 can supply all the customers. The unit transportation cost from site i to customer j is Qy. For each warehouse. Table 5.5 gives the data on capacity, annual investment, and operating costs. 

Site Capacity Initial Capital Investment ( ) Unit Operating Cost ( ) 

The optimization problem is to select the proper sites for the two warehouses which will minimize the total costs of investment, operation, and transportation. 

Each warehouse site has a fixed capital cost independent of the quantity stored, and a variable cost proportional to the quantity shipped. Thus the total cost of opening and operating a warehouse is a nonlinear function of the quantity stored. Through the use of binary integer variables, the warehouse location-distribution problem can be formulated as an integer program. 

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The balancing process must be in accord with the rotor dynamics, as specified by the operating environment. Unfortunately, the dynamic characteristics are often not properly recognized when the balancing procedure is specified. As a result, the unbalance distribution problem may not be identified not enough planes may be provided sensors may be located at nonoptimum positions, or critical speeds may be overlooked entirely. It is the responsibility of the machinery end user to satisfy himself that the manufacturer has considered ... 

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. 

In a recent article Oh and Karimi (2004) explore the effect of regulations (bilateral and multilateral international trade agreements, import tariffs, corporate taxes in different countries, etc.) on the capacity expansion problem. They point out that barring the work of Papageorgiou etal. (2001), who explore the effect of corporate taxes in the optimization of a supply chain for a pharmaceutical industry, very little attempt has been made to incorporate other regulatory issues in the capacity expansion problem. However, they point to other attempts in location-allocation problems and in production-distribution problems (Cohen etal., 1989 Arntzen etal., 1995 Goetschalckx etal, 2002), which include tariffs, duty drawbacks, local content rules, etc. for a multinational corporation. 

Next we apply these integer programming models to different supply chain network optimization problems, including warehouse location, network design, and distribution problems. The topic of risk pooling or inventory consolidation is presented next. In this portion of the chapter. 

By including the cost of building a warehouse at location j as K, we will minimize the total cost of building warehouses such that every customer region can be supplied by at least one warehouse. We will illustrate this with Example 5.3 in the next section. In addition to the warehouse location problem. Section 5.2 will also include other examples in supply chain network design and distribution problems using binary variables for modeling. 

The selection of optimal sites for warehouse location is a strategic decision. We shall now consider the tactical decision of distributing products to retail outlets from a given set of warehouses. The distribution problem is basically... 

Here we discuss two case studies illustrating the applications of integer programming (IP) for location and distribution problems. Both are based on the... 

Establishing reliable criteria for selecting the most efficient antioxidant, AO, for a particular application is a major unsolved problem in food emulsions and dispersions and one of general importance in nutrition and health. Recent reviews " point to multiple factors that affect activities of antioxidants including the properties and reactions of the antioxidant and the polyunsaturated lipids being oxidized the locations or distributions of the antioxidant within emulsified food the effect of other components on antioxidant activity and the relevance of the model system to real food. Frankel and Meyer s summarized the antioxidant distribution problem highlighthing the crucial role of the antioxidant distributiOTi into emulsifier-rich interfacial layers in hetero-phasic food emulsions[9, 17],... 

Placing a large number of cyclones in parallel in a common bin can result in distribution problems because it will be easier for the gas and solids to flow through the closest cyclone than one located some distance away from the inlet. Multiple inlets to the common vessel reduce this problem, but result in increased complexity and cost. 

The use of non-radial (tangential or offset) vapor inlet nozzles often leads to vapor distribution problems. Whenever two reboiler return nozzles are required, they should be installed radially and located 180 degrees apart so as to cancel kinetic energy effects. The invert of the vapor inlet nozzle should be at least 8 in. above the maximum liquid level in the bottom of the column. Submerging the vapor inlet into the liquid can lead to premature flooding of the packed bed caused by massive liquid entrainment. 

A thorough description of the internal flow stmcture inside a swid atomizer requires information on velocity and pressure distributions. Unfortunately, this information is still not completely available as of this writing (1996). Useful iasights on the boundary layer flow through the swid chamber are available (9—11). Because of the existence of an air core, the flow stmcture iaside a swid atomizer is difficult to analyze because it iavolves the solution of a free-surface problem. If the location and surface pressure of the Hquid boundary are known, however, the equations of motion of the Hquid phase can be appHed to reveal the detailed distributions of the pressure and velocity. 

Building the initial list of candidates for tolling outside the client company s home borders can create some unique problems in regard to their fair assessment. The list may include several good candidate companies that may unfortunately each be located in a different country or region. Each of them may be capable of meeting the distribution or marketing need that initially drove the international toll project. 

The models presented correctly predict blend time and reaction product distribution. The reaction model correctly predicts the effects of scale, impeller speed, and feed location. This shows that such models can provide valuable tools for designing chemical reactors. Process problems may be avoided by using CFM early in the design stage. When designing an industrial chemical reactor it is recommended that the values of the model constants are determined on a laboratory scale. The reaction model constants can then be used to optimize the product conversion on the production scale varying agitator speed and feed position. 

Computational fluid dynamics (CFD) is a very promising tool, and its use can be very helpful for analysis and design in industrial ventilation. It is suited for all types of problems where knowledge of a spatial distribution of flow quantities is desired, i.e., where local values at several locations are required. 

Uneven pressures can be exerted on the drive shaft due to irregularities in the packing rings, resulting in irregular contact with the shaft. This causes uneven distribution of lubrication flow at certain locations, producing acute wear and packed-box leakages. The only effective solution to this problem is to replace the shaft sleeve or drive shaft at the earliest opportunity. 

One of these is the "shape change" phenomenon, in which the location of the electrodeposit is not the same as that of the discharge (deplating) process. Thus, upon cycling, the electrode metal is preferentially transferred to new locations. For the most part, this is a problem of current distribution and hydrodynamics rather than being a materials issue, therefore it will not be discussed further here. 

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