CHAPTER 2 Literature review
2.5 MIP formulations
According to Rardin (1998), a mathematical program is a discrete optimization model if it includes any discrete variables at all. Otherwise, it is a continuous optimization model. In other words, if the system contains both discrete and continuous variables, the model is a mixed integer program. Many models have been formulated for the strategic design of supply chains.
Geoffrion and Graves (1974) is the first paper that presented a comprehensive MIP model for the supply chain network design problems. The model formulated in this study represented a production-distribution system with several plants with known capacities, distribution centers (DC), and a number of customer zones. The constraints considered in the model are capacity at plants, customer demand satisfaction, single sourcing by customer zone, bounds on the throughput at DC, and linear configuration constraints on binary variables. The study presented an algorithm based on Bender
Decomposition to solve the problem.
Hodder and Dincer (1986) presented an international plant location model with financial capabilities. The model considers exchange rate fluctuations, market prices, international interest rates, and fixed costs in a stochastic environment. Brown et al.
(1987) present a MIP multi-commodity model, where the costs is composed of variable production and shipping costs, fixed costs of equipment assignment and fixed costs of plant operations. Furthermore, Cohen and Moon (1991) presented a mixed integer multi-commodity model to determine inbound raw material flows, assignment of product lines and specification of production volumes, and outbound finished product flows in a production-distribution network. The main contribution of this study is to provide an algorithm to solve some production-distribution models with piecewise linear concave costs of production (Vidal and Goetschalckx, 1997).
Arntzen et al. (1995) considered multiple products, facilities, time periods, and transportation modes. The model aimed at minimizing a composite function of activity days and total production costs, inventory, transportation costs, etc. All the costs considered in the objective function are weighted by a factor α . The objective function represents a weighted combination of time and cost so that either measure or both can be used to derive recommendations (Meixell and Gargeya, 2005).
Jayaraman and Pirkul (2001) formulated a MIP model for locating production and distribution facilities in a multi-echelon environment. The main objective in this formulation is to minimize the total fixed and variable cost associated with the multiple products subject to constraints imposed on the demand, production capacity, warehouse capacity, raw material supply and requirements and the geography of customer zone outlets.
Amiri (2006) addressed the distribution network design problem in a supply chain system that involves locating production plants and distribution warehouses. The goal of this formulation is to select the optimal numbers, locations and capacities of plants and warehouses to open so that all customer demand is satisfied at minimum total costs of the distribution network.
2.6 Summary
There is vast literature conducting supply chain network problems. And the mixed integer programming (MIP) method has been extensively used to investigate the problems. These studies focused mainly on developing approximation procedures and on comparing the efficiency of their proposed heuristics with others in past literature.
In addition, though the capacity utilization of different-sized plants will result in various influences on their cost, its extent is seldom discussed. The impacts of high capacity cost, customer demand level and investment conditions on the optimal plant capacity and production among manufacturing plants with different sizes are seldom discussed.
Though optimal flows between demand and supply nodes have been discussed and have been included in the supply chain design problems, the shipping frequency and shipment size between different combinations of suppliers and manufacturing plants have not been discussed yet. Furthermore, production and shipping economies and their tradeoff relationships are seldom discussed when designing a supply chain network.
Past literature has demonstrated the importance of logistics functions on the efficiency of a supply chain. However, the shipping frequency and shipment size between different combinations of suppliers and manufacturing plants and of manufacturing plants and customers in different regions have not been discussed yet. Furthermore, shipping economies inhering in the supply chain are seldom discussed when design a supply chain network. The impact of spatial distance on the optimal shipping
frequency although having been studied in logistics literature, has not been integrated into the design of supply chain networks.
There are extensive studies addressing the impacts of uncertainty factors on company’s cost and customer service level performance with respect to demand and supply uncertainty. The literature also proposed various strategies to reduce the impacts of uncertainty under different scenarios. Most of these studies focused on the short-term operational issues and constructed analytical models in terms of operation research. In the network planning phase, the performance of the network under abnormal demand fluctuation was seldom evaluated.
Past studies have addressed the importance of logistics function on supply chain management. These studies aimed at investigate relationship between supply chain performance and logistics network using collected empirical data and by conducting hypothesis. However, the interaction of time and spatial dependent customer demand and logistics cost related to delivery service strategy in supply chain network has seldom been investigated. Previous empirical studies have investigated the impacts of delivery-related issues on consumer satisfaction with Internet shopping. The interaction of time-dependent consumer demand and logistics cost related to different delivery service strategies has seldom been investigated. Furthermore, while consumer demand for goods may increase by employing frequent and short delivery cycles, the extent depends on variations in consumer socioeconomic, temporal and spatial distribution and, furthermore, how Internet store operators set up service cycles during a given operating period of time. Although these issues have been previously addressed, there is currently no mathematical model that can determine an optimal delivery service strategy by integrating all issues.
Several important issues in the field of supply chain network design deserve
further investigation; however, these issues are rarely emphasized and theoretically formulated in supply chain design literature. This study aims at developing a series models to systematically investigate the supply chain design problems in response to production and shipping economies in an uncertain environment. Furthermore, the delivery service strategies for both the manufacturer and Internet shopping operators are explored by considering time-dependent consumer demand, demand-supply interaction and consumer socioeconomic characteristics.