Value- and Ambiguity-Based Approach for Solving Intuitionistic Fuzzy Transportation Problem with Total Quantity Discounts and Incremental Quantity Discounts

The cost of goods per unit transported from the source to the destination is considered to be fixed regardless of the number of units transported. But, in reality, the cost is often not fixed. Quantity discount is often allowed for large shipments. Furthermore, the transportation cost and the price break quantities are not deterministic. In this study, we introduce the concept of Value- and Ambiguity-based approach for solving the intuitionistic fuzzy transportation problem with total quantity discounts and incremental quantity discounts. Here, the cost and quantity price breakpoints are represented by trapezoidal intuitionistic fuzzy numbers. The Values and Ambiguities are defined as the degree of acceptance and rejection for trapezoidal intuitionistic fuzzy numbers. The trapezoidal intuitionistic fuzzy transportation problem is converted to a parametric transportation problem based on their Value indices and Ambiguity indices. Then, for different Values of the parameter, the transformed problem is reduced to the linear programming problem. Then, the linear programming problem is solved by using the classical methods. The proposed method is demonstrated with a numerical example. In conclusion, the intuitionistic fuzzy transportation problem with total quantity discounts is compared with the intuitionistic fuzzy transportation problem with incremental quantity discounts.

Integrated dynamic vendor selection and order allocation problem for the time dependent and stochastic data

Purpose In this paper, vendor selection and order allocation problem is considered for a buyer dealing in multiple products to be supplied by multiple vendors. Each product has an associated lead time with stochastic demand having stochastic capacity for each vendor across entire time period. Uncertainties related to costs which are further influenced by the periodically changing incremental quantity discounts offered by various vendors. The purpose of this paper is to find an optimal trade-off of vendor selection and order allocation in the presence of uncertainties involving multiple conflicting objectives such as cost minimization, service level/quality level maximization and delivery lead time minimization concurrently. Design/methodology/approach Vendor selection problem considered here has a multi-objective optimization design subject to a set of demand, capacity and quantity discount based constraints. These constraints as well as uncertainty related to lead time have been handled using chance constraint approach. The problem is titled as “integrated dynamic vendor selection problem (IDVSP).” The proposed multi-objective IDVSP is solved using both non-pre-emptive goal programming (GP) and weighted sum aggregate objective function (AOF) technique. Findings Findings indicate goal achievement for different objectives from both non-pre-emptive GP and AOF procedure. While the goals are satisfactorily achieved as per the target values for cost and lead time, quality/service level was somewhat compromised in order to find an appropriate trade off. Originality/value The research work is original as it integrates dynamic as well as stochastic (uncertain) nature of supply chain simultaneously coupled with the concept of incremental quantity discounts on lot sizes.