ارايه و بهينه‌سازي يك مدل رياضي چند‌هدفه مسيله‌ي بارانداز تقاطعي با استفاده از الگوريتم‌هاي فراابتكاري

Proposing and optimizing a multi-objective mathematical model for cross docking problem using meta-heuristic algorithms

در اين نوشتار يك مدل جديد چند‌هدفه‌ي بارانداز تقاطعي ارايه‌ مي‌شود. در مدل رياضي اين مقاله سه هدف كمينه‌سازي زمان كل عمليات حمل‌ونقل، كمينه‌سازي هزينه‌ي حمل‌و‌نقل، و كمينه‌سازي تعداد دفعات حمل‌ونقل در كل زنجيره‌ي تامين در نظر گرفته شده است. از آنجا كه مسيله‌ي بارانداز تقاطعي متعلق به رده‌ي NP-hard است و زمان حل مسيله با افزايش ابعاد مسيله به‌شدت افزايش مي‌يابد، براي پيدا كردن جواب‌هاي نزديك بهينه‌ي مسيله از دو الگوريتم فراابتكاري تكاملي ژنتيك با مرتب‌سازي نامغلوب و بهينه‌سازي ازدحام ذرات چند‌هدفه استفاده شده است. سپس اين الگوريتم‌ها با معيارهايي همچون فاصله از نقطه‌ي ايده‌آل با يكديگر مقايسه، و الگوريتم برتر در هر معيار مشخص شده است. نتايج نشان مي‌دهد كه الگوريتم ژنتيك با مرتب‌سازي نامغلوب در بيشتر معيارها به نتايج خوبي رهنمون شده است.

The supply chain management is regarded as an important infrastructure in managing material flow. Cross docking is considered to be as an efficient method in supply chain management to control the inventory flow, which is essential in supply chain management. The other objectives of the cross dock are inventory reduction, increased levels of customer responsiveness and better control of the distribution operation. Since this system plays a key role in the supply chain, setting up multi objective approaches may help to solve real world issues and problems of such systems, in which many of the objectives are different and even conflicting. This paper proposes a new multi-objective mathematical model which, unlike the previous works, considers transportation from suppliers to customers, from suppliers to other suppliers, from suppliers to cross sock, from cross dock to customers and from a customer node to other customer nodes. In this paper, three different types of objective functions are considered: to minimize the total time in supply chain, to minimize transportation cost, and to minimize the number of transportation times in the network. As mentioned earlier, these three objectives are in conflict with each other; and by considering three objective functions simultaneously the control of the supply chain is more appropriate. Since these three models belong to the NP-hard class, their solving time severely increases with increasing the problem dimensions. In this paper, to solve these three models, meta-heuristic algorithms have been used. The algorithms used in solving the model are Multiple Objective Particle Swarm Optimization and Non-Dominated Sorting Genetic Algorithm. The model is solved using both algorithms and computational experiments are reported.