考慮設施種類與顧客自我選擇之公共服務場所選址與設施規劃

Abstract

設施選址問題長年以來受到了廣泛的討論。在一般的設施選址問題中，決策者需要決定設施的位址、以及分配哪些使用者該前往哪些設施。然而，當我們討論到服務性設施時，我們會發現使用者會對不同設施擁有不同偏好，在這種情況下，使用者的行為便不能被決策者強制決定。除此之外，現實中的設施是具有負載量限制的，這使得使用者無法選擇已經滿載的設施。再者，不同的設施可能會提供不同的服務，成為另一個設施差異性的來源。因此，將不同的服務種類納入考慮能讓我們的問題更貼近現實情況。 在我們的研究中，我們考慮一個具有不同服務類型、附載量有限、且使用者偏好各異的設施選址問題，決策者需要決定設施的位址、規模、及其所提供的服務類型，目標是在給定的預算內最大化設施的總服務人數。為解決此問題，我們建立了一個混和整數規劃模型與一個以貪婪法為底、結合最大流問題的啟發式演算法，透過數值實驗，可以看到我們的演算法能在可接受的時間範圍內得到接近最佳解的 結果。

The facility location problems have been widely discussed for decades. In a typical facility location problem, a decision maker decides where to build facilities among some given locations. However, when it comes to service facilities facing end consumers, customers would have different preferences toward them. In this case, whether one customer should visit one specific facility cannot be determined by the decision maker. Besides, facilities have limited capacities, so customers cannot go to the one is fully occupied. Moreover, once a facility is built, it may provide several types of services and make facilities different from each others. Therefore, taking the service types into account may make our problem closer to reality. In our research, we consider a multi-types capacitated facility location problem with preference. The decision maker plans to choose locations and scale levels to build facilities and decide what services should they provide. The problem aims to maximize total served customers within budget constraint. We formulate a mixed integer programming model and provide a greedy-based heuristic algorithm (GSA) with maximum flow to solve this problem. In numerical study, we find that our algorithm can provide near-optimal solutions in reasonable time.