考量內生需求、資源分配與需求競食之設施選址

Abstract

競爭性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 到競爭性設施時，我們會發現各設施對於消費者的效用取決於決策者投放於設施的資 源以及設施與消費者的距離。在這種情況下，使用者的行為便不能被決策者強制決定， 而是消費者會依據設施的效用來選擇前往的設施。此外，決策者除了透過建設設施來 增加其吸引力之外，也能將不同的有限資源投放於設施中。不同的資源被分配至不同 設施時將產生不同的吸引力，這成為另一個設施及資源差異性的來源。將不同的資源 種類分配方式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資源類型、各資源類型有限、資源吸引 力於各設施不同的競爭性設施選址問題，決策者需要決定設施的位址、數量、以及分 配於各設施的資源種類，目標是吸引儘可能多的總服務人數以最大化利潤。為解決此 問題，我們建立了一個混合整數規劃模型並開發一個啟發式演算法，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 competitive facility location (CFL) problem has been widely discussed for many years. In a typical facility location problem, decision makers need to determine the loca- tions of facilities and allocate which users should go to which facilities. However, when we discuss CFL problems, we find that the utility of each facility for consumers depends on the resources allocated by decision makers to the facilities and the distance between the facilities and consumers. In this case, user behavior cannot be forcibly determined by decision makers; instead, consumers choose facilities based on their utility. In addition to increasing attractiveness level of facilities by constructing additional enhancements, decision makers can allocate different limited resources to the facilities. Different alloca- tions of resources to different facilities result in varying attractiveness, creating another source of facility and resource heterogeneity. Considering different resource types in the allocation process makes our problem more realistic. In our study, we consider a competitive facility location problem with different re- source types, limited quantities for each resource type, and varying resource attractiveness for different facilities. Decision makers need to determine the locations and quantities of facilities and allocate resource types to each facility, aiming to attract as many served users as possible to maximize profit. To solve this problem, we developed a mixed- integer programming model and a heuristic algorithm. Through numerical experiments, we observed that our algorithm produces results close to the optimal solution within an acceptable time frame.