Exact methods and a heuristic for the optimization of an integrated replenishment-storage planning problem

In this paper we study the coordination of different activities in a supply chain issued from a real case. Multiple suppliers send raw materials (RMs) to a distribution center (DC) that delivers them to a unique plant where the storage of the RMs and the finished goods is not possible. Then, the finished goods are directly shipped to multiple customers having just‐in‐time (JIT) demands. Under these hypotheses, we show that the problem can be reduced to multiple suppliers and one DC. Afterwards, we analyze two cases; in the first, we consider an uncapacitated storage at DC, and in the second, we analyze the capacitated storage case. For the first case, we show that the problem is NP‐hard in the ordinary sense using the Knapsack decision problem. We then propose two exact methods: a mixed integer linear program (MILP) and a pseudopolynomial dynamic program. A classical dynamic program and an improved one using the idea of Shaw and Wagelmans are given. With numerical tests we show that the dynamic program gives the optimal solution in reasonable time for quite large instances compared with the MILP. For the second case, the capacity limitation in DC is assumed, which makes the problem solving more challenging. We propose an MILP and a dynamic programming‐based heuristic that provides solutions close to the optimal solution in very short times.     

HIV infection in pregnant women in Dakar (Senegal)

The epidemiologic and sociodemographic characteristics of human deficiency virus (HIV) infection vary from one country to another. The objective of this study was to determine the prevalence of HIV infection in pregnant women in Dakar and associated factors. Systematic anonymous screening was performed in pregnant women admitted to the maternity ward. Women whose seropositivity was confirmed by Western blot retroviral serology were included. One woman out of four was assigned by simple random selection to the case control group. Over a 24 month period, 12,498 women were tested. 104 were seropositive (44 HIV1, 58HIV2, and 2 HIV1-HIV2 giving a prevalence of 0.8%. Factors associated with HIV1 and HIV2 were different: mean age 21.7 years for HIV1 versus 30.6 for HIV 2 (p = 0.05); origin in Guinea-Bissau for HIV2 (p = 0.001); mean number of pregnancies 2.6 for HIV1 versus 5.9 for HIV2 (p = 0.001); mean parity 1.5 for HIV1 versus 4.5 for HIV2 (p < 0.01); vitality of the conception product in 85.1% for HIV2 versus 67.5% for HIV1 (p = 0.0001). These data confirm the low prevalence of HIV infection in pregnant women, with a predominance for HIV2. The factors identified in associated with virus type suggest a different mode of transmission and/or reduced virulence or HIV2 compared with HIV1. Knowledge of these factors helps orient management strategies, especially in pregnant women.